Abstract
In many systems of interest, most of the structure is well approximated as linear but some parts must be treated as nonlinear to get accurate response predictions: significant nonlinear effects are due to the connections between coupled subsystems, such as in automotive or aerospace structures. The present work aims at predicting the nonlinear behavior of coupled systems using a substructuring technique in the modal domain. This study focuses on the effects of nonlinear connections on the dynamics of an assembly in which the coupled subsystems can be considered as linear. Each connection is instead considered as a quasi-linear substructure with stiffness that is function of amplitude or energy. The iterative procedure used here is enhanced with respect to previous works by enforcing a better control of the total energy at each iteration allowing to obtain the solution for a prescribed set of energy levels. Also, the initial guess and the convergence criterion have been modified to speed up the procedure. This technique is applied to a system made of two continuous linear subsystems coupled by nonlinear connections. The numerical results of the coupling are first compared to the ones obtained by using the Harmonic Balance technique on the model of the complete assembly to evaluate its effectiveness and understand the effects of modal truncation. Besides, a nonlinear connecting element, specifically designed in order to have a nearly cubic hardening behavior, is used in an experimental setup. Substructuring results are compared to experimental results measured on the assembled system, in order to evaluate the correlation between mode shapes and the accuracy in the resonance frequency at several excitation levels.
Highlights
During the last decades, the use of Finite Element Methods spread in many engineering fields, allowing to achieve very accurate results
The substructuring technique in the modal domain was successfully employed to study the dynamics of linear subsystems connected through nonlinear connecting elements
The choice of the initial guess based on the results obtained at the two previous energy levels and the definition of a stopping criterion that compares the energy distribution between two consecutive iterations lead to a more rapid convergence of the procedure
Summary
The use of Finite Element Methods spread in many engineering fields, allowing to achieve very accurate results. In 2008 De Klerk et al gave an extensive review of the substructuring techniques developed so far [8], and proposed a general framework to formulate substructuring problems either in physical, modal and frequency domains These methods have become very popular since their range of application is very broad: it is possible to obtain the dynamic behavior of complex systems starting from the known dynamic behavior of its component substructures (coupling) [9,10]; on the other hand the behavior of one substructure can be achieved from the known behavior of the complete structure and that of the residual substructures (decoupling) [11,12,13]. The advantages of using nonlinear substructuring techniques, such as the one presented in this paper, with respect to other methods that require the model of the entire system, such as the HB method, shooting and pseudo-arclength continuation, FEM, are implicit in the substructuring approach: combining experimental and numerical models, considering simpler subsystems instead of a unique complex one, performing indirect analyses and allowing a reduction of the computational burden.
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