Multiscale thermoelastic vibration analysis of functionally graded nanobeams using nonlocal and memory-dependent effects

This study examines the vibration analysis of a functionally graded (FG) nanobeam with exponential material variation (metal to ceramic). It integrates Eringen’s nonlocal theory to account for size effects and the Moore-Gibson-Thompson theory of generalized thermoelasticity, including memory dependence. The simply supported beam, exposed to sinusoidal pulse heating, is investigated using the Laplace transform and Zakian method. Results demonstrate the influence of the nonlocal parameter, FGM grading, pulse width, kernel functions, and delay time on the nanobeam’s lateral vibration, temperature, and displacement, offering insights for microstructure design and optimization.