# Master's Theses

Layered beams are often used in engineering because the properties of different materials can be used advantageously e.g. in terms of weight or strength. Adhesives or metal connectors are common to connect the layers. This results often in an interlaminar flexibility, which can only be taken into account approximately in manual calculations, such as the Gamma method in Eurocode 5. In addition to Finite Element (FE) solutions, the beam theory proposed in Adam et al. provides information on how nonlinearities due to immovable support conditions or imperfections affect the moderately large response of layered single-span beams. This beam theory is extended in the present work for the three-layer, symmetrically layered single-span beam with interlayer slip by the influence of eigenstrains. The basis of this beam theory is the layerwise validity of the Euler-Bernoulli assumptions. First, the differential equations of equilibrium for the linear, three-layer beam are derived. These equations are solved using the program ``Mathematica'' and the results are compared with the outcome of a corresponding FE analysis based on the plane stress assumption. Subsequently, the geometrically non-linear beam with initial deflection is considered. Since an analytical solution of the problem is no longer possible, the Galerkin method is used. Given the approximation for the deflection of the beam as a series of functions, series formulations for the solution of the problem are derived and presented. This procedure is carried out in several examples and validated with a comparative FE analysis. Although only a few examples were investigated, the influence of imperfections on the section forces in the beam is significant. In addition to the sine series as an approximation for the deflection of the beam, orthogonal functions obtained with the Gram-Schmidt algorithm are used. The underlying beam theory is extended by the influence of constant and sinusoidal eigenstrain distributions. The developed equations and series formulation for describing the problem can be implemented with little effort and used for parameter studies on the three-layer, symmetrically layered beam with interlayer slip.

This thesis deals with the dynamic behavior of cross-laminated timber panels. Using a rectangular cross-laminated timber panel with free-free boundary conditions, modal parameters, which are natural frequencies, mode shapes and damping ratios, in the frequency range from 90 to 750 Hz are determined by an experimental modal analysis. The aim of the work is to reproduce the experimental results by means of numerical modeling. The main unknowns for the numerical model, which is based on the finite element method (FEM), are the material properties of the cross-laminated timber panel. By means of model updating, these are determined as the solution of an optimization problem. By varying the underlying objective function error measures and starting points of the optimization, it is shown that a global optimum can be achieved for the unknown material parameters. The special feature of the FE model is the use of plate elements based on a higher order plate theory, which offer a significant saving in computing demands compared to modeling using solid elements, with sufficiently good quality of the results.

Since cracking due to shrinkage occurred on the cross-laminated timber over a period of three months, both the experimental modal analysis and the determination of the material parameters by means of optimization were repeated in the cracked state. Again, the experimental and numerically determined modal parameters show good agreement, especially in the lower frequency range. However, due to cracking, nonlinear effects occur, which manifest themselves, for example, in a “splitting" of modes, which cannot be represented by the linear numerical model.

In this master thesis, the influence of the soil-structure interaction of railway bridges on their dynamic vibration response during the passage of high-speed trains is investigated and the influence of various parameters is evaluated. A holistic view of the dynamic interaction system with its essential components train, track, bridge and soil is taken. The parameter study of the soil-structure interaction is carried out for bridges made of reinforced concrete and steel with different span widths, as well as for varying stiffness modulus of the soil and varying bedding stiffness of the track. Two different models are used for the train, to study their dynamic impact on the structure at different speeds. The analyses are based on the simplified mechanical model of König et al. (2021), which considers all the necessary parameters of the physical problem. The first analyses are carried out within the framework of a preliminary study. In this first study, the interaction system consisting of bridge and soil is considered and the modal parameters, equivalent damping coefficients and natural frequencies of the bridge-soil interaction model are determined. The results of this preliminary study are intended to show the dependence of the damping coefficients and the natural frequencies on to the span width, the construction material of the bridge, the stiffness modulus of the soil and to illustrate the influence of the foundation mass. Following the preliminary study, a parameter study of the dynamic soil-bridge-train-track interaction system is conducted. The resulting dynamic vibration response of the bridge is investigated in more detail using a single-load model (SLM) and a mass-spring-damper system (MSD) of the train. Furthermore, the influence of the bedding stiffness of the track is addressed. The evaluation of the obtained results with the model of König et al. (2021) is carried out with regard to the dynamic deflection and acceleration of the bridge structures in form of response spectra. The results of this parameter study allow a more precise statement about the response behavior of bridges under dynamic train loading can be made.

The objective of this Master thesis is to investigate the maximum vertical accelerations of flexible nonstructural components (NTCs) in steel structures. The multi-story load-bearing structure is modelled as a frame and the acceleration-sensitive NTCs as a single-degree-of-freedom oscillator. In a first step, two mechanical models of an eight-story steel frame are created. In the first coupled model, the NTC and the frame structure are considered as one interacting system and the response of the NTC on this entire system subjected to earthquake excitation is determined. For the uncoupled model, the acceleration response of the load-bearing structure is computed without attached SDOF oscillator. Subsequently, the acceleration response of the connection node serves as the excitation of the SDOF oscillator. Moreover, the vertical accelerations of NTCs attached to one-, two-, four-, eight- and twelve-story steel frames subjected to the ground motions of a record set are computed and compared to the response of the decoupled modeling approach. The natural frequency of the NTCs is varied in the range from 0.1 to 30.5 Hz. In a comparative study on the eight-story steel frame, the mass ratio between the mass of the NTC and the floor mass of the frame is determined, where the coupled and decoupled modeling give practically the same result. The investigations of the response of the NTCs on the other frame structures are performed on a decoupled model to reduce the computation times. The vertical accelerations of the NTCs reach maximum values at the outer column lines and on the symmetry axis. The highest vertical accelerations of the NTCs are predicted at the roof floor. The results of this Master thesis show that the vertical acceleration at NTCs can be up to six times larger than the vertical acceleration at the frame node.

