Investigation On Thermoelastic Damping Of Functionally Graded Material Micro/Nano-Plate Based On Levinson's High-order Shear Deformation Theory

Thermoelastic damping(TED)as an internal energy dissipation mechanism,when the resonators are in the micro/nano scales,it will become the main energy dissipation of Micro/Nano-Electro-Mechanical Systems(MEMS/NEMS),and cannot be reduced by improving the external conditions.Functionally graded materials(FGM)are a new kind of non-uniform composite materials in which the volume fraction of the material constituents can change continuously in a specified direction.Since FGM have better material properties than homogeneous materials,FGM resonators will get more and more practical applications in MEMS/NEMS.Most of the mechanical analysis models of micro/nano resonators can be simplified to beams or plates.Therefore,accurate analysis and evaluation of the thermoelastic damping of functionally graded material resonators is of great significance to reveal the energy dissipation mechanism and quality factor optimization design of non-uniform material resonators.In this paper,based on Levinson's high-order shear deformation plate theory and one-way coupled heat conduction theory,both analytical and numerical methods are used to study the TED of FGM rectangular micro/nano plates under simply supported boundary conditions at the four edges.The research content in this thesis mainly includes:1.Based on the Levinson plate theory,considering the thermo-elastic coupling effect,stretching-bending coupling effect and high-order shear deformation,the governing differential equations of FGM micro/nano plates in laterally free vibration are established.Ignoring the in-plane variation of the temperature gradient,the one-way coupled heat conduction equation of the FGM micro/nano plate unidirectional coupling is derived.Due to the non-uniformity of material properties in the thickness direction,the heat conduction equation is a second-order partial differential equation with variable coefficients.Using the layer-wise homogenization method,the differential equations with variable coefficients are simplified to 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 at the interfaces,the analytical solution of the temperature field of the FGM plate is obtained.Substituting the obtained temperature field into the structural vibration equation expressed only by the deflection function,and using the similarity of the boundary value problem of the differential equation with simply supported boundary conditions,the complex natural frequency of the FGM Levinson plate is expressed by the natural frequency of the undamped homogenous Kirchhoff plate.Finally,a semi-analytical solution of the inverse quality factor representing thermoelastic damping is obtained by the complex frequency method2.We select FGM rectangular micro/nano plates composed by the constituents of silicon nitride(Si3N4)-nickel(Ni)and silicon carbide(SiC)-aluminum(Al)with the material properties to be varied continuously according to the power function and the exponential function along the thickness direction of the plate,respectively,numerical results of TED depending on the material parameters,geometric parameters,and vibration modes are presented in the tables and figures The influences of material gradient,geometry and vibration modes on TED are analyzed in detail The results show that:(1)The TED of Levinson plate theory is smaller than that of classic plate theory,and the difference between the two theories increases significantly as the aspect ratio(a/h)is small.The results show that the classical plate theory overestimates the TED;(2)The maximum of TED of Levinson plate is smaller than that of Kirchhoff plate,however,the critical thicknesses corresponding to the maximum TED evaluated by the two theories are the same.(3)The maximum values of TED for different vibration modes keep the same,but the corresponding critical thickness will decrease with the increase of the mode order;(4)Generally,as the constituent of metal increases,the TED of the micro/nano plates increases,however,for an very thin plate,the TED of the FGM plate will reach a minimum value(silicon nitride-nickel FGM)or a maximum value(silicon carbide-aluminum FGM)at some specific values of the gradient index.3.The novelty of this paper is that TED of FGM micro/nano rectangular plates is first studied based on the high-order shear deformation plate theory.By using the layer-wise homogenization approach,analytical solution of the quasi-one dimensional and one-way coupled heat conduction equation is obtained.The effect of shear deformation on the predicted value of TED is quantitatively analyzed.The research results have theoretical significance for further understanding the energy dissipation mechanism of the non-homogenous material resonators,and have reference value for the research and design of new high-quality resonators.