The wave equation of the elastic theory was discretized with the spectral method.Then,the equation was converted to a corresponding generalized eigenvalue problem by taking Chebyshev polynomials as base functions. Considering the boundary conditions at fluid-structure interface and damping layer-structure interface of a cylindrical shell structure,a generalized eigenvalue equation of this complex cylindrical shell system was built.The wave numbers for a given frequency were calculated with MATLAB eigenvalue solver.Then the dispersion curve of the cylindrical shell was gained.The dispersion curves of the cylindrical shell with a damping layer and water filled or not were discussed.Some valuable conclusions were obtained according to the dispersion curves.%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。
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