High energy absorption is one of the most important design criteria in the automotive industry. At the same time, low weight is required, since fuel consumption and the range of electrical cars depend significantly on the weight. Two ways to achieve better overall performance are the use of materials with a favourable strength-to-weight ratio and structural optimization. In particular, Al-Mg-Si alloys, which have a high strength-to-weight ratio and exhibit high mouldability, are often used for crushing components in cars e.g. bumper systems or battery containers. The alloying constituents of aluminium are decisive for the characteristic properties, which is why new compositions are frequently tested to achieve enhanced ductility and strength. FE-based numerical simulations can be effectively used to simulate crushing responses without the need for time-consuming and material-intensive testing if a valid constitutive model and a correct discretization of the geometry are established. In this work, an approach to establish an appropriate constitutive model based on experimentally performed tensile tests for aluminium alloys is described. Besides, a numerical model of a crash box is established and validated against experimental data. Structural design is particularly in demand where optimized material compositions are already used. In this work, it is investigated whether the energy absorption of a multi-chamber battery container can be increased by changing the geometric shape of the profile, considering different load cases. To validate the numerical material model used for the optimization, quasi-static and dynamic component tests are performed. Additionally, the influence of different discretization approaches of the profile is examined and the response behaviour is compared.

Dynamic soil compaction is a common soil compaction measure in civil engineering. Technical progress in recent decades has been accompanied by increasing automation. Work-integrated and continuous control of the compaction effect is required for soil compaction methods. In order to verify the experimentally developed control procedures with regard to the proposed compaction parameter, numerical simulations are used. For the theoretical research, the behavior of the soil must be described with a suitable constitutive model and implemented in the used software package.

In this Master thesis, a basic and extended (intergranular strains) hypoplastic constitutive model in the form of a UMAT is implemented in the FEM software ABAQUS. Two variants are coded for the numerical solution of the material tangent (consistent tangent and continuum tangent). The implementation is verified by element tests in the form of the oedometer and the triaxial test as well as by comparison with experimental and simulation results from published literature. The parameter studies performed show the large influence of the compression exponent on the behavior of the soil, which is already known from previous studies. Furthermore, the comparison of the simulation results of the oedometer test with those of the triaxial test shows a different sensitivity with respect to the critical friction angle. Practical applicability and numerical stability are verified by numerical simulation of dynamic soil compaction with the vibratory compactor on a simplified, three-dimensional vibrator-soil interaction model. The displacement controlled simulations with the hypoplastic constitutive model can qualitatively represent the propagation of the pressure wave and the increasing range of compaction over time. The selected parameter studies (vibrator amplitude, initial soil density) are numerically stable up to 100 cycles

This master thesis deals with the dynamic behavior of ropeway cabins and investigates the possibilities of passive vibration control of pendulum-type structures in the low-frequency range. Theoretical investigations show that liquid absorber devices are a promising methodology for this problem. The Tuned Liquid Damper (TLD)-Floating Roof (FR) is identified as the most suitable type of vibration absorber. After initially explaining the basics of ropeway construction, the theory of vibration and corresponding experimental methods is explained in more detail. Subsequently, a planar model of a cable car is set up and the equations of motion are derived. Investigations show that the first natural mode of vibration of this system can be represented as a mathematical pendulum for small deflections in a good approximation. Since the decoupled absorber system can also be described by a single degree of freedom system, the systems are combined, resulting in a model with two degrees of freedom. These are the pendulum system and the absorber. The pendulum-TLD system obtained is then verified by experimental investigations. The results clearly show that passive vibration control by means of liquid dampers can work for the considered system. Comparisons with a pendulum-Tuned Mass Damper system, known from literature, also show the same effectiveness of these systems with equivalent mass and absorber damping. The final investigations on a ropeway cabin show that the considered absorber can be used as an effective method for vibration mitigation in ropeway construction.

Natural hazards have always been among the most dangerous events for humanity. Despite all technological progress, recent seismic events have demonstrated their destructive power. Particularly in an urban environment, handling the effects of earthquakes on buildings and infrastructure remains a core responsibility for the engineering community. In earthquake engineering, seismic collapse assessment is among the most important concerns in the evaluation of a seismically excited structure. Non-linear dynamic analyses provide the opportunity to realistically predicting building behavior under seismic excitation. These analyses are computationally demanding and, therefore, rarely used in practice. For this reason, as part of a large-scale study of the Unit of Applied Mechanics of the University of Innsbruck, a database is generated that yields the calculations' results of multi-storey frame-like structures and thus provides the basis for a deeper understanding of their collapse behavior under earthquake excitation. The long-term goal is to sidestep the computationally expensive calculations for seismic collapse assessment with machine learning-based predictions. Based on the NGA-West2 ground motion database, 17 000 ground motions are used for Incremental Dynamic Analysis. Within the scope of this Master thesis, an 8-storey moment-resisting steel frame structure is considered. The introduction includes a composition of the necessary fundamentals of earthquake engineering and provides insights regarding the modeling and implementation of the steel frame structure. The evaluation of the results reveals a significant shift of the deformation pattern in the collapse limit state compared to the evaluation point just previously to collapse. Common intensity measures are assessed according to the criteria of efficiency, sufficiency, and scalability. When examining the influence of individual storeys on the overall collapse behavior, it is observed that particularly the collapse of upper storeys strongly correlates with a high scale factor, which in turn distorts the ground motion record and thus presumably provides limited information. Finally, the machine learning algorithm K-means clustering aims to structure the database of ground motion records according to similar characteristics and group them into data sets. Based on the intentionally selected sets, the prediction accuracy of existing generalized linear machine learning models is supposed to be increased.

In engineering practice, force-based design procedures have been used in recent decades due to the low calculation effort. The response spectrum method is the standard method for predicting the structural response. The internal forces obtained are compared with component resistance. Thus, this design strategy is referred to as force-based. The basis of this linear elastic structural analysis is the so-called behavior coefficient q which is used to estimate any inelastic deformation capacity as well as the overstrength in advance according to the standard. The value of q can be selected by the engineer within a relatively large range suggested by the standard.

