Natural frequencies and mode shapes of variable thickness elastic cylindrical shells resting on a Pasternak foundation
Natural frequencies and mode shapes of variable thickness elastic cylindrical shells resting on a Pasternak foundation
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DOI：
10.1177/1077546314528229
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发表时间：
2016-01
影响因子：
2.8
通讯作者：
M. Ahmed
中科院分区：
文献类型：
--
作者：
M. Ahmed
根据fl<s:1> gge壳理论、Winkler和Pasternak基础模型、传递矩阵法和Romberg积分法的框架，研究了变厚度各向同性和正交异性圆柱壳的振动特性。建立了基于帕斯捷尔纳克地基模型的壳体控制方程，并对其进行了求解。该分析是为了克服由壳体变曲率和变厚度引起的模态耦合的数学困难而制定的。将壳体的振动方程在周向坐标系下简化为8个一阶微分方程。利用壳的传递矩阵，这些方程可以写成矩阵微分方程。采用该模型得到了对称振动模态和非对称振动模态的振动频率和相应的振型。研究了频率参数和弯曲变形对温克勒和帕斯捷尔纳克基础模量、厚度比和正交各向异性参数的敏感性。
According to the framework of the Flügge’s shell theory, the Winkler and Pasternak foundations model, the transfer matrix approach and the Romberg integration method, the vibration behavior of an isotropic and orthotropic cylindrical shell with variable thickness is investigated. The governing equations of the shell based on the Pasternak foundation model are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling which comes from the variable curvature and thickness of the shell. The vibration equations of the shell are reduced to eight first order differential equations in the circumferential coordinate. Using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for the symmetrical and antisymmetrical modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the Winkler and Pasternak foundations moduli, the thickness ratio, and the orthotropic parameters are demonstrated.