On frequency dependences of material damping and dynamic elastic properties

Abstract

The various solid materials may exhibit diverse damping and dynamic elastic behavior as a function of frequency over a wide range extending from zero hertz up to the meaningful high frequencies. Nevertheless, some general characters in the dynamic behavior of materials can be experienced, especially if a limited frequency range is concerned. The aim of this paper is to establish and classify the general characters of frequency dependence of linear damping and elastic properties with special emphasize to the sonic range and the materials used for sound and vibration control. Based on simple physical views, the frequency dependences of damping properties (loss modulus and loss factor) are established as a first step. It is shown that basically two types of damping behavior can be distinguished, namely, (a) damping increasing with frequency and (b) damping exhibiting a peak. All other types of damping (e.g., the decreasing and the hysteretic damping) can be interpreted through the above mentioned ones. The dynamic elastic properties (shear or bulk modulus, etc.) as a function of frequency are determined from the damping by considering causality principle. The frequency dependences predicted for the dynamic moduli are discussed.