Modern earthquake engineering proposes the use of deformation-based design procedures. The structural response is obtained by non-linear static or dynamic analysis methods. In the design procedures, the calculated non-linear deformations or rotations are compared to the corresponding capacities depending on the component. This type of design is referred to as deformation-based and fully utilizes the non-linear load reserves.

The basis of this master thesis is a reinforced concrete frame structure, asymmetrical in ground plan and vertical section, designed according to the modal response spectrum method based on a 3D-model by the engineering office BHM-Ingenieure. The proof of the earthquake resistance is carried out on a selected cross frame by means of a non-linear static and a non-linear response history analysis. The adequate representation of geometric nonlinearity, appropriate modelling of damping and the effects of mass distribution are discussed. The results of the nonlinear analysis are compared with the results of the modal response spectrum method. It can be shown that requirements of over-dimensioning and the fact that the earthquake load case was not decisive for the design of some nodes lead to bending moments in the response history analysis that are many times higher than the design moments of the reference project. Subsequently, the static capacity is compared with the dynamic capacity of the structure and the overstrength is estimated by a non-linear static analysis. In addition, for the frame structure as well as for a single column, the influence of cyclical deterioration on collapse capacity is studied. This leads to the conclusion that for the structures under consideration the effects of cyclical deterioration are small and that not all deteroriation mechanisms are equally important for overall deterioration.

This master thesis deals with vibration predictions in the soil caused by tram traffic. In particular, the decrease of the vibration amplitudes with increasing distance from the source due to geometric damping is studied. For this purpose, open-field measurements were conducted in Berlin and Chemnitz and the results analyzed. The velocity amplitudes decrease at different rates in both measurements, and the frequency content also differs. The decrease of the vibration amplitudes of the measurements in comparison with the prognosis method according to DIN4150-1 does not correspond to the expected values for geometric damping. The soil properties have a large influence on the measured results. The prognosis method is based on a solution for plane wave propagation in the elastic half-space. It applies to velocity amplitudes while displacement amplitudes are eommonly investigated in analytical solutions. Therefore, an analytical solution is used to investigate the extent to which geometric decay-functions for displacements and velocities differ. Analytical solutions for the wave propagation in the elastic half-space due to impulsive excitation at the surface are evaluated, derived for the velocities and compared with the prediction method. The analytical solution shows a clear time dependence of the wave propagation at the surface, and thus the velocity amplitudesolutionfunction decreases differently compared to the displacement amplitudes.

The increasing expansion of rail traffic routes and rising urban densities mean that there is a growing need for protective measures to reduce the impact of vibrations and noise on residents. For this reason, a realistic prognosis and an assessment of the effects before the start of construction work is of great importance. For this purpose, approaches using numerical methods as well as procedures based on measurements are possible in the project planning phase. The results of these approaches allow a statement on expected vibrations to be made in the early stages of planning and emission-reducing measures to be integrated directly into the planning process in order to avoid additional costs later on.

The present master thesis deals with the preparation of an empirical procedure based on metrological surveys for the prognosis of the effects of planned rail traffic routes on the neighbouring population. The aim is to develop a universally applicable forecasting method that allows a standardised approach to the prediction of vibrations, especially in view of the lack of regulations for forecasting.

The work includes a summary of the necessary basics regarding measurement technology and signal processing as well as the Austrian standardisation for the assessment of vibration effects of rail traffic. Following these basics, the force-based as well as the velocity-based procedure for vibration prediction is presented and the evaluation of a corresponding measurement set-up is carried out. Both methods have in common that the detection of vibration propagation is approximated by a number of point sources according to the track-bound line source.

Any measurement recordings are critically examined and influences on the forecast are shown. In the course of this metrological investigation, improvements with regard to the measuring setup as well as the method used for vibration excitation are also shown, paving the way for future applications and further validation of the methodology.

When designing dynamically exited foundations, the soil-foundation interaction must be taken into account to ensure sufficient load-bearing capacity and, above all, serviceability of the foundations. It is therefore necessary to consider the dynamic properties of the soil during the design process. One possibility is to fully model the subsoil in the calculation models used for the design. However, this approach usually leads to very extensive models, which result in uneconomically long computing times. An alternative way to avoid this is to replace the soil with a simple mechanical system consisting of springs, dampers and masses. Such a model was proposed in the literature in 1942, then further developed by several authors until 1993 and subsequently successfully applied in the field of soil-structure-interaction and soil-machine-interaction. The subsoil is regarded as a linearly elastic isotropic homogeneous half-space, from which however only a truncated cone-shaped section is considered. The top surface of the downwardly infinite truncated cone forms the vibrating foundation which is converted into a circular foundation of the same area. Assuming a one-dimensional wave propagation in this cone, this model is equivalent to a spring-damper-mass-system with frequency-independent coefficients. A further development based on this one-dimensional wave propagation in cones is a transfer function for foundation vibrations on stratified half-spaces developed in 1994.

The aim of this master thesis is to investigate the applicability of these cone models using finite element (FE) modelling. In particular, the half-space replacement models for vertical vibrations are examined. At the beginning, a FE-model for a homogeneous and stratified subsoil using a rotationally symmetric model, in which the infinite region of the half-space is modelled using infinite elements, is developed. These FE-models are then used to carry out parameter studies, the results of which are compared with the cone model or the transfer function.

For homogeneous half-spaces, a very good agreement with the FE-results is achieved, whereby the vibration amplitudes tend to be slightly overestimated by the cone model. In the domain around the resonant frequency of the foundation-subsoil system, however, large deviations occur, which may be due to the different damping coefficients. The transfer function for stratified half-spaces also shows good agreement with the FE-results. Here, the deviations are in the same order of magnitude, in the case of “soft” layers on “stiff” half-spaces the deviations are at their greatest.

