Thermoelastic Damping In Micro/nano Resonators With Non-fourier Heat Conduction

Micro/nano-resonators,which are representative devices of micro/nano-electro-mechanical systems(MEMS/NEMS),can realize the conversion of mechanical energy and other physical energies,such as the magnetic energy and the electric energy.Studying the damping mechanisms of micro/nano-resonators is a significant and crucial issue to obtain a high quality factor and improve the resonator performance including measurement accuracy,signal-to-noise ratio,sensitivity,and resolution.As one of intrinsic mechanisms of energy dissipation in MEMS/NEMS resonators,thermoelastic damping(TED)determines the upper-limitation of quality factor and cannot be eliminated completely by the manufacturing technologies.In the case that micro/nano-resonators are operated in some extreme situations including the ultra-low temperatures and ultra-high frequencies,the TED models established by the classical Fourier's law of heat conduction are unavailable to evaluate TED values.Therefore,establishing the generalized TED models with non-Fourier heat conduction is of significance for scientific researches and engineering applications.Micro/nano beam,plate and ring are three typical and fundamental elements applied in MEMS/NEMS devices.They are widely used as the core components of sensing systems or actuating systems.Utilizing the generalized theory of non-Fourier heat conduction including the single/dual-phase-lagging theories,the analytical TED models for these three representative resonators are derived in the series form.The main contents and contributions of this dissertation are summarized as follows:First,this dissertation focuses on micro/nanobeam resonators with rectangular cross-section.By employing the generalized theory of non-Fourier heat conduction(single/dual-phase-lagging theory),the governing equation of temperature gradient is established.Then the quasi-one-dimensional temperature function considering the heat conduction only along the direction of beam thickness is obtained by the integration method of trial function.Finally,the generalized TED models are developed basing on the method of energy definition.In special,the generalized TED models for beams with circular cross-section are in the same with those of beams with rectangular cross-section.The model convergence,the effect of non-Fourier heat conduction on the temperature distribution,and the influences of the phase-lagging time,the material selection and the equilibrium temperature on TED spectra are analyzed.It is found that the results of the present model are in excellent agreement with those of the existed numerical model.However,the present model is capable to explain the phenomenon of TED spectra with single,double or multiple peaks considering the effect of non-Fourier heat conduction.Second,the analytical generalized TED models for rectangular and circular micro/nanoplate resonators are developed by utilizing the vibration theory of Kirchhoff-Love plate and the single/dual-phase-lagging theory of non-Fourier heat conduction.The derived TED models are independent of the plate shape.Comparing with TED models of beams,TED models of plates contain a constant coefficient including the Poisson's ratio.Therefore,TED behaviors of plates are similar to those of beams.Additionally,the present models are suitable for circular plates operating in arbitrary vibration modes.Third,this dissertation focuses on micro/nanoring resonators with rectangular cross-section.The one-dimensional heat conduction only along the direction of ring thickness and two-dimensional(2D)heat conduction along the radial thickness and the circumferential direction are considered,respectively.Basing on the theory of non-Fourier heat conduction,the 2D generalized TED models for micro/nanorings with rectangular cross-section are derived.The results show that the effect of non-Fourier heat conduction affects the TED behaviors of ring resonators significantly.In addition,the one-dimensional(1D)generalized TED models for rings and beams possess a unified form.For 2D cases,TED results depend on the modal order of the ring.The present models developed in this dissertation can provide reasonable predictions of TED in the fundamental MEMS/NEMS resonators including beams,plates and rings with the effect of non-Fourier heat conduction.This work may be useful in the design and optimization of resonators operated in extreme situations.