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On the Nonlinear Vibrations of Clamped Oval Shells

机译:夹紧椭圆形壳体的非线性振动

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摘要

In the present study, the nonlinear dynamic response of clamped immovable oval cylindrical shells subjected to radial harmonic excitation in the spectral neighborhood of the free vibration frequency is investigated. The formulation is based on the first order shear deformation theory. Geometric nonlinearity is inducted in the formulation considering moderately large deformation effects employing the Sanders type kinematic relations. Governing equations are discretized in space and time domains, respectively, employing computationally efficient finite-strip method and Newmark time marching scheme. Resulting nonlinear algebraic equations are solved using Newton-Raphson iterative technique. A detailed parametric study is conducted to bring out the influence of ovality parameter on the nonlinear vibration characteristics of different modes of vibrations of isotropic and angle-ply oval shells. For isotropic oval shells, it is observed that moderately oval shells show softening type nonlinearity whereas shells of large ovality show hardening type nonlinearity. The response of oval shells with large ovality reveals different temporal variation near to the semi-major axis region compared to that in the semi-minor axis region.
机译:在本研究中,研究了在自由振动频率的频谱邻域中受到径向谐波激励的固定的椭圆形圆柱壳的非线性动力响应。该公式基于一阶剪切变形理论。考虑到适度的大变形效应,采用桑德斯型运动学关系在公式中引入了几何非线性。使用计算有效的有限条带方法和Newmark时间行进方案,分别在时域和时域离散控制方程。使用牛顿-拉夫森迭代技术求解所得的非线性代数方程。进行了详细的参数研究,以得出椭圆度参数对各向同性和角铺层椭圆壳的不同振动模式的非线性振动特性的影响。对于各向同性的椭圆形壳,可以观察到中等椭圆形的壳表现出软化类型的非线性,而大椭圆形的壳表现出硬化类型的非线性。与半短轴区域相比,具有大椭圆度的椭圆形壳体的响应显示出在半长轴区域附近的时间变化不同。

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