Vibro-compaction represents a soil improvement method for deep compaction of cohesionless granular soils, which has been used successfully for several decades. The soil around to the vibrator is primarily excited horizontally. This leads to a reduction in pore ratio and consequently to an increase in soil density. The excitation generated by deep vibro-compaction is based on an eccentrically arranged mass, so-called imbalance, which rotates around the vertical axis of the vibrator at a constant angular velocity. Due to the compaction control, which up to now has only been possible after the compaction process and also only selectively by means of probing, the compaction success essentially depends on the experience of the machine operator. The methods for quality control of the compaction works are largely empirical in nature and therefore often unreliable. There is currently no approved method for a reliable continuous compaction control for this ground improvement technique available. For this reason, a work-integrated testing tool is required. That means, the vibrator should not just serve as a compaction device but at the same time as a measurement tool, too.

Despite the compaction process itself, a compaction state is assumed in this master's thesis. As a consequence, the vibration response on the surface due to excitation by the vibrator at a certain depth is investigated. The quite complex behavior of the soil in close proximity to the vibro-compaction device is neglected completely. Furthermore, the subsoil is considered as an isotropic linearly elastic homogeneous half-space. In this work three modelling approaches of the current problem are chosen comprising semi-analytical as well as numerical models. On the one hand these semi-analytical models use numerical solutions of analytical solutions of the dynamic half-space problem documented in the literature. On the other hand, a commercial toolbox based on similar analytical solutions is used. Plausibility checks and sensitivity studies have shown that the semi-analytical approach mentioned first cannot be applied effectively. Furthermore, the numerical model represents a three-dimensional finite element model. This work only observes the acceleration response on the surface of the half-space because in previous field tests the surface response was recorded.

In a first step, the excitation representing the vibrator is idealized as a horizontally periodic single force. A decrease of the maximum amplitude in the time domain of the acceleration response is observed with increasing distance to the vibrator, depending on the shear modulus. The decay of the acceleration on the surface predicted by the semi-analytical and the numerical model is in good agreement with respect to shape and quantitative values as the shear modulus increases.

To model the rotational movement of the deep vibrator more realistically, two horizontal, orthogonally positioned, periodic single forces are superposed. The two horizontal soil accelerations resulting at the surface are superimposed in each point, and the area within these so called Lissajous curves is plotted with increasing distance to the idealized vibrator. It is shown that the circle in the center of the model (i.e. origin of the Cartesian coordinate system) degenerates to a rotated ellipse due to the change in phase shift with increasing distance from the origin. The results of the semi-analytical and numerical model are both qualitatively and quantitatively in good agreement. Furthermore, the depth of the idealized vibrator as well as the shear modulus have an impact on the superposition figures.

The development of the existing railway network for high-speed trains provides new challenges in the dynamic design of new and especially existing bridge structures. High-speed train crossings can cause resonance phenomena in bridges, leading to large deformations, accelerations and stresses in the bridge structure. As a consequence, the maintenance intervals must be reduced, and in the worst case, the train may derail or the structure may fail. Damping of the structure has a great influence on the response at critical resonance state. In comparison to measured damping values, the damping values used in structural analysis are chosen very conservatively based on design guidelines and codes. Especially in the case of portal frame bridges with short span widths, economic dimensioning is often not possible. Due to their integration into the subsoil, they show a strong soil-structure interaction during train passage, which leads to a high geometric damping due to wave propagation in soil. This master thesis investigates the dynamic soil-structure interaction of portal frame bridges and the geometric damping effect of the soil.

For the present numerical studies, simple plane finite element models are created, consisting of the frame structure and the soil. These models are used to perform parametric studies by varying the geometry of the frame structure and the soil properties. The portal frame bridge model is excited by an impulse in the center of the span and the frame-wall. The subsequent the decay behavior of the free vibration is used to identify the geometric damping. The soil-structure interaction of railway bridges is evaluated based on natural frequencies, mode shapes and global damping coefficients. In particular, the first horizontal and the first vertical bending mode of the frame, are considered.

It is shown that the natural frequency of the horizontal bending mode experiences a significant stiffening due to a lateral bedding of the frame-walls. In contrast, the natural frequency of the vertical bending mode is not noticeably influenced by the surrounding soil. It is shown that the damping coefficient of the first vertical bending mode is significantly affected by soil-structure interaction if the spans are very short. For spans larger than 20 m this effect is negligibly small. The damping value depends on the soil stiffness and is higher for soft soil. With increasing frame height and integration into the soil damping becomes larger.

This Master’s thesis addresses the effects of track irregularities on the numerical prediction of the vibration response of railway bridges. Results of numerical parameter studies are compared to design rules of the current codes. The bridge is represented by a simply supported Euler-Bernoulli beam, and different multi-body systems model the crossing high-speed train. Track imperfections are described by geometric irregularity profiles, which are generated based on the assumption of a stationary stochastic process. By applying a substructure approach, bridge, train and irregularity profiles are combined to a single model. The equations of motion of the coupled system are solved numerically. Maximum values of acceleration and deflection of the railway bridge, shown as functions of the train speed, represent the vibration response of interest. The results of the system with irregular rails are compared with the dynamic response of a bridge with perfect tracks and a statistical assessment about the influence of track irregularities is made. In contrast to a deterministic dynamic computation with perfectly smooth rails, the response considering rail irregularities can only be described by statistical parameters such as mean and standard deviation. In order to determine these statistical parameters of the vibration response, Monte Carlo simulations are conducted. A convergence analysis reveals the number of required irregularity profiles, which is a trade-off between accuracy and computational effort. Based on the obtained results, the influence of various model parameters on the maximum bridge response is studied. The power spectral density function and the range of wavelengths are varied when generating irregularity profiles. With respect to the train model, multi-body systems of different degrees of sophistication and various train types are considered. The variation of the bridge span, fundamental frequency, damping, and mass provides an overview of factors that affect the vibration response in the presence of track irregularities. On the basis of these outcomes a comparison between the aforementioned factors and the ones defined by design rules of the current code is conducted.

