ANLYTICAL SOLUTION OF THERMOELASTIC DAMPING IN RECTANGULAR MINDLIN MICRO PLATES

Abstract

Analytical solution of thermoelastic damping for rectangular Mindlin micro plate with the four edges simply supported is presented for the first time. Based on the Mindlin plate theory and the one-way coupled heat conduct theory, governing differential equations for thermo-elastically coupled free vibration of the micro plate are formulated. Ignoring the in-plane variation of the temperature gradient, analytical solution of temperature field in terms of the kinematic parameters is obtained under the adiabatic boundary conditions at the top and bottom surfaces. Furthermore, the equations of structural vibration including the thermal bending moment are transformed into a fourth-order partial differential equation only in terms of the deflection. By using the mathematical similarity between the eigenvalue problems under the simply supported boundary conditions, analytical solution of the complex natural frequency of the Mindlin plate is expressed in terms of the frequency of isothermal Kirchhoff plate. Then the inverse quality factor which represents the level of the thermoelastic damping is obtained. Finally, the effects of the shear deformation, the material and the geometry parameters on the thermoelastic damping are examined in detail by the numerical results. The numerical results show that thermoelastic damping estimated by Mindlin plate theory is less than that by Kirchhoff plate theory. The difference between the values evaluated by the two plate theories becomes very significant near the critical thickness. Moreover, along with the increase of the side-to-thickness aspect ratio,the maximum of the thermoelastic damping in micro Mindlin plate increase monotonically, however, that of micro Kirchhoff plate keeps constant.