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The natural vibration of a symmetric cross-ply laminated composite conical-plate shell

机译：对称交叉层压的复合圆锥板壳的固有振动

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摘要

The feasibility of using the transfer matrix method to analyze a composite laminated conical-plate shell is explored theoretically. With the vibration theory and the transfer matrix method combined, the dynamic characteristics of a symmetric cross-ply laminated conical shell with an annular plate at the top end are investigated in detail. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrixes and joining matrix are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth order Runge-Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix and the joining matrix can compose the matrix of entire structure. The frequency equations, mode shape and force vector are formulated in terms of the elements of the structural matrices. The 3D finite element numerical simulation has validated the present formulas of natural frequencies and mode shapes. The conclusions illustrate that this investigation will provide an important foundation for the advanced development of the laminated composite combination shells.
机译：从理论上探讨了采用传递矩阵法分析复合材料叠合锥形板壳的可行性。结合振动理论和传递矩阵法，详细研究了顶端为环形板的对称交叉叠层圆锥壳的动力特性。用矩阵微分方程表示该系统的振动控制方程，并导出系数矩阵和连接矩阵。建立传递矩阵与系数矩阵的关系后，采用四阶Runge-Kutta方法数值求解矩阵方程。一旦获得了单一组分的转移矩阵，每个组分矩阵与连接矩阵的乘积就可以构成整个结构的矩阵。频率方程，模态形状和力矢量是根据结构矩阵的元素来表示的。 3D有限元数值模拟已经验证了自然频率和振型的当前公式。结论表明，该研究将为层合复合壳的进一步开发提供重要的基础。

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