The oscillating roller is a dynamic compacting machine mainly used for nearsurface compaction of asphalt and soil in road construction of earthworks (dams and embankments). The core of an oscillating roller is the drum. An oscillating moment induced by two opposite rotating eccentric masses, whose shafts are mounted eccentrically with respect of the drum axis and applied in the centre of the drum, leads to a cyclic forward and backward motion of the drum. Through friction in the contact surface between the drum and the soil, shear forces are applied to the subsoil, which propagate in the form of waves in the subsoil resulting in soil compaction, i.e. the pore volume is reduced. The tangential application of forces to the soil reduces vibrations in the surrounding area in comparison to vertically vibrating vibratory rollers. In the case of vibratory rollers, roller-integrated Continuous Compaction Control (CCC) firstly proposed by Adam [2], is used as standard to optimize the compaction process. CCC assesses the soil compaction based on the change of motion behavior of the drum. A theoretical validation and possible optimization of the CCC measurement system for oscillating rollers according to Pistrol [24] is still pending and is subject of current research by Paulmichl [23]. Another focus of ongoing research, which is closely linked to the CCC methodology for oscillating rollers, concerns the optimum machine and operating parameters. The compaction effect should be as high as possible and wear of the drum should be minimized. Based on numerical simulations of a roller-soil system, the present work aims at creating a framework to verify and enhance existing criteria for CCC of oscillating rollers and to optimize machine parameters without the need of further expensive field tests.

At the beginning of this thesis a simplified numerical roller-soil model with linear elastic soil behavior is developed in an effort to better understand the basic behavior of the drum and to identify the impact of machine parameters on the drum´s response. It is shown that all considered parameters affect the accelerations at the drum center. Frequency analyses of the accelerations suggest that individual frequencies can each be assigned to at least one parameter.

With another model, which considers an elasto-plastic top soil layer, in a parametric study optimum machine parameters with regard to drum wear are identified. Qualitatively, proper machine parameters can be determined. To reduce wear of the drum, the oscillation amplitude should be as low as possible, the roller should be extremely light or very heavy and the roller speed should be as high as possible. However, without taking the compaction effect into account, these parameters optimized in such manner are of secondary importance. The same model is used to investigate the influence of material damping on drum-soil-interaction. It is shown that material damping has a decisive influence on the compaction depth of the roller.

In the third model, the hypoplastic material law with intergranular strain concept is implemented for the top soil layer that has to be compacted. To avoid numerical instabilities, viscous damper elements are attached to the surface of the soil. Hence the compaction process for a moving oscillating roller can be simulated. It is shown that a non-cohesive soil is loosened up on the surface during one pass, but is compacted underneath till the lower limit of the 0,5 m thick hypoplastic soil layer. Numerically derived accelerations at the center of the drum show a good qualitative match with measurement results from field tests. With this model, the basis for the further numerical investigations of soil compaction with oscillating rollers has been accomplished.

Every year timber as construction element becomes more important because wood is a biodegradable sustainable building material that also contributes to a pleasant room climate. The area of application of lumber is constantly expanded, however, there is still a lack on reliable technological foundations for this building material. This master thesis examines the mechanical properties of cross-laminated timber made of spruce wood. In a first step, static three-point bending tests on cross-laminated timber plates composed differently arranged wood laminates are performed. Based on a finite element model of the test objects, a numerical optimization procedure is applied to identify the material parameters such that the numerical load-displacement curve matches the experimental counterpart. In this respect, the elastic and plastic material parameters are separately optimized. The plastic behavior is described by means of Hill‘s criterion. This criterion is capable of reproducing the orthotropic strength values of lumber. Once the local material properties have been determined, two different homogenization procedures are applied based on the laminate plate theory respectively on a repeating unit cell. The result is the homogenized plate-shell stiffness matrix applicable to thin shells. Since, however, the considered cross-laminated timber elements behave more as a moderately thick shell, also the transverse shear stresses are identified. The outcomes of the homogenization procedures are validated, analyzing a point-supported slab utilizing a volume model and a corresponding shell model. In particular, the natural frequencies are used as an indicator of the stiffness distribution. It is shown that the plate and shell stiffness matrix of the repeating unit cell modeled shell and of the volume element are in an excellent agreement. Subsequently, the unit cell homogenization is extended into the inelastic domain. A failure surface is identified and implemented into a finite element code as post-processing variable. This variable is used to estimate the domains of plastic strains. Application to the slab in its ultimate limit state shows that the estimated plastic domains of the shell model are close to the ones of the volume model.

Apart from time consuming numerical methods, in earthquake engineering experimental procedures can be utilized to predict the seismic response of buildings. In the experiment usually a shake table is employed to excite dynamically the building model.

Due to limited space and high costs, in civil engineering it is more reasonable to test small-scale models than the original scale building, which will be further referred to as prototype. For this reason, the aim of the first part of this thesis is to perform a dimensional analysis on a building similar to the one of the Department of Engineering Science of the University of Innsbruck. Simulations on a detailed finite element model of the prototype predict its inelastic seismic response, evaluated for a particular column in the top floor. Dimensional analyses yield two different small-scale models of the prototype. Advantages and disadvantages of both outcomes are discussed, and subsequently, the dynamic response of the feasible small-scale model is set in contrast with the one of the prototype.

Secondly, after the dimensional analysis, the shake table is implemented in Abaqus, the same finite element program that has been used to model the prototype and the small-scale test object. Here, in particular, the effect of different methods to fasten the shake table with the concrete foundation is investigated. The hydraulic actuator serves as input device for the earthquake excitation imposed by means of a displacement time history. Thus, the underlying earthquake recorded must be integrated twice. It needs to be verified that the resulting input acceleration is equivalent to the recorded ground acceleration. In this thesis three different integration algorithms are evaluated, and appropriate preprocessing of the excitation signal is proposed to avoid filtering of the signal in the low frequency range.

After verification of the imposed shake table displacement, a finite element model of the entire system composed of foundation, shake table and small-scale test object is created, and the vibration response is analyzed. Since the test object is driven into its inelastic branch of deformation, the computational costs of these numerical analyses are very high, leading to a computing time of several days for one run. Consequently an equivalent single degree of freedom (SDOF) system of the test object is derived, reducing the analysis time to a few hours.

