Analytic solution of one-dimensional problem for partial integro-differential equations which have partial continuous coefficients in thermoviscoelasticity theory

Abstract

In this paper, a non-stationary problem on thermomechanic wave propagation is solved in environent, which is, consists of a finite thick plate connected with a semiinfinite space. Materials of the plate and the space are in confirmity with linear viscoelasticity and heat transfer for each environment independently, initial conditions and on the connection surface of environment conditions of increasing temperature and normal stress, depending only on time which are given as known functions. ıt is assumed that temperature and mechanical fields depend on each other. as a system, parabolic type partial integro-differential equation of temperature and hyperpolic type partial integro-differential equation of wave are solved. ıt is assumed that kernels of integral operators are difference kernels. Depending on boundary conditions, functions onf temperature and mechanical magnitudes become only functions of time and a space axis which is perpendiicular to free surface. In this case the problem turns out to be a one-dimensional one.