轴对称自由振动功能梯度材料微圆板中的热弹性阻尼

基于经典弹性薄板理论和单向耦合热传导理论，研究了材料性质沿厚度连续变化的功能梯度微圆板的热弹性阻尼特性．首先，考虑热力耦合效应,建立了功能梯度微圆板轴对称横向自由振动微分方程．然后，忽略温度梯度在面内的变化，建立了单向耦合变系数一维热传导方程．采用分层均匀化近似方法，将变系数热传导方程转化为一系列常系数的微分方程，利用上下表面的热边界条件和层间连续性条件获得了微圆板温度场解析解．将所得温度场代入微圆板的自由振动微分方程，得到了包含热弹性阻尼的复频率，从而获得了反映热弹性阻尼水平的逆品质因子．最后，针对材料性质沿板厚按幂函数变化的陶瓷-金属功能梯度微圆板，定量地分析材料梯度指数、几何尺寸、边界条件、温度环境等对微圆板热弹性阻尼的影响．

Thermoelastic Damping in Functionally Graded Material Micro Circular Plates Vibrating Axisymmetrically

Based on the classical plate theory and the one-way coupled heat conduction theory, the characteristics of thermoelastic damping (TED) in the functionally graded material (FGM) micro circular plates with material properties varying continuously along the thickness direction were studied. Firstly, differential equations governing the axisymmetric out-of-plane free vibration of the thin FGM micro plates considering the thermoelastic coupling effects were established. Secondly, by ignoring the in-plane variation of the temperature gradient, the one-dimensional one-way coupled heat conduction equation with variable coefficients was established. Then, by using the layer homogenization approach, the heat conduction equation with variable coefficients was transformed into a number of differential equations with constant coefficients. Analytical solutions of the temperature field in the FGM circular plates were obtained by using the boundary conditions at the top and bottom surfaces and the continuity conditions at the interfaces. Substituting the temperature field into the structural vibration equation, the complex frequency including TED was obtained, and thereby the inverse quality factor representing the level of TED was extracted. Finally, the ceramic-metal FGM micro circular plate with the given material properties varying as power-law functions was investigated. Effects of the material gradient, geometric size, the boundary conditions and temperature environment on TED were analyzed quantitatively.