Finally, for the system of foundation, shake table and simplified test object an analytical three degree of freedom model is developed. The solution of the corresponding equations of motion is implemented in Matlab. This simple model allows to evaluating parametrically the forces of the hydraulic actuator, the displacement of the shake table and the velocity and acceleration of the concrete foundation for various test objects exhibiting different masses and natural frequencies. Force and displacement restrictions as given by real hydraulic actuators are considered.

The thesis concludes with a summary of the gained knowledge of the dimensional analysis, the numerical investigations on the shake table and the small-scale model, and the parametric study on the simplified analytical model of the system foundation-shake-table-test object.

Nowadays, lawn care by private persons and professional applicants is supported by lawnmowers of various sophistication. Strong competition and varied applications force manufacturers of lawnmowers to continuously enhance their products. Computer-assisted analysis and simulation support the efficiency of product development, or even make it possible. In this master thesis, the basis for a computer-assisted simulation model in terms of a multi-body system of the professional lawn mower MB756, produced by the company VIKING, is laid. Modal analysis, both analytically, numerically and experimentally, provides the natural frequencies and mode shapes of the considered lawnmower. Due to the elaborate geometry of the lawnmower housing, numerical modal analysis is based in a finite element model, solved efficiently with powerful commercial software packages running on fast computers. Numerical modal analysis provides useful information about natural frequencies and mode shapes of the considered object during the development and construction phase. Experimental modal analysis serves essentially the system identification, as well the verification of numerical respectively analytical results. With todays knowledge on measurement systems, accurate test benches can be built very quickly. In the present study, test setup for the investigated lawnmower and applied methodology were validated and verified using a simple beam model. Based on the outcomes it can be concluded that numerical simulation and measurement technology are suitable to identify natural frequencies of this test object with a maximum relative error of three percent. The analytical results of the test beam serve as basis for a convergence analysis investigating various finite mesh configurations. The outcomes of numerical and experimental modal analysis of the lawn mower body, including the four-wheel suspensions, almost coincide with a maximum relative error of eight percent. The development of a multi-body model for the casing considering also wheel suspension and knife assembly could not be implemented in the first step. The knife assembly includes engine, clutch, knife and knife mount. Rigid coupling of the knife assembly as a mass point with rigid massless beams to the casing is shown to be too stiff, and thus, with such a numerical model the experimentally determined eigenmodes could not be confirmed.

"Traditionally earthquake engineering has been concerned primarily with the assessment

of the horizontal response of load-bearing structures, because the structure is in general

in vertical direction relatively stiff. In the last decades, however, the effect of the vertical

ground motion component on buildings has been controversially discussed. While in the

past the focus was on the prediction of relative response quantities (i.e. measured relative

to the motion of the foundation) such as displacement and internal force, more recently

the importance of the total acceleration response has been recognized. The reason is

that seismic induced damage of stiff nonstructural components (NSCs) is directly related

to the total acceleration of their attached point at the load bearing structure. Several

studies examined the horizontal peak floor acceleration (PFA) demand of structural

systems. However, there is no comprehensive study on vertical PFA (PFAv) demands

of frame structures considering also the behaviour of flexible beams.

In this Master’s thesis the PFAv demand of steel moment-resisting frames excited by

earthquakes is assessed. In particular, the PFAv demand at column lines and along the

beams of various appropriate generic planar multistory frame models varying the number

of stories, fundamental periods and di↵erent refinement of discretization of the beams

is predicted based on response history analysis. The outcomes are presented in terms

of ratio PFAv over the vertical peak ground acceleration (PGAv), and they illustrate

the amplification of the PGAv in vertical direction. Assuming that NSCs are rigid, the

PFA of the frames correspond to the peak acceleration of attached NSCs.

An important conclusion of this thesis is that the median PFAv demand is up to five

times larger than the corresponding PGAv. Thus, the examined structures have no rigid

behaviour in vertical direction, and in the seismic assessment of acceleration sensitive

NSCs the PFAv demand should be considered."

The seismic collapse capacity of a building depends both on the supporting structure and the imposed earthquake record. Most of the investigations in earthquake engineering are based on regular systems, where all structural and geometric properties are continuously distributed as specified in the design process. However, in reality many buildings exhibit some irregularities, as a result of errors in the construction work or modifications during life cycle. Consequently, it is obvious to study the effect of those irregularities on the seismic behavior of buildings subjected to earthquake excitation.

In this Master’s Thesis the seismic collapse capacity of planar multi-story generic frame structures with various imposed irregularities (in vertical direction) is investigated, performing both non-linear static analysis and incremental dynamic analysis. In particular, strength, stiffness, or stiffness and strength simultaneously, of certain elements are reduced in specified locations of the structure. At the beginning the underlying methods of analysis as well as the theoretical background is described. Then, the structural models used for the assessment of the global collapse capacity are specified. These models are vulnerable to the P-delta effect. That is, in the inelastic range of deformation the post-yield stiffness becomes negative due to gravity loads, and consequently, these structures are prone to collapse when subjected to severe earthquake excitation. Material deterioration is, however, not considered. The next session describes the computational implementation of the models and the process of analysis conducted by means of the simulation software OpenSees. The obtained results are illustrated and explained in detail. The emphasis is on the comparison of the seismic collapse capacity and its record-to-record variability of the regular system with the ones based on systems with imposed irregularities in vertical direction. This thesis ends with a summary, provides conclusions gained from the derived results, and issues to be possibly studied in further investigations are outlined.

One important finding of this thesis is that the discontinuous reduction of strength and stiffness not necessarily leads to an impairment of the structural behavior in a seismic event. Depending on the location of the imposed „damage“, the global structural behavior may in some circumstances even be enhanced.

