Investigation of dynamic substructuring methods for systems with arbitrary viscous damping under stochastic excitation

1 February 2021

Abstract

During the development of a product, it is necessary to validate the quality of its mechanical components. A method of achieving this goal is by applying finite element method onto the computer aided design models. To increase the approximation to the analytical solution it is suggested to use an appropriate amount of finite elements. The high amount of finite elements results in an increase on the computational burden. To decrease the computational effort and simultaneously approximate properly the analytical solution, substructuring reduction methods prove useful. This study thesis concentrates on the implementation of substructuring methods onto mechanical systems with an arbitrary viscous damping under a stochastic excitation in state space. Goal of this thesis is after the implementation of Craig-Bampton, Hasselman & Kaplan Adaptation, Beliveau & Soucy and de Kraker’s reduction method to evaluate their quality regarding the approximation of the eigenvalues and the standard deviation error compared to the exact solution. The reduction methods aim to shrink the needed computational effort during calculations. In the first chapters a brief introduction on the basic theory shall take place, meaning fundamentals of vibration theory will be presented including also the implementation of modal analysis in physical and state space. In addition basic concepts and definitions of stochastic field will be explained to get more comfortable with this part of the thesis. Furthermore the examined reduction methods shall be introduced. As a follow up of the first chapters comes a further examination into the main concept of the study thesis based on the established fundamental knowledge. In this chapter the necessary equations and steps will be shown, which are needed and have to be executed in order to obtain the desired results for evaluation. An important part of this thesis concentrates on the simulations, which are conducted in order to evaluate the quality of the implemented reduction methods, compared to the exact solution as mentioned in the prologue. From the simulations the influence of modes, damping elements and geometry on the STD error will be investigated. Finally in the last chapter the overall conclusions of this thesis will be discussed, which are extracted from the simulations. Furthermore a glimpse in the future will be given on posibilities to expand this thesis

Literature

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