Analytical solution for nonlocal coupled thermoelasticity analysis in a heat-affected MEMS/NEMS beam resonator based on Green–Naghdi theory

Abstract

• An analytical solution is proposed for transient coupled thermoelasticity of NEMS. • The micro/nano beam resonator is excited by thermal shock loading. • The size effects are taken into account employing nonlocal Rayleigh beam theory. • The energy is dissipated in the employed model based on the GN theory. • The fields’ variables are presented in the close forms for a NEMS. In this article, an analytical solution is presented for coupled thermoelasticity analysis (with energy dissipation) in a micro/nano beam resonator, considering small scale effects on the transient behaviors of fields’ variables. The Green–Naghdi (GN) theory of generalized coupled thermoelasticity and nonlocal Rayleigh beam theory (NRBT) are employed to derive the temperature and lateral deflection in the closed forms. The presented analytical solution is based on Laplace transform. To find the dynamic and transient behaviors of fields’ variables in time domain, an inversion Laplace technique is utilized, which is called Talbot method. The effects of some parameters such as small scale parameter and dimensions of the beam on the dynamic behaviors of temperature and lateral deflections are discussed in details. The propagation of wave fronts in both temperature and lateral deflection domains are obtained and graphically illustrated at various time instants.