Vibration analysis of ring-stiffened conical–cylindrical–spherical shells based on a modified variational approach
Vibration analysis of ring-stiffened conical–cylindrical–spherical shells based on a modified variational approach
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DOI：
10.1016/j.ijmecsci.2013.01.026
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发表时间：
2013-04
影响因子：
7.3
通讯作者：
Y. Qu;S. Wu;Yong Chen;H. Hua
中科院分区：
文献类型：
--
作者：
Y. Qu;S. Wu;Yong Chen;H. Hua
本文用改进的变分方法研究了带环肋的圆锥-柱面-球壳组合的自由振动特性。理论模型采用Reissner-Naghdi薄壳理论，并结合加筋壳体组合、壳体构件和壳段的多层划分技术。每个壳段的位移场被表示为沿子午线方向的正交多项式和沿圆周方向的傅立叶级数的乘积。壳体组合中的环肋被视为离散单元。在不同边界条件(如自由、固支和弹性支承边界条件)下，对无加筋和加筋锥柱球壳进行了收敛和对比研究，以验证本方法的可靠性和准确性。为了加深对本研究课题的理解，文中还给出了一些振型。结果表明，该方法具有稳定、快速收敛的特点，计算结果包括固有频率和振型，与有限元分析结果吻合较好。研究了加劲肋的数目和几何尺寸对潜艇耐压船体固有频率的影响。
In this paper, free vibration characteristics of conical–cylindrical–spherical shell combinations with ring stiffeners are investigated by using a modified variational method. Reissner–Naghdi's thin shell theory in conjunction with a multilevel partition technique, viz., stiffened shell combination, shell component and shell segment, is employed to formulate the theoretical model. The displacement fields of each shell segment are expressed as a product of orthogonal polynomials along the meridional direction and Fourier series along the circumferential direction. The ring stiffeners in shell combinations are treated as discrete elements. Convergence and comparison studies for both non-stiffened and stiffened conical–cylindrical–spherical shells with different boundary conditions (e.g., free, clamped and elastic supported boundary conditions) are carried out to verify the reliability and accuracy of the present solutions. Some selected mode shapes are illustrated to enhance the understanding of the research topic. It is found the present method exhibits stable and rapid convergence characteristics, and the present results, including the natural frequencies and the mode shapes, agree closely with those solutions obtained from the finite element analyses. The effects of the number and geometric dimensions of ring stiffeners on the natural frequencies of a submarine pressure hull are also investigated.