Inverse component-mode synthesis method for damped large structural systems

Abstract

A new formulation for an incremental inverse problem is proposed to enhance computational efficiency of redesign of damped large structural systems. A large structural system is regarded as an assemblage of substructures. In the present formulation, mechanical properties of some substructures are given, and those of the other substructures are taken as the design variables. This problem is a hybrid inverse problem. Those design variables are determined so that the fundamental natural frequency and the transfer function amplitude ratios would attain the target values. It is shown that the inverse use of the conventional component-mode synthesis (CMS) technique within the scope of the hybrid inverse problem enables one to develop an efficient computational procedure for updating the design variables in the design problem. The proposed method can deal with a damped structural system with a general damping system (proportional or non-proportional, viscous and/or hysteretic, Voigt-type or Maxwell-type), in a unified manner. Different from the conventional CMS method utilized for redesign, component modes of the substructure are fixed during the redesign process. The validity and order of approximation of the proposed method is demonstrated through an example model.