Publication

Abstract : This study utilizes the nonlocal strain gradient theory (NSGT) to establish a generalized, size-dependent thermoelastic framework for transversely isotropic piezo-thermoelastic (PTE) microbeam under the Euler-Bernoulli beam theory. The model incorporates two different length-scale parameters, viz. nonlocal elasticity and strain gradient effects to characterize microscale structural behavior. To address thermal lagging phenomena, the heat conduction equation is derived based on the Moore-Gibson-Thompson (MGT) framework, which introduces memory-dependent derivatives over a variable time interval. By employing coupled Laplace transform and finite Fourier sine integral methods, analytical solutions for thermoelastic distributions (e.g., deflection, bending moment, thermal moment) are derived for a simply supported microbeam. The Laplace-domain solutions are obtained via Fourier inversion, and their time-domain counterparts are reconstructed using the Zakian’s algorithm. Numerical simulations based on PZT-5A material investigate the influence of kernel functions on heat transport behavior and evaluate the performance of the proposed nonlocal strain gradient model against classical formulations. The results demonstrate a strong sensitivity of physical responses, such as thermal moment and deflection to time delay parameter, revealing the potential for controllable vibration damping. Overall, the study offers valuable design insights for microscale beams in MEMS/NEMS applications, bridging advanced theoretical modeling with practical optimization strategies.