Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach

The vibration characteristics of a functionally graded material circular cylindrical shell filled with fluid are examined with a wave propagation approach. The shell is filled with an incompressible non-viscous fluid. Axial modal dependence is approximated by exponential functions. A theoretical study of shell vibration frequencies is analyzed for simply supported-simply supported, clamped-simply supported, and clamped-clamped boundary conditions with the fluid effect. The validity and the accuracy of the present method are confirmed by comparing the present results with those available in the literature. Good agreement is observed between the two sets of results.

Free vibration of layered cylindrical shells filled with fluid

The vibration of the layered cylindrical shells filled with a quiescent, incompressible, and inviscid fluid is analyzed. The governing equations of the cylindrical shells are derived by Love＇s approximation. The solutions of the displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of the displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for the frequency parameter and an associated eigenvector of the spline coefficients. Two layered shells with three different types of materials under clamped-clamped （C-C） and simply supported （S-S） boundary conditions are considered. The variations of the frequency parameter with respect to the relative layer thickness, the length-to-radius ratio, the length-to-thickness ratio, and the circumferential node number are analyzed.

Vibration of Three-Layered FGM Cylindrical Shells with Middle Layer of Isotropic Material for Various Boundary Conditions

In the present study, vibration analysis of a three-layered cylindrical shell is performed whose inner and outer layers are composed of functionally graded materials whereas the middle one is assumed to be of isotropic material. This formation of a cylindrical shell influences stiffness modulii and the resultant material properties. The shell problem is formulated from the constitutive relations of stresses and strains with the displacement deformations and they are taken from Love’s thin shell theory. This problem is transformed into the integral form by evaluating the expressions for the strain and kinetic energies of the shell. Rayleigh-Ritz method is employed to solve the shell dynamic equations. Vibration characteristics of these cylindrical shells are investigated for a number of physical parameters and configurations of the fabrication of shells. The axial modal dependence is approximated by the characteristic beam functions that satisfy the boundary conditions. Results evaluated, show good agreement with the open literature.

功能梯度材料圆柱壳的振动特性研究

研究了具有指数型体积分数的功能梯度材料圆柱壳自由振动的固有频率。根据Love薄壳理论,确定功能梯度材料圆柱壳的内力、位移、应变和曲率的关系式;利用Rayleigh-Ritz方法建立了功能梯度材料圆柱壳自由振动固有频率的特征方程,推导出一端固定一端自由、两端简支两种基本边界条件下的固有频率参数表达式。最后通过两类材料组分的算例,分析了材料组分、体积分数、边界条件以及几何尺寸等因素对功能梯度材料圆柱壳的固有频率的影响。研究表明,构成功能梯度材料的材料组分对FG圆柱壳的频率特征有着明显的影响,体积分数所产生的影响则相对有限;而不同边界条件对FG圆柱壳固有频率的影响主要表现在壳体长度与半径比较小和周向波数较小的情况下。

改进傅里叶级数法求解封口锥柱球组合壳的自由振动

提出了一种改进傅里叶级数的半解析方法分析封口锥柱球组合壳的自由振动特性。基于能量泛函,结合经典薄板理论和Love壳体理论,建立了组合结构的理论模型,研究了不同柱壳长度,不同锥球半角以及不同厚度端板下锥柱球组合壳的固有频率。该方法下的各子壳结构位移由标准的傅里叶级数和辅助收敛函数组成,既克服了传统傅里叶级数在子壳结构交接处的不连续性,又提高了计算的收敛精度和速度。研究表明:该方法收敛性较好,所得理论计算结果与有限元结果比较一致。通过分析固有频率,发现改变长度,半角,端板厚度均会对锥柱球组合壳的自由振动产生较明显的影响。

功能梯度材料圆柱壳固有频率解的均匀化表示

本文研究了功能梯度材料(FGM)圆柱壳与相应均匀材料圆柱壳固有频率解之间的相似转化关系。假定FGM圆柱壳材料性质按体积分数幂指数沿厚度方向连续变化,利用梯度材料和均匀材料物理性质和力学行为影响规律,针对不同边界条件,建立FGM圆柱壳固有频率解与参考均匀材料圆柱壳之间解析转换关系,给出计算转换系数公式。将针对FGM圆柱壳固有频率求解简化为具有相同尺寸、边界条件和载荷工况的均匀材料圆柱壳固有频率求解以及这两者之间转换系数计算问题,最终实现FGM圆柱壳宏观力学行为均匀化表示。经算例分析比较,验证了本方法的有效性、正确性与工程应用的便利性。本研究采用简便有效的计算方法求解FGM圆柱壳的振动问题,为非均匀结构力学行为分析提供新的探索途径。