Thermoelastic damping analysis in nanobeam resonators considering thermal relaxation and surface effect based on the nonlocal strain gradient theory

Abstract

With the extensive applications of the micro/nano-electro-mechanical systems, a great deal of attention has been paid to explore the influences of the arising size-dependent effect and surface effect on their performance. Along with these effects, the nonlocal elasticity, strain gradient theory, and surface elasticity theory were successively proposed. Moreover, it is inevitable for MEMS/NEMS to work in a variable temperature environment, correspondingly, the thermal-induced stress or deformation becomes another issue that needs serious concern. Thermoelastic damping (TED), as a main energy dissipation source, is a major challenge in designing higher-quality factor resonators. However, considering the thermoelastic coupling effect, the aforementioned theories are not capable enough to depict the thermoelastic performance of micro/nano-resonators. To amend this deficiency, based on nonlocal strain gradient theory, a new model for assessing the TED of nanobeam resonators by incorporating the thermal relaxation effect and the surface effect is developed. The corresponding governing equations for the Euler–Bernoulli microbeam resonator model are formulated, and then, solved by means of a complex frequency method. The influences of the nonlocal parameter, strain gradient coefficients, aspect ratio, surface stress and surface elasticity on the TED are examined and discussed in detail.