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首页> 外文期刊>International Journal of Solids and Structures >Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1 : 1 : 2 internal resonance
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Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1 : 1 : 2 internal resonance

机译：自由边缘薄球壳的非线性振动：模态相互作用规则和1：1：2内部共振

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This paper is devoted to the derivation and the analysis of vibrations of shallow spherical shell subjected to large amplitude transverse displacement. The analog for thin shallow shells of von Karman's theory for large deflection of plates is used. The validity range of the approximations is assessed by comparing the analytical modal analysis with a numerical solution. The specific case of a free edge is considered. The governing partial differential equations are expanded onto the natural modes of vibration of the shell. The problem is replaced by an infinite set of coupled second-order differential equations with quadratic and cubic non-linear terms. Analytical expressions of the non-linear coefficients are derived and a number of them are found to vanish, as a consequence of the symmetry of revolution of the structure. Then, for all the possible internal resonances, a number of rules are deduced, thus predicting the activation of the energy exchanges between the involved modes. Finally, a specific mode coupling due to a 1:1:2 internal resonance between two companion modes and an axisymmetric mode is studied. (C) 2004 Elsevier Ltd. All rights reserved.
机译：本文致力于大振幅横向位移的浅球形壳体振动的推导和分析。使用了冯·卡曼（von Karman）理论的薄薄壳薄板的大挠度的类似物。通过将分析模态分析与数值解进行比较来评估近似值的有效范围。考虑自由边缘的具体情况。支配的偏微分方程被扩展到壳的固有振动模式。该问题由具有二次和三次非线性项的无穷耦合二阶微分方程组代替。由于结构旋转的对称性，得出了非线性系数的解析表达式，发现其中一些消失了。然后，对于所有可能的内部共振，推导出许多规则，从而预测所涉及模式之间能量交换的激活。最后，研究了由于两个伴生模式与轴对称模式之间的1：1：2内部共振而引起的特定模式耦合。 （C）2004 Elsevier Ltd.保留所有权利。

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