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首页> 外文期刊>Journal of Fluids and Structures >Reduced-order models for nonlinear vibrations of fluid-filled circular cylindrical shells: Comparison of POD and asymptotic nonlinear normal modes methods
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Reduced-order models for nonlinear vibrations of fluid-filled circular cylindrical shells: Comparison of POD and asymptotic nonlinear normal modes methods

机译：充满流体的圆柱壳非线性振动的降阶模型：POD与渐近非线性法线模式方法的比较

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摘要

The aim of the present paper is to compare two different methods available for reducing the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD), and an asymptotic approximation of the nonlinear normal modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the partial differential equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed. The response is investigated also for a fixed excitation frequency by using the excitation amplitude as bifurcation parameter for a wide range of variation. Bifurcation diagrams of Poincare maps obtained from direct time integration and calculation of the maximum Lyapunov exponent have been used to characterize the system.
机译：本文的目的是比较两种可用于减少薄壳大振幅，几何非线性振动所表现出的复杂动力学的不同方法。这两种方法是：适当的正交分解（POD）和系统的非线性法线模（NNM）的渐近逼近。用于进行比较的结构是一个充满水的简单支撑的圆柱壳，在基本固有频率的频谱邻域中受到谐波激励。通过使用包含16个本征模的Galerkin扩展离散化运动的偏微分方程（PDE），可以获得参考解决方案。 POD模型是通过使用Galerkin模型计算出的响应来构建的。通过使用由Galerkin方法获得的离散运动方程，并考虑阻尼项的转换，建立了NNM模型。 POD和NNM都可以显着减小原始Galerkin模型的尺寸。比较所计算的非线性响应，以验证这两种方法的准确性和局限性。对于等于壳厚度1.5倍的振动幅度，这两种方法与原始Galerkin模型的结果非常接近。通过增加激励和振动幅度，可以观察和讨论明显的差异。通过使用激励幅度作为宽范围变化的分叉参数，还研究了对于固定激励频率的响应。通过直接时间积分和最大Lyapunov指数计算获得的Poincare映射的分叉图已用于表征系统。

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