Thermal shock-induced Moore-Gibson-Thompson generalized coupled thermoelasticity analysis based on the strain gradient Love-Bishop theory in a nanorod resonator

This paper develops the Moore-Gibson-Thompson (MGT) generalized coupled thermoelasticity analysis in a Love-Bishop nanorod resonator using strain gradient theory to simulate the laser-shock induced thermoelastic wave propagation for the first time. The dynamic governing equations of MGT coupled thermoelasticity are derived using the energy balance equation (MGT heat conduction) and the variational principle. The size dependent MGT heat conduction equation is obtained for the first time, which is employed to derive the governing equations. The governing equations are transferred to Laplace domain and analytical solution is proposed to solve them for a Love-Bishop nanorod resonator under thermal shock loading. To obtain the temporal variation of fields' variables, a proper Laplace inversion technique is employed in the problem. The size effects in the nano-sized Love-Bishop rods are taken into account with five small-scale parameters including three higher-order materials length parameters, the micro-length inertia and thermal parameters. The effects of the higher-order materials length parameters and the micro-length inertia and thermal parameters on the propagation of thermal and elastic waves are studied in detail. The obtained governing equations based on the strain gradient elasticity and MGT theories and also the proposed analytical solution can be employed for a realistic simulation of a Love-Bishop nanorod resonator as micro-electro-mechanical system, which is subjected to a laser excitation. The proposed analytical solution and results are verified with the reported data in the published literatures.