Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions

Abstract

Thermoelastic dynamic analysis of micro-/nano-beams is essential in the field of micro-/nano-electro-mechanical systems (MEMSs/NEMSs). However, the classical coupled thermoelastic theory is not suitable for the microscopic/nanoscopic case. As elementary parts of MEMSs/NEMSs, the size effect of micro-/nano-beams must be considered in their thermoelastic vibrations. This work originally explores analytical solutions of coupled thermoelastic forced vibrations of micro-/nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory. The heat conductivity equation is obtained by using the type Ⅲ Green-Naghdi theory. Coupled thermoelastic dynamic equations are decoupled by use of Green's function method and expressions of displacements, temperature fields, and thermal moments of micro-/nano-beams are derived. Furthermore, movement behaviors of an “ice core” of the temperature field are used to explain dynamic phenomena of the coupled system. Results from finite element analysis are compared with analytical solutions for verification purposes. This work primarily discusses influences of a small-scale parameter on coupled displacement and temperature fields and those of other important physical parameters, such as heating positions and height-to-length ratios of micro-/nano-beams, on system responses.