Nonlinear thermo-mechanical-diffusive vibrational response of a spherical microshell incorporating memory-dependent and size-dependent effects

The rapid advancement of micro-electromechanical systems (MEMS) and the extensive utilization of ultra-short time heating technology in the precision machining of these devices have underscored the critical importance of studying the interplay between thermodiffusion and mechanical deformation. At the microscale, the size-dependent effect in elastic deformation and the memory-dependent effect in thermal transport processes become increasingly significant and must be taken into account. Meanwhile, many experimental and theoretical investigations suggest that, in practical analyses, thermal conductivity and diffusivity in materials should not be considered as a constant value. This paper addresses the thermoelastic diffusion response of a spherical microshell subjected to sinusoidal thermal and concentration loading including the simultaneous effects of the fractional-order parameter, the nonlocal parameter, and the variable thermal conductivity and diffusivity. Taking into account the variable thermal conductivity and diffusivity, the nonlinear governing equations are derived by the Laplace and Kirchhoff transformations. The results show that the nonlinear thermoelastic diffusion response of the spherical microshell can be adjusted by the suitably modified parameters, which strongly depend on the size-dependent effect, memory-dependent effect, and the variable thermal conductivity. It is hoped that the obtained results would be helpful in designing the microstructures induced by an ultra-short time heating.