Nonlinear Vibrations and Chaos in Floating Roofs
Nonlinear Vibrations and Chaos in Floating Roofs
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DOI：
10.1115/1.4005437
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发表时间：
2012-04
影响因子：
2
通讯作者：
R. Shabani;S. Tariverdilo;H. Salarieh
中科院分区：
文献类型：
--
作者：
R. Shabani;S. Tariverdilo;H. Salarieh
本文用变分原理推导了圆柱形储液罐浮顶在基底简谐激励下的非线性响应。由于浮顶的大挠度，该公式考虑了非线性。推导出的浮顶晃动响应的非线性控制方程具有与Duffing方程类似的三次非线性刚度项。结果表明，占大挠度可以大大减少近共振谐波激励的波高程。评估的非线性模型的响应增加振幅的近共振谐波激励引起的外观的子和超级谐波的响应。以频谱的宽带结构、Poincare映射的分形结构和分岔图为定性判据，以李雅普诺夫指数演化为定量判据，研究了混沌响应的产生.
Variational principle is used to derive the nonlinear response of the floating roof of cylindrical liquid storage tanks due to harmonic base excitations. The formulation accounts for nonlinearity due to large deflections of the floating roof. The derived nonlinear governing equation for the sloshing response of the floating roof has a cubic nonlinear stiffness term similar to the well known Duffing equation. It is shown that accounting for large deflections could substantially reduce the wave elevation for near resonance harmonic excitations. Evaluating the response of the nonlinear model for increasing amplitudes of near resonance harmonic excitations gives rise to the appearance of sub and super harmonics in the response. The broadband structure of the frequency spectrum, the fractal structure of the Poincare maps, and the bifurcation diagram as qualitative criteria and Lyapunov exponent evolution as quantitative criterion are used to investigate the emergence of chaotic response.