Thermoelastic damping in microbeam resonators based on modified strain gradient elasticity and generalized thermoelasticity theories

Abstract

The present study aimed to investigate the size-dependent quality factor of thermoelastic damping in a microbeam resonator based on modified strain gradient elasticity theory. The governing differential equation of motion is derived by using the principle of virtual displacements. The generalized thermoelasticity theory of the well-known Lord–Shulman model is also utilized to derive the equation of coupled thermoelasticity. The quality factor of thermoelastic damping in the microbeam is obtained based on both the complex frequency and the entropy generation methods. Further, by applying the generalized thermoelasticity theory and entropy generation method, explicit formulae for the quality factor of thermoelastic damping in the microbeam resonators are developed in the frameworks of both classical and modified couple stress elasticity theories. The effects of several parameters including size effect are investigated on thermoelastic damping in cantilever and clamped–clamped silicon microbeams as case studies. The results are validated by observing an excellent agreement regarding the comparison of the results of the present study and with previously published results.