正交各向异性矩形薄板振动的一种半解析方法

Semi-analytical approach for the vibration analysis of orthotropic thin rectangular plates

使用半解析的多项康氏法分析对边简支、对边固定和对边固定-简支的正交各向异性矩形薄板振动问题。选择多个梁特征函数作为试函数,精确满足对边所有边界条件。通过Gakerkin积分将偏微分振动方程转化为常微分方程组并整理为状态方程形式。强迫满足另一对边的边界条件,获得频率方程,确定固有频率。文献结果比较不仅证实了该方法的有效性,而且揭示通过该方法获得的对边简支板的解是精确解。最后,研究了不同长宽比下试函数项数对无量纲固有频率的影响。

The semi-analytical multi-term Kantorovich method（ MTKM） was adopted for the vibration analysis of orthotropic thin rectangular plates with two opposite edges both simply-supported,both clamped and one clamped the other simply-supported. Multiple beam characteristic functions were used as trial functions,which can satisfy the boundary conditions on two opposite edges exactly. With the Galerkin integral,the partial differential equation of motion was turned into several ordinary differential equations,which were then rewritten in the form of a space-state equation. Being enforced to satisfy the boundary conditions on the other two opposite edges,the transcendent frequency equation was derived and the non-dimensional frequencies were determined. Good agreements are shown between the present results and those from the references. It is revealed that the results from present method are exact for thin plates with two opposite edges both simply-supported. Moreover,the effect of the term number of trail functions on the non-dimensional frequencies under different aspect ratios was also investigated.