Abstract
In this work, mechanical and thermal properties of a viscoelastic thick plate under the effect of a random ramp-type heating are investigated. The problem is considered in the context of the generalized theory of thermoviscoelasticity. One surface of the plate is considered traction free and subjected to a known random temperature, while the other surface is considered thermally insulated. Laplace and Fourier transforms are used to obtain the analytical solution in the transformed domain for the temperature, components of displacement and stress tensor. A numerical technique based on a Fourier series expansion is used to invert the transformed solution to the time and space domain. Numerical results are represented graphically and discussed.