We study the thermal vibration characteristics of graded porous Mindlin circular plates using the differential quadrature method and Hamilton’s principle. It is assumed that the performance of gradient porous materials varies continuously in the whole thickness and the plates have uniform and non-uniform porosity distributions across their thickness. Based on the Hamilton’s principle, the free vibration equation of the axisymmetric graded porous circular plates was derived in terms of the middle surface angles of rotation and lateral displacement. Then, using the DQ method to solve the coupled ordinary differential equations with different boundary conditions, the natural frequencies of graded porous Mindlin circular plates were obtained numerically. The effects of various factors such as porosity distribution pattern, porosity coefficient, temperature rise and boundary conditions on the natural frequencies are discussed.

我们使用微分正交法和汉密尔顿原理研究了分级多孔 Mindlin 圆板的热振动特性。假设梯度多孔材料的性能在整个厚度上连续变化，并且板在其厚度上具有均匀和不均匀的孔隙率分布。基于哈密顿原理，推导出轴对称梯度多孔圆板的自由振动方程，由中面旋转角和侧向位移角决定。然后，利用DQ方法求解具有不同边界条件的耦合常微分方程，数值获得了梯度多孔Mindlin圆板的固有频率。孔隙度分布模式、孔隙度系数、