This thesis deals with railway bridges, which are excited to vibrations when crossed by high-speed trains. Increasing travel speeds may induce resonance phenomena, which cannot be captured appropriately with a static structural analysis even in combination with dynamic load factors. Multi-track bridges are subjected eccentric crossing trains, and thus, excited not only to bending vibrations but also to torsional vibrations, or in special cases, to coupled bending-torsional vibrations.

In the scope of this master thesis the influence and contribution of torsional vibrations on the global dynamic response behavior is investigated. In this respect, the design of the bridge cross-section plays an important role. The numerical response predictions are conducted by means of simple beams models and by means of more sophisticated special finite element models. In particular, the accuracy of the results based on the simple models is evaluated.

To evaluate the structural dynamic properties of structures, it is beneficial to verify the numerically predicted response by experiments. Based on experiments on models with suitable scale the behavior of the corresponding structure can be predicted numerically. The design of a small-scale three-dimensional modular frame structure at the Unit of Applied Mechanics of the University of Innsbruck serves to verify, to analyze and to visualize complex vibration phenomena of real structures.

The first three chapters of this master thesis describe design, construction and properties of the experimental model. Various variation possibilities of the experimental model are explained in detail. Subsequently, the applied excitation and measurement techniques are discussed. A thorough understanding of all measurement devices is significant because measurements are at risk for disruption by external influences that could lead to inaccurate results.

The following chapter addresses the development of a numerical model for the experimental model. Initially, the simplifications for the numerical model are discussed in detail. Then, the applied equations and relations used to calculate the model parameters and the amplitude frequency response are elaborated.

In section five the acquirement of the model parameters and the material properties needed for the calculation model is described.

In the final chapter the results of the experimental and calculation model are compared.

The objective of this master’s thesis is the identification of mass and stiffness of a structure by means of different dynamic methods, based on mathematical modelling in Matlab and on experiments on a small-scale vibratory frame with four dynamic degrees of freedom.

At the beginning the calculation of the vibration response of a multi-degree-of-freedom system is described analytically and subsequently implemented into Matlab. Then the modal parameters of the system, i.e. eigenfrequencies, mode shapes and damping coefficients, are identified using the Peak-Picking method and the Stochastic Subspace Identification technique. In all the experiments so-called Operational Modal Analysis is adopted, which means that just the vibration response is measured, but not the excitation. A large part of this work is dedicated to scaling of the mode shapes by application of additional masses. Additional masses are collocated differently in an effort to reveal its optimal distribution within the structure. Scaled mode shapes are needed to identify mass and stiffness matrix. The stiffness matrix and its inverse, the flexibility matrix, are used in the last part of the thesis to detect and to locate damage of a gradually damaged frame based on different approaches.

In this thesis the dynamic interaction between railway bridges and high speed trains is investigated.

The Bernoulli-Euler beam model is used to create a numerical model of railway bridges. Five different load models for the train moving with constant speed are evaluated:

• moving concentrated forces

• moving lumped masses

• single-degree-of-freedom (SDOF) oscillators

• two-degrees-of-freedom oscillators (two SDOF oscillators connected in series)

• multiple-degree-of-freedom oscillators (several oscillators connected in parallel and series, with pitching)

The mechanical problem of vibrating beams is solved using the modal superposition method. The differential equation of the coupled bridge-train interaction system is solved by means of the numerical method of Newmark. The influence of variation of parameters and choice of the mechanical train model on bridge-vehicle-interaction is subject of the studies. Varied parameters are for example bridge span, the ratio vehicle frequency to first bending frequency of the bridge, the ratio mass of the bridge to mass of the train and damping of the vehicle respectively bridge. The Austrian train Railjet is used as train-model. For parameter variation a generic train model has been created. In the last section of the work the influence of the acceleration of the body on travelling comfort is investigated.

The seismic load-bearing capacity of buildings depends on many factors. The seismic load as well as the structure itself plays a highly important role. In this respect on primary goal of earthquake engineering is to check the stability of a building in case of a severe seismic event. The assessment of seismic induced global structural collapse requires a high computational effort that depends on the selected numerical model. The adequate model should provide the desired results with low calculation effort.

This Master’s thesis investigates different types of mechanical models and their properties to approximate the seismic response of real elastoplastic structures. The frame properties are varied and the effects on the seismic collapse capacity are analyzed via static and dynamic methods of analysis. The first part describes these methods as well as their theoretical background. Subsequently, simple models such as the single-degree-of-freedom system but also generic frame models with a higher complexity are investigated. Model properties and their advantages and disadvantages are discussed. The procedure of generation of the frame models is specified and shown in an example. All considered models are more or less vulnerable to the P-delta effect. The next part concerns the implementation of the models and analysis methods in an opensource Earthquake Engineering Simulation Software (OpenSees). Significant parts of the code are presented and explained. Then, the influence of different frame parameters such as number of stories, payload, mass distribution, damping-methods and member-models on the results is discussed. Pushover analysis performed with and without the consideration of gravity loads. The frame behavior, but also the internal forces of frame components such as beam, column and springs, is investigated trough dynamic time history analysis. In the final part of the thesis a summary of the results and a prospect to further investigations is provided.

