A non-Fourier magneto-thermo-viscoelastic problem of a two-dimensional plate

Abstract Viscoelastic materials is a kind of damping materials which has been wildly applied in vibration control of ocean and civil engineering, and viscoelastic materials mostly work in a complex thermoelectric multi-field coupled environment. In this work, a two-dimensional viscoelastic plate is studied with stain relaxation time and viscoelastic relaxation time. The two-dimensional viscoelastic plate is placed in a magnetic field, and the upper surface is subjected to a thermal shock. The problem is investigated by a modified L-S thermo-viscoelastic model with stain, viscoelastic relaxation time, and magnetic field. Normal mode analysis is used to achieve exact analytical expressions of temperature distribution, displacement component and thermal stresses. Numerical computations are conducted for copper-like material and dimensionless results are illustrated graphically. Based on the results, the influence of magnetic field on the distributions of the nondimensional temperature, displacement and stresses are discussed.