RATIONAL POLYNOMIAL APPROXIMATION MODELLING FOR ANALYSIS OF STRUCTURES WITH VE DAMPERS

Abstract

The objective of this paper is to introduce a Rational Polynomial Approximation (RPA) method for modelling the response of structures that contain discrete elements with linear frequency-dependent stiffness and damping characteristics. The RPA method consists of two steps: First, system identification is performed to obtain a rational polynomial approximation for the system's transfer functions. Then, a time-domain model for the system is realised. The main advantage of the RPA method is that the resulting model is a system of ordinary differential equations, facilitating time history analysis of both linear and nonlinear structures using standard time-step integration algorithms and procedures. Viscoelastic (VE) dampers comprise one of the primary classes of frequency-dependent dampers with both frequency-dependent stiffness and damping. VE dampers are used for mitigation of seismic- and wind-induced structural vibration. When using VE dampers in analysis, effective modelling of the frequency-dependent characteristics of the VE damper plays a key role in accurate simulation of structural responses. Following a description of the theory behind the RPA method, the efficacy of the method is verified through several numerical examples employing VE damped structures. The results are compared with Kasai's fractional derivative model for VE dampers. Application of the RPA method to nonlinear structures is also given. The RPA method is shewn to be effective and efficient for modelling VE damped structure.