弹性基础上正交各向异性圆柱壳的自由振动  

FREE VIBRATION OF THIN-WALLED ORTHOTROPIC CYLINDRICAL SHELL ON ELASTIC FOUNDATION

作　　者：杨永宝[1] 危银涛[1] YANG Yong-bao;WEI Yin-tao(Tsinghua University State Key Laboratory of Automotive Safety and Energy,Beijing 100084)

机构地区：[1]清华大学汽车安全与节能国家重点实验室,北京100084

出　　处：《工程力学》2018年第4期24-32,共9页Engineering Mechanics

摘　　要：该文希望得到正交各向异性圆柱壳在弹性基础暨一般边界条件下自由振动频率的半解析解,以便为这类典型工程结构的参数化分析与设计提供可靠的理论基础。所提方法包含3项关键内容:1)依据Donnell-Mushtari柱壳理论和Hamilton原理,导出了弹性基础上有径向预压力作用的正交各向异性圆柱壳的振动微分方程;2)指出该微分方程存在9种不同组合形式的解,澄清了有关文献中的错误,避免了可能的漏解;3)采用二分法得到了圆柱壳振动频率的解,所提出的方法与经典文献结果对比吻合良好,验证了所提出方法的适用性。将该方法应用于两端支撑弹簧圆柱壳振动频率的参数化分析,发现弹簧刚度和内压力对固有频率的影响都呈现非线性规律。该文所提出的方法适用于一般边界条件下的圆柱壳振动问题,避免漏解,精确可靠,适用性强,为这类工程结构的振动分析提供了可靠的方法。The semi-analytical solutions of the free vibration frequency of orthotropic cylindrical shell under elastic basis and the general boundary condition were obtained in this paper to provide a reliable theoretical basis for the parametric analysis and design of typical engineering structures.The proposed method contains three key parts:1)Differential equations of vibration of cylindrical shells with radial preloading on the elastic foundation were derived based on the Donnell-Mushtari shell theory and Hamilton principle;2)It is pointed out that there are a total of nine different combinations of solutions for the differential equation,which clarifies the errors in the literature and avoids the possible omission of solutions;3)The general solutions of the vibration frequency were obtained by the dichotomy,which were in good agreement with those of classical literature and validated the applicability of the proposed method.It is found that the influence of the spring stiffness and the internal pressure on the natural frequency is non-linear,while the method is applied to parametric analysis of the cylindrical shell with springs supported at both ends.The method developed in this paper is applicable to the vibration of cylindrical shell under general boundary conditions,which is accurate,reliable,can avoid omitted solutions with strong applicability,and provides a reliable method for vibration analysis of such structures.

关 键 词：一般边界条件 自由振动 正交各向异性圆柱壳 Donnell-Mushtari理论 弹性基础 

分 类 号：O343[理学—固体力学] O327[理学—力学]