Linear models with nearly frequency independent complex stiffness leading to causal behaviour in time domain

Abstract

AbstractIn the paper, several causal linear models leading to nearly frequency independent complex stiffness are studied in time and frequency domains. Along with Biot model other three hereditary models are introduced into analysis. They all ensure practical constancy for damping properties but have limitations concerned with an increase in the real part of complex stiffness of corresponding material elements, as frequency grows. A new suggested method deals with given mechanical system as a whole: the imaginary part of the system compliance is constructed assuming that all elements have constant stiffness (with a modification for imaginary parts near zero frequency) and further the imaginary part of the system is used directly for studying transient vibrations supposing causality of the given mechanical system. The corresponding real part (not needed in the transient response analysis) is determined by Hilbert transformation. Examples relating to systems with one, two and infinite (shear beam) degrees of freedom are carried out for five compared models, allowing to reveal advantages and shortcomings of the models. Copyright © 2006 John Wiley & Sons, Ltd.