Magneto-Thermoelastic Coupling Dynamic Responses of Narrow Long Thin Plates Under Memory Effects and Size Effects

Abstract

The dual-phase-lag thermoelasticity theory with memory-dependent derivative can perfectly describe the phenomenon of non-Fourier heat conduction, nevertheless, it has not been comprehensively considered: the mechanical response of materials aroused by the size-dependent effects and the influence of multiple coupling effects such as magnetic, thermal and elastic fields. A dual-phase-lag thermoelasticity theory considering memory dependent effect and non-local effect is established. Based upon the revised theory, the magneto-thermoelastic coupling problem of a thin plate subjected to a cyclical heat source is investigated. First the governing equations of the problem are formulated. Then combining the boundary conditions and initial conditions, the solution of the problem is obtained by using Laplace transform and inverse transform techniques. Last, the effects of magnetic field, phase lag, time-delay, kernel function, non-local effect and time on the dimensionless quantities were investigated respectively, which provided a powerful reference for the dynamic response of micro-scale materials.