典型边界条件下任意截面纵肋加筋圆柱壳固有特性计算与分析  

Calculation and analysis of inherent properties of stiffened cylindrical shells with longitudinal stiffeners of arbitrary cross section under typical boundary conditions

作　　者：牛宁 孙玲玲[1] 邢泽智 赵国栋 王秀和[2] 吴优优 NIU Ning;SUN Ling-ling;XING Ze-zhi;ZHAO Guo-dong;WANG Xiu-he;WU You-you(Key Laboratory of High Efficiency and Clean Mechanical Manufacture,Ministry of Education,Shandong University,Jinan 250061,China;School of Electrical Engineering,Shandong University,Jinan 250061,China)

机构地区：[1]山东大学高效洁净机械制造教育部重点实验室,山东济南250061 [2]山东大学电气工程学院,山东济南250061

出　　处：《振动工程学报》2023年第1期96-106,共11页Journal of Vibration Engineering

基　　金：国家自然科学基金重点项目(51737008)。

摘　　要：针对纵向加肋圆柱壳自由振动问题,考虑结构边界条件的复杂性和纵肋截面的任意性,在壳体两端引入连续可变的弹性约束,推导任意截面纵肋剪切中心与圆柱壳中面位移协调关系,并利用Gram⁃Schmidt正交法构造的级数表示壳体轴向振型函数。采用Novozhilov壳体理论,计及壳体和纵肋能量泛函中各向平移与转动惯性项贡献,基于Rayleigh⁃Ritz法得到结构自由振动的特征方程表达式,建立纵向加肋圆柱壳自由振动的统一动力学分析模型。调整约束弹簧刚度等效不同边界条件,应用该模型探究了相应边界下肋条附加位置、肋条数量和肋条偏心距对纵向加肋圆柱壳固有频率的影响。研究表明:在一定周向波数范围内,外部加肋和内部加肋圆柱壳固有频率之差的绝对值与周向波数n的变化呈正相关;增加肋条数量会降低内部加肋圆柱壳的固有频率;增大肋条偏心距会降低内部加肋圆柱壳固有频率,且偏心距与肋条数量对固有频率的影响会产生叠加效应。研究结果与验证了所提的统一动力学分析模型的精确性和有效性。Aiming at the problem of free vibration of longitudinal stiffened cylindrical shells,considering the complexity of the boundary conditions of the stringer stiffened cylindrical shell and the arbitrariness of the stringer section,the elastic constraints that can vary continuously were introduced at both ends of the shell and the displacement relationship between the displacement compati⁃bility between the center of a stiffer with arbitrary cross section and the middle surface of a cylindrical shell was deduced,the axial mode shape function of the shell was constructed by Gram-Schmidt orthogonal method.Based on the Novozhilov shell theory,tak⁃ing into account the contribution of the each translational and rotational inertia terms in the energy functional of shell and stringer,a unified dynamic analysis model for free vibration of stringer stiffened cylindrical shell was established by the Rayleigh-Ritz method.The accuracy of the results was verified by literature model.The stiffness of restrained spring was adjusted to simulate different boundary conditions,and the model is used to explore the influence of the additional position of the ribs,the number of ribs and the rib eccentricity on the natural frequency of the longitudinally ribbed cylindrical shell under the corresponding boundary.Studies have shown that within a certain range of circumferential wavenumbers:the absolute value of the difference between the natural frequen⁃cy of the external ribbed and the internally ribbed cylindrical shell is positively correlated with the change of the circumferential wavenumber n;increasing the number of ribs reduces the natural frequency of the internally ribbed cylindrical shell Increasing the eccentricity of the ribs reduces the natural frequency of the internally ribbed cylindrical shell,and the effect of the eccentricity and the number of ribs on the natural frequency produces a superposition effect.The comparison between the research results and the lit⁃erature verifies the accuracy and validity of the unifie

关 键 词：自由振动 圆柱壳 典型边界条件 任意非对称截面 Gram⁃Schmidt正交法 Rayleigh⁃Ritz法 

分 类 号：O326[理学—一般力学与力学基础]