Michael KAWRZA

Assessment of the capacity and the operating range of a uniaxial shake table for model testing in structural dynamics

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.



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