基于Rayleigh-Ritz法的含T型环肋及舱壁圆柱壳自振特性研究

Rayleigh−Ritz method for free vibration characteristics of cylindrical shell with T-sectione rings and bulkheads

  • 摘要:
    目的 旨在基于Rayleigh-Ritz法研究不同边界条件下含T型环肋及舱壁圆柱壳自由振动特性。
    方法 根据经典的Love壳体和薄板理论,建立圆柱壳以及舱壁的数学物理模型。采用欧拉−伯努利梁理论,将T型环肋视为离散单元,通过其截面形心与壳体中面位移转角的关系,经坐标转换后建立其数学模型。选取改进傅里叶级数作为位移惩罚函数,统一圆柱壳−板−T型环肋的位移表达形式。引入惩罚函数,改变相应的弹簧刚度模拟舱壁柱壳间的连续条件及两端的边界条件。通过能量泛函得到耦合结构振动控制方程。
    结果 通过与数值方法结果的对比,验证了所提方法的收敛性、准确性和可靠性。
    结论 研究表明,T型环肋及舱壁数量、位置与耦合结构的自由振动特性关系密切,本文工作可对舰船工程设计及应用提供参考。

     

    Abstract:
    Objectives This paper seeks to study the free vibration characteristics of a cylindrical shell with T-shape ring stiffeners and bulkheads under different boundary conditions based on the Rayleigh−Ritz method.
    Methods The classical Kirchhoff−Love shell theory and thin plate theory are used to establish a mathematical and physical model of the cylindrical shell and bulkheads. Using the Euler−Bernoulli beam theory, the T-shape ring stiffeners is regarded as a discrete element and the mathematical model is established by coordinate transformation through the relationship between its cross-section centroid and the displacement angle of the mid-surface of the shell. Modified Fourier series are selected as displacement penalty functions to integrate the displacement expression of the cylinder, plate, and T-shape ring stiffeners. The penalty functions are introduced to change the spring stiffness to simulate the continuous conditions between the bulkhead shells and the boundary conditions at both ends. The governing equations for the vibration of the coupled structure are obtained by means of energy functions.
    Results The convergence, accuracy, and reliability of the proposed method are verified through a comparison with the numerical method results.
    Conclusion This paper shows that the number and position of the T-shape ring stiffeners and bulkheads are closely related to the natural vibration characteristics of the coupled structure, providing certain references for engineering design and applications.

     

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