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| 双参数地基上功能梯度多孔双曲浅壳随机振动分析 |
| Stochastic Vibration Analysis of Functionally Graded Porous Doubly-Curved Shallow Shells Resting on Two-Parameter Elastic Foundations |
| 投稿时间：2025-05-29 修订日期：2025-07-18 |
| DOI： |
| 中文关键词: 功能梯度多孔材料 双曲浅壳 随机振动 切比雪夫谱方法 双参数地基 |
| 英文关键词:Functionally graded porous materials double curved shell stochastic vibration Chebyshev spectrum method Two-parameter foundation |
| 基金项目:国家自然科学基金面上项目(52075554) |
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| 中文摘要: |
| 本文提出了一种双参数地基功能梯度多孔(FGP)双曲浅壳随机响应分析模型。该模型基于一阶剪切变形理论,结合切比雪夫谱方法与虚拟激励法(PEM),实现了双参数地基以及弹性边界条件下结构随机振动的统一求解。首先建立了统一双曲浅壳动力学控制方程与能量泛函,并推导了双参数地基的能量表达式。基于罚函数法整合各子系统能量,构建了系统的整体能量泛函。通过切比雪夫谱方法构造位移容许函数,采用瑞利-里兹法求解获得结构振动特征方程。在此基础上,采用虚拟激励法分析平稳随机激励下的系统响应问题。通过与现有文献数据和有限元数值模拟结果的对比分析,验证了所提出模型的准确性和可靠性。参数化研究进一步揭示了地基弹性模量、地基剪切模量、FGP材料孔隙率、孔隙分布形式和曲率参数对双曲浅壳随机振动响应的影响,为工程结构设计提供了理论依据。 |
| 英文摘要: |
| This paper proposes a stochastic response analysis model for functionally graded porous (FGP) double curved shallow shells resting on two-parameter elastic foundation. The developed model, based on the first-order shear deformation theory, integrates the Chebyshev spectral method with the pseudo-excitation method (PEM), enabling a unified solution for structural random vibration under two-parameter foundation and elastic boundary conditions. The study initially establishes a unified set of dynamic governing equations and energy functionals for double curved shallow shells, followed by the derivation of energy expressions for the two-parameter foundation. The total energy functional of the system is constructed by incorporating subsystem energies through the penalty function method. Displacement admissible functions are formulated using the Chebyshev spectral method, and the structural vibration characteristic equation is obtained through the Rayleigh-Ritz method. Subsequently, the PEM is employed to analyze the system response under stationary random excitation. The accuracy and reliability of the proposed model are validated through comparative analyses with existing literature data and finite element numerical simulations. Parametric studies further elucidate the influence of foundation elastic modulus, shear modulus, FGP material porosity, pore distribution patterns, and curvature parameters on the stochastic vibration response of double curved shallow shells, providing theoretical foundations for engineering structural design. |
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