The goal of this diploma thesis is the implementation of a theoretical non-linear material model for fibre-reinforced plastic (FRP) in a finite element program. Fibre-reinforced plastic is rather a composite than a material, consisting of the two components fibre and matrix. These two components are characterized by the large difference in material stiffness. Hence, the total stiffness of fibre-reinforced plastic depends on the alignment of the fibre. Consequently, the FRP exhibits anisotropic material behaviour. Moreover, the material behaviour of fibre-reinforced plastic is non-linear. These material non-linearities with simultaneous consideration of anisotropy can be described only with highly complex material models, which require questionable assumptions and simplications. To make the calculation process as simple and clear as possible, the fibre and the matrix are treated separately in the material model used in this diploma thesis. Thereby, the stiffness matrices of the two components are calculated separately and assembled to a single matrix of material stiffness volumetrically. For the polymer matrix isotropic material behavior is assumed. The fibre is treated as a one-dimensional continuum, which transfers forces only in its longitudinal axis. Multiple layers of fibres with different orientations in the composite are possible. With the help of these assumptions the material non-linearities can be described with relatively simple constitutive relations. For the fibre-reinforced plastic component matrix elasto-plastic material behaviour is considered. Yielding is determinated by the yield hypothesis of von Mises. The numerical implementation is based on the return mapping algorithm and an isotropic hardening law. For the fibre-reinforced plastic component fibre a damage model describes the degradation of the material properties. Cracking under tensile loading and microbuckling under compressive loading is predicted with the fraction hypothesis of Rankine. To prevent the spreading of damage under load redistribution from the tensile to the compressive regime, the theory of compressivestiffness-recovery is applied. Convergence with respect to the discretization within the framework of the finite element method is achieved by adjusting the stress-strain relation by means of a consistent characteristic length and the specfic fracture energy. To obtain consistency, furthermore linear softening is expected. A comparison of the received results with the results of test runs assuming exponential softening and a non-consistent characteristic length respectively, justify this approach. The underlying mathematical formulations are described and a function test in terms of example problems is conducted. The developed source codes are listed in the appendix.

In this thesis the effect of the Rapid Impact Compactor on the subsoil is investigated numerically. Thereby, the focus is on the appropriate numerical formulation of the contact between the impact components of the device and the subsoil. Note that the Rapid Impact Compactor is used for middle-deep compaction and the improvement of soils. Based on numerical simulations extensive parameter studies are performed to evaluate wave propagation and compaction effect of this soil improvement method, which hardly can be realized in this extent by means of on-site experimental field measurements. Furthermore, outcomes based on the simplified assumption of impulse loading are compared with results of the actually utilized contact formulation of this impact problem. Modeling of the contact by means of impulse loading is efficient, in particular since the computational effort is reduced significantly.

Through rapid development of new measurement techniques nowadays a wide range of measurement procedures is available to reveal the condition of a construction. In a modern approach the dynamic response of a considered structure is recorded followed by data analysis to determine its dynamic structural parameters. In this diploma thesis the method of modal damage detection/identification and the energy cascading phenomena, which are both based on this basic concept, are applied. The first part of this thesis deals with the functionality of a Laser--Doppler--vibrometer, which is the utilized measurement system, its hardware components and the provided software. This measurement device allows contactless analysis of parts of the structure from distance and forms the basis of all performed measurements. Subsequently the theory of damage identification (or rather damage detection) from studying the recorded vibration data is treated. This includes the identification of damage due to the analysis of modal parameters. Furthermore, a method for damage detection based on an energy observation (energy cascading phenomena) is briefly described and discussed. In the second part the two test specimens as well as the performed measurements are described. After specifying the structure, the choice of the considered connection detail of the railway bridge is discussed. Based on the gathered knowledge a second test object -- a generic specimen in form of a steel plate -- is selected and analysed. The third part deals with the analysis of the measurement records of the railway bridge and the test specimen with respect to the described theories. It is investigated, whether the described effects of damage can be detected through the analysis of the recorded measurement data. In particular, the relevance of the theory of the energy cascading phenomena is verified. Finally the compiled knowledge is summarised and an outlook to further damage detection methods is provided.

This thesis deals with the dynamic behaviour of railway bridges for high-speed trains. In particular, resonance phenomena need to be investigated utilizing dynamic analysis, since bridge spans and train velocities are increasing nowadays. These analyses need a lot of effort. Thus, there is a demand for quick and yet accurate methods to evaluate the dynamic response of these bridges. The Bernoulli-Euler beam model is used to create a numerical model of railway bridges. Both, simply-supported single-span and continuous two-span beams are examined. A repetition of concentrated loads moving with constant speed models the impact of trains on the bridge. The mechanical problem of vibrating beams is solved using the modal superposition method. The influence of the number of modes on the dynamic response is studied. Furthermore, the impact of the span length to wagon length ratio and other parameters on the resonance behaviour is subject of the present investigation. However, the main objective of this thesis is to generate diagrams, which can be used by the practicing engineer as simple design tool to determine the dynamic peak bridge response (such as deflection, acceleration, bending moment). Application of these diagrams requires only the knowledge of the non-dimensional maximum travel speed and the type of train.

This diploma-thesis deals with the numerical calculation of the seismic response of elastic vibratory secondary structures. Secondary structures are parts of the building, which do not belong to the load-bearing structure. Seismic excitation may lead to large vibration responses when natural frequencies of the load-bearing and the secondary structure are tuned. The main structure is modeled by a generic frame structure with nonlinear material behavior. The first part of this thesis deals with the fundamentals of this study and the derivation of the equations of motions. In addition to the linear elastic - ideal plastic material model the method of static condensation and modal analysis are explained. In the second part the solution algorithm is described. The incremental-iterative formulation of the equations of motions is explained. Furthermore, two di erent iteration procedures for the determination of vibration response of constant ductility are presented. The third section deals with the numerical analysis and interpretation of results. The results of single-degree-of-freedom oscillators and two-degree-of-freedom oscillators are graphically displayed and explained. Finally, the calculations on the frame structures are described and improvements of the approximated solution are demonstrated.

In this thesis numerical procedures for the computation of stability points and the post-buckling

behaviour of slender structures are presented.

The Finite-Element equations for plane beam structures are derived from the principle of virtual

displacements. Thereby no restrictions are made on the magnitude of the displacements.

The arc-length method is used to compute unstable parts of the equilibrium path. The iterative

load changes are calculated utilizing a quadratic constraint condition.

Extented equation systems, containing the equilibrium equations and additional equations describing

the stability point, are formulated for the direct computation of critical points. These

equation are solved by means of the Newton-Rapson method and a bordering algorithm. At bifurcation

points a branch switching algorithm is employed to compute a equilibrium point on the

secondary path. The remaining part of this path is calculated by means of the arc-length method.

With the above mentioned procedures the complete structural response of spatially trusses, plane

beam structures and a cylindrical panel are successfully computed.