Study on Thermoelastic Damping in Micro/nano-Beam Resonators with Linearly-varying Thickness

The non-uniform micro/nano-beams have been found widely applications in resonators because of their special structural properties. Thermoelastic damping (TED) is confirmed as a fundamental and momentous energy dissipation mechanism of operated-vacuum resonators. TED-limited quality factor (Q-factor) in uniform micro/nano-beam resonators has been investigated sufficiently. In contrast, TED in non-uniform micro/nano-beam resonators has not been studied adequately. Moreover, there are proofs that Zener's model and the model of Lifshitz and Roukes are failed to provide an appropriate estimation of TED in non-uniform beam resonators. In this paper, a TED model of linearly tapered micro/nano-beam resonators with rectangular cross-section is proposed basing on the Zener's framework and the energy definition method, and the tapered micro/nano-beam with linearly-varying thickness is considered as the major object. The mode parameters of tapered beams are calculated by using Adomian decomposition method (ADM). The results obtained from our models agree well with the finite element method results and the published results. It is indicated that TED in tapered micro/nano-beams depends on modal parameters including the vibration frequency and the modal shape function, and is significantly affected by boundary conditions and geometrical parameters. The proposed models are able to be used to optimize the design of linearly tapered micro/nano-beam resonators with high Q-factor by choosing the most appropriate boundary condition and geometrical parameter.

I. Introduction

In recent decades, the manufacturing technology of micro/nano-electro-mechanical systems (MEMS/NEMS) develops rapidly, and some special micro/nano-beam devices with discontinuously or continuously variable cross-section have already been produced and applied extensively. Thermoelastic damping (TED) is identified as a fundamental and momentous energy loss mechanism of operated-vacuum micro/nano-resonators [1] . TED, which originates from the irreversible thermal flow generated due to the expansion and compression of anelastic structures in harmonic vibration, is an intrinsic dissipation mechanism [2] . TED determines an upper limitation on the attainable quality factor ( Q -factor) of resonators.