Significance of memory-dependent derivative approach for the analysis of thermoelastic damping in micromechanical resonators

Abstract

Thermoelastic damping is becoming a leading factor for determining the quality of the micromechanical resonators in terms of their sensitivity. The present study is devoted to the analysis of thermoelastic damping of a micro-beam resonator by employing the concept of three-phase-lag (TPL) theory of thermoelasticity in the context of the memory-dependent derivative (MDD). The memory-dependent derivative is characterized by its time delay and the kernel function that can be chosen freely with imposed restrictions. Analytical expressions of thermoelastic damping, attenuation as well as frequency shift have been derived. Computational results for the prominent parameters of micromechanical resonators such as thermoelastic damping, attenuation, and frequency shift are obtained. The influence of the constituents of memory-dependent derivative, i.e. time-delay and kernel functions, on the parameters of the micro-beam resonator has been analyzed through graphical results. Furthermore, numerical results are compared with the results obtained in the absence of a memory-dependent derivative through numerical simulations. The significant role of the memory-dependent derivative has been identified and it has been found that the insertion of the memory-dependent derivative is capable of providing accurate results as compared to the results obtained in its absence.