基于谱方法分析有阻尼负载圆柱壳频散特性

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (6) : 13-17.

论文

基于谱方法分析有阻尼负载圆柱壳频散特性

以Chebyshev多项式系为基函数，采用谱方法离散弹性理论的波动方程，建立对应的广义特征值问题。依据壳体结构波运动、内部流体及外部阻尼材料在界面处的位移、应力连续条件，构造此复杂圆柱壳系统广义特征值方程。通过数值求解特征值获得对应频率下波数，进而获得圆柱壳结构的频散曲线。分别讨论充水与否、有阻尼负载圆柱壳的频散曲线，获得有价值结论。

作者信息 +

Spectral method for dispersion characteristics of cylindrical shell boarded with a damping layer

The wave equation of elastic theory is discretized by spectral method. Then the equation can be converted to a corresponding generalized eigenvalue problem by employing Chebyshev polynomials to be a primary function. After considering the boundary conditions at the fluid-structure interface and damping layer-structure interface, a generalized eigenvalue equation of a complex system can be obtained. The wave numbers for a given frequency are calculated by MATLAB eigenvalue solver. Then modal dispersion in elastic guiding structure can be solved quickly. This paper supplies the dispersion curves of cylindrical shells containing bare, fluid filled and layered. Some valuable conclusion has been given according to the dispersion curves.

Author information +

文章历史 +

摘要

以Chebyshev多项式系为基函数，采用谱方法离散弹性理论的波动方程，建立对应的广义特征值问题。依据壳体结构波运动、内部流体及外部阻尼材料在界面处的位移、应力连续条件，构造此复杂圆柱壳系统广义特征值方程。通过数值求解特征值获得对应频率下波数，进而获得圆柱壳结构的频散曲线。分别讨论充水与否、有阻尼负载圆柱壳的频散曲线，获得有价值结论。

Abstract

The wave equation of elastic theory is discretized by spectral method. Then the equation can be converted to a corresponding generalized eigenvalue problem by employing Chebyshev polynomials to be a primary function. After considering the boundary conditions at the fluid-structure interface and damping layer-structure interface, a generalized eigenvalue equation of a complex system can be obtained. The wave numbers for a given frequency are calculated by MATLAB eigenvalue solver. Then modal dispersion in elastic guiding structure can be solved quickly. This paper supplies the dispersion curves of cylindrical shells containing bare, fluid filled and layered. Some valuable conclusion has been given according to the dispersion curves.

导出引用

王献忠1, 2 吴卫国1,2 庞福振3,孔祥韶1,2. 基于谱方法分析有阻尼负载圆柱壳频散特性[J]. 振动与冲击, 2015, 34(6): 13-17

WANG Xian-zhong1，2 WU Wei-guo1，2 PANG Fu-zhe3，KONG Xiang-shao1,2. Spectral method for dispersion characteristics of cylindrical shell boarded with a damping layer[J]. Journal of Vibration and Shock, 2015, 34(6): 13-17

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