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Geometrically nonlinear forced vibrations of circular cylindrical shells containing flowing fluid

机译:包含流动流体的圆柱壳的几何非线性强迫振动

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The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. Nonlinearities due to moderately large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using the model proposed by Paidoussis and Denise. For different amplitude and frequency of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic resonse of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect fo the flow velocity on the nonlinear periodic response of the system has also been investigated. Poincare maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude-modulated motions, multi-periodic solutions, chaotic responses and the so-called "blue sky catastrophe" phenomenon have been observed for different values of the system parameters; the latter two have been predicted here probably for the first time for the dynamics of circular cylindrical shells.
机译:对于不同的流速,研究了在最低固有频率之一的频谱邻域中,输送流体的壳体对谐波激励的响应。通过使用非线性Donnell浅壳理论,可以考虑由于中等幅度的壳运动引起的非线性。运用线性潜在流理论,利用Paidoussis和Denise提出的模型来描述流固耦合。对于不同的激励幅度和频率以及不同的流速,将对以下内容进行数值研究:(i)系统的周期性共振; (ii)不稳定和随机的运动; (iii)跳转到分支分支而失去稳定性。还研究了流速对系统非线性周期响应的影响。 Poincare映射和分叉图用于研究系统的不稳定和随机动力学。对于不同的系统参数值,已经观察到调幅运动,多周期解,混沌响应和所谓的“蓝天灾难”现象。后两者可能是首次针对圆柱壳的动力学进行了预测。

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