Modelling of dynamic behaviour of viscoelastic materials in the frequency domain

Abstract

The modern methods of acoustical and vibration calculus require accurate material models to take properly into account the damping and dynamic elastic properties of the viscoelastic materials used for sound and vibration control. The usual modeling methods (spring-dashpot models, fractional calculus) start out of the stress to strain relations defined in the time-domain, which are then transformed into the frequency domain to find the appropriate material functions. In contrast, the damping and elastic properties are known from measurements made in the frequency domain; therefore, it seems to be reasonable to model the material behavior directly in this domain. The aim of this paper is to show that the typical dynamic behavior of solid viscoelastic materials can efficiently be modeled in the frequency domain. This modeling method is based on simple theoretical considerations, the frequency domain experiences and the causality principle. Two fundamental material models are developed in this way, namely one for the damping increasing with frequency, and the other one for the damping peak, which can be either symmetrical or asymmetrical with respect to the logarithmic frequency. The relation of the frequency domain models to the popular fractional derivative models defined in the time-domain is shown and discussed.