Scale Effects on Thermoelastic Coupling Wave Propagation of Micro-Beam Resonator Using Nonlocal Stain Gradient and Generalized Thermoelasticity

Abstract

Coupled thermoelastic analysis in the study of microscale solid mechanics has attracted considerable attention along with the miniaturization and functionalization of devices. Higher-order continuum mechanics theories have considered scale effects; however, the theories to predict thermoelastic performances of structures in micro-scale are still incomplete. The purpose of this paper is to study scale and thermal-induced effects by considering stress nonlocality and strain gradient elasticity in micro-structure resonators. The thermoelastic constitutive relations are established based on the nonlocal strain gradient (NSG) theory. The wave propagation problem of a Timoshenko micro-beam in conjunction with Green and Naghdi’s generalized thermoelastic (G–N) theory is investigated. The governing equations are derived and analytically solved by the eigenvalue method. Finally, the dispersion relation of a frequency spectrum is determined and the influences of scale parameters and coupled thermoelastic effect are discussed; in addition, the analysis results are compared with those under different size-dependent theories accordingly.