Toward a theory of governing equations of nonlinear thermoviscoelasticity for periodic deformation

The study of vibrations and vibrational heating of solids with amplitude-dependent characteristics is important for designing vibration-damping systems containing elements made of high-filler-content polymers [6, 12], metalwaveguides in ultrasonic welding units [i], etc. The most recent results obtained in this broad area at the juncture of physics and mechanics were generalized in the monographs [7-9]. The main tasks to be performed in the problem in question are: selection of governing equations, suitable formulation of the coupled thermoviscoelastic problem, development of methods of its numerical realization, and study of the therm0mechanical behavior of bodies. The present study is devoted to the first and part of the second questions, i.e., to analysis of different approaches to the construction of approximate governing equations of nonlinear viscoelastic bodies subjected to small periodic, deformations. i. Construction of the Governing Equations. Wewill study the structure of the governing equations of stable, nonlinear viscoelastic media, These equations describe the polyharmonic reaction to the stresses