各向异性矩形板和环扇形板横向自由振动的一种通用解法

A Generalized Solution Procedure for Free Transverse Vibration of Anisotropic Rectangular Plates and Annular Sectorial Plates

提出各向异性矩形板和环扇形板在弹性边界约束下横向自由振动的通用解法.对于各向异性环扇形板,引入径向对数坐标简化其基本理论.两种不同形状板的几何参数和势能可建立统一的表达式,基于改进Fourier级数和Hamilton原理,从而实现板自由振动问题的统一求解.两种形状板自由振动问题的通用解法具有广泛适用性、高精度和高效性.其收敛性和精度得益于位移的改进Fourier级数的表达,可消除初始横向位移函数及其导数在整个区域内的潜在不连续.所提方法的这些特征通过若干数值算例得到验证.

Anisotropic plates are widely applied in many engineering fields.A generalized solution procedure is presented for free transverse vibration of anisotropic rectangular plates and annular sectorial plates with elastic boundary conditions.For an anisotropic annular sectorial plate,the basic theory is simplified through the introduction of a logarithmic radial coordinate.Unified expressions for the geometric parameters and potential energy of the two different shapes are established.Based on the improved Fourier series and Hamilton principle,ageneralized solution procedure is realized.This generalized solution approach for free transverse vibration of rectangular plates and annular sectorial plates has the advantages of generality,good precision and efficiency.It is found that good convergence and precision of the presented method are attributed to the improved Fourier series of the displacement function,which can eliminate the potential discontinuity of the deflection function and its derivatives.These features of the generalized method are demonstrated by a few numerical examples.The generalized method can be further applied to the bending problems of plates with regular shapes.