任意边界条件下环扇形板的静动态特性分析

Static and Dynamic Characteristics Analysis of Annular Sector Plates with General Boundary Conditions

采用改进傅里叶级数方法(Improved Fourier Series Method,IFSM)对环扇形薄板的静动态特性进行计算分析。位移函数被表示为一个包含正弦与余弦的二维改进傅里叶级数,通过引入正弦项有效地解决了边界上可能存在的不连续或跳跃现象;基于能量原理建立了环扇形薄板的计算模型,利用IFSM方法推导了环扇形板结构的质量矩阵和刚度矩阵,通过求解标准特征值问题得到未知傅里叶展开系数,从而求得环扇形板结构的静动态特性。通过数值分析计算验证了方法的正确性和可靠性。

In this investigation, an Improved Fourier Series Method（IFSM）/s employed to analyze the static and dynamic cha- racteristic of annular sector plates with general boundary conditions. Firstly, the displacement function is expressed as a modified two -dimensional fourier series containing sine and cosine function. It is capable of dealing with the possible discontinuities （or jump） at boundary edges. Then, the analysis model of annular sector plate is constructed based on energy method. The mass and stiffness matrix of annular sector plate are derived with IFSM method. So the eigenvalues and eigenvectors cart be obtained easily with solution of a standard matrix eigenvalue equation. Finally, the unknown fourier coefficients are also determined. The static and dynamic characteristics of annular sector plate are determined with the＂ displacement expression. The accuracy and reliability of the current method are illustrated through＇all the numerical examples.