Forced Resonant Vibrations and Self-Heating of Solids of Revolution Made of a Viscoelastic Piezoelectric Material

Abstract

The concept of complex characteristics is used to formulate the coupled nonlinear boundary-value thermoelectroviscoelastic problem of the forced harmonic vibrations and self-heating of inelastic three-dimensional bodies of revolution taking into account the nonlinearity due to the dependence of the mechanical and electrical characteristics on temperature. An iteration method is used to reduce this nonlinear problem to a linear electroviscoelastic problem and a linear heat-conduction problem with a known heat source, which are solved using the finite-element method. This approach is used to solve a coupled nonlinear thermoelectroviscoelastic problem of the forced harmonic vibrations and self-heating of a hinged sandwich cylindrical panel. The numerical data obtained are analyzed, and the effect of nonlinearity on the amplitude–frequency and temperature–frequency responses is studied