目的 针对功能梯度圆柱壳随机振动响应特性分析问题,提出一种可快速有效计算平稳随机载荷作用下功能梯度圆柱壳振动响应的动力学模型,并探究关键参数对相应结构随机振动特性的影响规律。方法 采用人工弹簧技术模拟功能梯度圆柱壳的任意边界约束,结构位移容许函数采用以简洁三角函数为核心的谱几何法进行表征。在一阶剪切变形理论框架下,引入虚拟激励法建立随机载荷作用下功能梯度圆柱壳能量泛函,进而基于Rayleigh-Ritz法获得功能梯度圆柱壳平稳随机响应分析模型。结果 通过数值算例分析,文中所构建模型计算获得的不同边界条件下圆柱壳功率谱密度响应结果与有限元结果基本一致,且模型预测固有频率与均方值根结果偏差分别在0.5%以及1%以内。分析了梯度指数p、长径比L/R、厚径比h/R等参数对功能梯度圆柱壳随机振动特性的影响规律。结论 文中模型能够高精度、高效率地分析圆柱壳自由振动与平稳随机振动响应特性。同时,通过变参分析发现,梯度指数p和长径比L/R的增加会削弱功能梯度圆柱壳刚度,增大圆柱壳壳体的振动幅值;相反地,厚径比h/R的增大会提高结构刚度,降低圆柱壳壳体的振动幅值。研究可为实际工程中相应结构的动力学设计提供理论参考。
Abstract
The work aims to propose a dynamic model that can quickly and effectively predict the random vibration responses of functionally graded (FG) cylindrical shells under stationary random load, while investigating the influence of key parameters on the random vibration characteristics of the corresponding structures. The artificial spring technology was used to simulate arbitrary boundary constraints of FG cylindrical shells. The displacement admissible functions of cylindrical shells were characterized using the SGM which consisted of concise trigonometric function. Within the framework of the first order shear deformation theory, the PEM was applied to establish the energy functional of FG cylindrical shells under random load. Further, an stationary random response analysis model for FG cylindrical shells was obtained with the Rayleigh-Ritz method. Through several numerical examples analysis, the power spectral density (PSD) response results of cylindrical shells under different boundary conditions calculated by the model constructed in the article were basically consistent with the finite element results. Moreover, the deviation of natural frequencies and RMS values was within 0.5% and 1%, respectively. On this basis, the effect of some parameters, such as gradient exponent p, length-radius ratio L/R and thickness-radius ratio h/R, on the random vibration behavior of FG cylindrical shells was discussed in detail. In conclusion, the model established in the paper can analyze the free vibration and steady random vibration response characteristics of cylindrical shells with high precision and efficiency. Besides, an increase in p and L/R can weaken the stiffness of FG cylindrical shells and improve the vibration amplitude of cylindrical shells; on the contrary, the increasing h/R will enhance the structural stiffness and reduce the vibration amplitude of cylindrical shells. This research may provide theoretical reference for the dynamical design of corresponding structures in practical engineering.
关键词
功能梯度 /
圆柱壳 /
谱几何法 /
任意边界条件 /
随机振动 /
功率谱密度
Key words
functionally graded material /
cylindrical shells /
spectro-geometric method (SGM) /
arbitrary boundary conditions /
random vibration /
power spectral density (PSD)
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基金
国家自然科学基金（52375136）; 中国兵器工业试验测试研究院青年托举基金（QTKT-4-19）
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