中文摘要：

为研究考虑面内振动时FGM圆板的动态响应,首先基于经典板理论,同时考虑横向振动和面内振动,并利用Hamilton原理推导出轴对称情况下功能梯度材料圆薄板线性自由振动的控制方程。采用打靶法对无量纲控制方程进行数值求解,并将方程退化为一般均质板,求解其固有频率,得到了与相关文献非常接近的结果。对具体问题的数值结果进行对比分析,结果表明,面内振动会影响FGM圆板振动频率大小,忽略面内振动的影响会过高估计FGM板的频率。

英文摘要：

In order to study the dynamic response of FGM circular plate considering in-plane vibration, based on the classical plate theory, and considering the transverse vibration and in-plane vibration, using Hamilton principle,the governing equation of linear free vibration of functional gradient material circular thin plates under axisymmetric condition was derived.The dimensionless governing equation was solved numerically by shooting method,and the equation was degenerated into a general homogeneous plate.The natural frequency was obtained,and the results were very close to the related literatures.The numerical results for specific problems were compared and analyzed.The results showed that the in-plane vibration would affect the vibration frequency of the FGM circular plate, and ignoring the influence of in-plane vibration would overestimate the frequency of FGM plate.