A Generalized Dynamic Analysis Method for the Linear Structural System with Viscoelastic Elements

The high-damping viscoelastic (VE) materials are widely used to reduce unwanted vibrations in civil structures. However, the significant frequency and temperature dependences from high-damping VE materials cause a challenge in efficiently analyzing the structural dynamic behaviors. The aim of this study is to propose a generalized dynamic analysis method for the linear structural system with VE elements. The implementation steps and advantages of the dynamic analysis method are presented. In this method, the frequency-dependent matrices and non-proportional damping induced by VE elements are fully considered in modal coordinates, and then the state-space representation converted from the modal-based transfer function is adopted to implement the time-domain simulation. Any popular VE constitutive models which accurately describe frequency-dependent matrices can be applied to the method. The number of the state-space representation can be adjusted according to the interested frequency range. Numerical applications performed on a viscoelastically damped structure, a VE base-isolated structure, and a structure with a VE tuned mass damper (TMD) demonstrate the numerical accuracy, efficiency, and generality of the proposed dynamic analysis method.