Investigation On Thermoelastic Damping In Functionally Graded Material Micro Circular Plate

Because of their high sensitivity and fast response speed,the micro-scale resonators are widely used as sensors,actuators and modulators in micro-scale mechanical systems(MEMS).There are inevitably a variety of energy dissipations in the MEMS,in addition to external damping,such as air damping and support damping,there also exists internal damping,named thermoelastic damping(TED).TED cannot be eliminated by improving the external conditions,and then it will become the main energy dissipation form in the MEMS.In recent years,functionally graded material(FGM)resonators have been applied in the MEMS.And the mechanical models of many resonators can be simplified as thin plates.So it is an important research direction to study the TED of functionally graded micro plate resonators in the thermoelastic coupling dynamics of microstructures.In this paper,characteristics of TED in FGM micro circular plates under the free vibration were studied,the main contents and results of this study are as follows:1.Based on the classical plate theory,the differential equations in terms of the displacements governing the free vibration of the thin FGM micro circular plate including thermoelastic coupling effects are derived.Then based on the classical heat conduction theory,ignoring the in-plane variation of the temperature gradient,one dimensional and one-way coupled heat conduction equation with variable coefficients is established.By assuming the harmonic vibration,the time variable and the in-plane displacements are eliminated.Then,the equations of motion containing thermal membrane force and thermal bending moment are finally reduced one differential equation including the complex natural frequency parameter in terms of the amplitude of the lateral displacement.2.For the two cases of axisymmetric and non-axisymmetric free vibration,by using the layer wise homogenization approach,the heat conduction equation of the FGM micro plate with variable coefficients is transformed into a series of differential equations with constant coefficients defined on each layer.Analytical solutions of the temperature change field in the FGM circular plates are obtained by using the boundary conditions at the top and the bottom surfaces and continuity conditions at the interfaces.By substituting the temperature rise field into governing equation of structural vibration of the plate,the complex frequency containing TED is obtained,and then the inverse quality factor representing level of TED is extracted.3.Finally,by giving the ceramic-metal FGM micro circular plate with material properties varying along the plate thickness of the power functions,effects of the material gradient index,geometric size,the boundary conditions,vibration modal orders and temperature environment on the TED are analyzed quantitatively in detail.The numerical results show that,the change of modal orders and boundary conditions have no effect on the maximum value of TED,but the increase of vibration mode order and the enhance of the constraint stiffness will decrease the critical thickness;when the thickness is large,with the increase of volume fraction of metal,the maximum value of TED and critical thickness increase monotonically;while the plate thickness is less than a certain value,the minimum value of TED can be obtained by adjusting the material gradient index,and the minimum value is even less than the TED of the pure ceramic micro circular plate;with the environment temperature increasing,TED will increase as a whole,and the corresponding critical thickness will decrease slowly.