ABSTRACT
This chapter discusses the nonlinear vibrations of a layered viscoelastic solid. It proposes a macroscopic wave equation taking into account the properties of the microstructure. Through use of the developed model, the chapter analyzes the interplay between the effects of nonlinearity and dissipation. Viscoelastic properties of the medium can be governed by the well-known Kelvin-Voigt model. In hydrodynamics, it corresponds to the classical behavior of a viscous gas, where shear stresses are proportional to the deformation rates and the proportionality coefficients are determined by the gas density. Palmov studied nonlinear vibrations of semi-infinite and finite rods subjected to a dissipation. He employed the method of harmonic linearization, which gave first-order approximation coinciding with the Rayleigh-Ritz approach. High-frequency deformations of nonlinear rate dependent materials induced by the propagation of transient waves were considered by Varley and Rogers and Seymour and Varley. Vibrations of continuous structures can be described by dynamical systems having infinite number of degrees of freedom.
