Three-dimensional vibration analysis of paraboloidal shells
Three-dimensional vibration analysis of paraboloidal shells
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DOI：
10.1299/jsmec.45.2
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发表时间：
2002-03-01
期刊：
影响因子：
--
通讯作者：
Kang, JH
中科院分区：
文献类型：
--
作者：
Leissa, AW;Kang, JH
本文提出了一种确定任意厚度开口抛物面旋转壳自振频率和振型的分析方法。与数学上二维（2-D）的传统壳理论不同，本方法基于3-D动态弹性方程。壳体的端部以及内弯曲表面和外弯曲表面可以是自由的，或者可以受到任何程度的约束。变形的应变能，以及运动的动能，制定在三个位移分量，这是切线或垂直于壳的中表面。位移在周向坐标和时间上被视为周期性的，在另外两个坐标上被视为任意次数的多项式，并且使用Ritz方法来制定特征值问题。收敛性研究，并给出频率为中等厚度和厚，中等深度和深度，抛物面壳均匀和可变厚度。
A method of analysis is presented for determining the free vibration frequencies and mode shapes of open paraboloidal shells of revolution having arbitrary thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell, as well as the inner and outer curved surfaces, may be free or may be subjected to any degree of constraint. The strain energy of deformation, as well as the kinetic energy of motion, are formulated in terms of three displacement components which are tangent or normal to the shell middle surface. The displacements are taken as periodic in the circumferential coordinate and in time, and as polynomials of arbitrary degree in the other two coordinates, and the Ritz method is used to formulate the eigenvalue problem. Convergence studies are presented, and frequencies are given for moderately thick and thick, moderately deep and deep, paraboloidal shells of uniform and variable thickness.