层合圆锥壳及组合壳的受迫与自由振动特性分析

Analysis of Forced and Free Vibration Characteristics of Laminated Conical Shells and Combined Shell Structures

  • 摘要: 为研究层合圆锥壳及其组合壳结构的振动特性,本文基于层合薄壳理论,采用谱元法推导了复合材料层合圆锥壳的基本动刚度矩阵,并利用单个圆锥壳的边界条件和锥顶角变化拼接构建了组合壳体结构的动力学模型。通过与有限元计算的固有频率与振动响应对比,验证了本文计算方法和层合圆锥壳动力学模型的正确性。本文分析了圆锥壳两端任意弹性刚度边界、层合铺设角度、铺设层数以及圆锥壳锥顶角等参数对层合圆锥壳振动特性的影响。研究发现铺设角度与弹性边界对固有频率存在影响;锥顶角越大,共振峰向低频移动。本文的研究结果可为层合圆锥壳及其组合壳结构的参数化设计和振动计算提供有效的分析工具。

     

    Abstract: This study presents a comprehensive investigation into the vibration characteristics of composite laminated conical shells and combined structures through the integration of laminated thin shell theory and spectral element method. The dynamic model of the combined shell structure is constructed by combining the boundary conditions of individual conical shells and the variation of semi-vertex angles. A novel vibration analysis methodology is formulated, establishing the dynamic stiffness matrix for multi-layered conical shell structures. The validity of both the computational framework and dynamic modeling approach has been rigorously verified through comparative analyses of natural frequencies and vibration responses against finite element method (FEM) simulations, demonstrating excellent agreement. The systematic parametric investigation examines critical factors influencing vibrational behavior, including: elastic boundary constraints at shell extremities, ply orientation angles, number of laying layers and semi-vertex angle configuration. Key findings reveal that ply orientation and boundary stiffness significantly influence natural frequency spectra. Semi-vertex angle variation demonstrates frequency-dependent effects, where increased semi-vertex angles induce progressive downward shifts in resonance peaks toward lower frequency ranges. The developed methodology offers valuable analytical tools for vibration prediction and parametric optimization in laminated conical shell and combined shell structures design. This research particularly contributes to the accurate modeling of complex boundary conditions and anisotropic material effects in composite shell structures, providing essential insights for aerospace, mechanical, and civil engineering applications requiring precision vibration control.

     

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