Thermoelastic Damping in Partially Covered Bilayer Microbeam Resonators with Two-Dimensional Heat Conduction

Abstract

Thermoelastic damping (TED) has been proved as an intrinsic mechanism of energy dissipation in the microelectromechanical systems (MEMS) resonators. However, the previous TED models developed for the fully covered bilayer beam resonators cannot be used for the partially covered cases. This paper firstly derives an analytical TED model for partially covered bilayer microbeams. The bilayer beam performs small-amplitude vibration in pure bending mode, and the mode shape is achieved from the dynamic of Euler-Bernoulli beam. To obtain the coupled temperature field, Green's functions are utilized to solve the heat conduction along thickness and length directions within the framework of Fourier's law. The expression for TED is derived in the form of an infinite series. The present TED model can reduce to that of a fully covered bilayer beam, and matches well with the finite element method (FEM). The behaviors of TED spectrum are investigated comprehensively. Two comparable Debye peaks are noticed at approximately two corresponding critical frequencies. The partial coating greatly reduces the peak values at high critical frequency, but causes an additional TED peak at low critical frequency. The TED peaks of the coating slightly increase as the length increases. The effects of the length and position of the metal coating on the TED at the fundamental frequency are significant. To reduce TED, the metal coating should be located away from the substrate clamped end. This paper provides a developing methodology for controlling TED.