Abstract

In this article, the free vibration behavior of functionally graded circular Levinson plates is investigated. Hamilton’s principle is adopted to derive the governing equation of the system, which effectively takes into account the effects of both thermal stress and physically neutral surfaces. With the devised formulation, three typical temperature distributions and temperature-dependent (TD) features are studied. The natural frequencies of the corresponding functionally graded plates can be computed through the use of the differential quadrature method. Hence the impacts due to temperature fields, volume fraction index, TD characteristics, and thickness-to-radius ratio on the natural frequency of functionally graded circular plates can be quantitatively analyzed.

摘要

在本文中，研究了功能梯度圆形莱文森板的自由振动行为。采用汉密尔顿原理推导了系统的控制方程，有效地考虑了热应力和物理中性表面的影响。通过设计的公式，研究了三种典型的温度分布和温度相关（TD）特征。相应的功能梯度板的固有频率可以通过使用微分求积法来计算。因此，可以定量分析温度场、体积分数指数、TD特性和厚径比对功能梯度圆板固有频率的影响。