| Resonators are widely used in micro/nano mechanical systems(MEMS/NMES)such as accelerometers,gyroscopes,sensors,actuators,etc.,which makes the quality of the resonator a critical factor in the high quality operation of these devices.Thermoelastic damping(TED)is the internal energy dissipation mechanism of MEMS/NMES and cannot be eliminated by the improvement of external environmental conditions.However,most of the existing work is on the TED of homogenous material resonators,and there is a lack of quantitative analysis of the TED of functionally graded material(FGM)micro-beam/micro-plate resonators.Therefore,based on Mindlin plate theory and one-way coupled heat conduction theory,the analytical and numerical methods are used to quantitatively analyze the TED of FGM micro/nano plates with continuous changes in material properties along the thickness.The thermoelastic coupling energy dissipation mechanism of a non-homogenous material resonator.Research work mainly includes:1.Based on the Mindlin plate theory,considering the first-order shear deformation and thermo-elastic coupling effect,the differential equation of the laterally free vibration of the functional gradient micro/nano-plate is established.Based on the theory of heat conduction in one way coupling,the variation of the temperature gradient in the plate is neglected,and a quasi-1D heat conduction equation of one-way thermoelastic coupling is established,in which the coefficients are a function of the lateral coordinate.Using layer-wise homogenization approach,the heat transfer equation with variable coefficients is transformed into a series of constant coefficient differential equations defined in each layer.Using the adiabatic boundary conditions of the upper and lower surfaces and the continuity conditions between the layers,the analytical solution of the temperature field of the functionally graded material microplate is obtained by the recursive solution method.The temperature field is substituted into the vibration differential equation,and the complex frequency of the FGM Mindlin micro/nano-plate is obtained by the mathematical similarity between the eigenvalue problems of free vibration of FGM Mindlin plate and the homogenous Kirchhoff plate.The analytical solution of inverse quality factor which represents the TED is obtained2.Selecting a FGM rectangular micro/nano-plate made of metal-ceramic(nickel-silicon nitride,aluminum-silicon carbide),considering the material properties along the plate thickness according to the power function and the exponential function,two gradient variations are given.The numerical solutions of TED under different geometric parameters,material parameters and vibration modes are analyzed.The effects of material property gradient index,plate thickness,width-thickness ratio and vibration mode order on TED are analyzed in detail.And compared with the results of classical plate theory,the influence of shear deformation on TED is analyzed.The results show that:(1)The TED obtained by the classical plate theory is always greater than that of the Mindlin plate for the width-to-thickness ratio of a given plate.However,as the aspect ratio increases,the values obtained by the two theories are closer.(2)The vibration mode order has no effect on the maximum value of the thermoelastic damping,but the higher the modal order,the smaller the corresponding critical thickness(the thickness corresponding to the maximum value of the thermoelastic damping);(3)For the given plate geometric dimensions,the maximum values of TED by using the classical theory and Mindlin theory are different,but the corresponding critical thicknesses are the same. |
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