Mechanisms Of Energy Dissipation In MEMS And NEMS Resonators

Micromechanical/nanomechanical resonators have gained widespread applications in ultra-high sensitive sensing,high precision measurement,and high-frequency signal processing,due to their unprecedented advantages of ultra-high frequency,high sensitivity,and high quality factor.Resonant frequency and energy dissipation are two important characteristics of micromechanical resonators.Better device performance can be achieved via high frequency and low energy dissipation.The miniaturization of devices below submicron scale could lead to increased energy dissipation,which indicates that the influences of micro-effect in micro/nanostructures become significant and cannot be neglected in further study of energy dissipation of M/NEMS-based devices.Therefore,it is necessary to understand various underlying mechanisms of energy dissipation in MEMS and NEMS resonators.This work discusses several dissipation sources,as well as possible ways to reduce them,based on continuum theory.The research topics in the dissertation includes:(1)Evaluation of thermoelastic damping(TED)in micromechanical resonators operating as mass sensors is studied by means of the thermal energy approach.Both quasi-one-dimensional model and two-dimensional model are proposed and analytical expressions of TED in infinite series form for micro-beam resonator-based mass sensors are derived.Effects of various factors on TED,such as the position of attached mass particle,boundary conditions,geometry of resonators and mode shape of vibration are examined.In addition,the expressions of mass sensitivity and minimum detectable mass imposed by thermomechanical noise process for resonant mass sensors of bridge and cantilever configurations are derived.(2)Based on thermal energy method,an analytical model for evaluating thermoelastic damping in micromechanical resonators with axial pretension is proposed,in which thermal conductions in both thickness direction and axial direction are considered.An explicit expression for thermoelastic damping in the form of infinite series has been obtained.Effects of beam geometry,mode shape and axial pretension on thermoelastic damping are explored.In addition,Finite Element analysis(FEA)is employed for validation of the proposed analytical model.(3)An analytical study on evaluation of support loss in micromechanical resonators undergoing in-plane flexural vibrations is conducted.Based on two-dimensional elastic wave theory,and by adopting Fourier transform and Green's function technique,analytical expressions of support loss in terms of quality factor,taking into account distributed normal stress and shear stress in the attachment region,and coupling between the normal stress and shear stress as well as material disparity between the support and the resonator,have been derived.Effects of geometry of micro-beam resonators,and material dissimilarity between support and resonator on support loss are examined.In addition,the Perfectly Matched Layer(PML)numerical simulation technique is employed for validation of the proposed analytical model.(4)An analytical model is proposed to examine effects of axial pretension on support loss.Based on Two-dimensional elastic wave theory,and by adopting Fourier transform and Green's function technique,an explicit expression for support loss,taking account of axial pretension,has been obtained.The Perfectly Matched Layer(PML)numerical simulation technique is employed for validation of the proposed analytical model.In addition,the comprehensive energy dissipation consisting of support loss and thermoelastic damping in the resonator under axial tension is further discussed.Effects of geometry of micro-beam resonators,and axial pretension on comprehensive energy dissipation are examined.(5)An analytical study on the evaluation of Casimir effect-induced energy loss in nanobeam resonators undergoing in-plane flexural vibration is presented.Two-dimensional elastic wave theory is employed to determine the energy transmission from the vibrating resonator to the substrate.Fourier transform and Green's function technique are adopted to solve the problem of wave motions on the surface of the substrate excited by the Casimir force.Analytical expressions of Casimir effect-induced energy loss in terms of quality factor,taking into account both pressure wave propagation in the noncontact substrate and shear wave propagation in the supporting substrate,as well as linear and nonlinear terms of time-varying Casimir force,have been derived.Effects of beam geometry,initial separation gap and structural boundary conditions on damping are examined.Thermoelastic damping,support loss and Casimir effect-induced energy dissipation in micromechanical/nanomechanical resonators,operating in the linear regime,have been studied systematically in this dissertation.We have proposed more precise analytical models,which provide important theoretical bases and guidelines for the design and optimation of micromechanical/nanomechanical resonators.