Pang Fuzhen, Li Haichao, Jing Fengmei, Du Yuan
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China.
Materials (Basel). 2018 Dec 25;12(1):69. doi: 10.3390/ma12010069.
The paper introduces a semi-analytical approach to analyze free vibration characteristics of stepped functionally graded (FG) paraboloidal shell with general edge conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement components along axial direction are represented by Jacobi polynomials, and the Fourier series are utilized to express displacement components in circumferential direction. Based on penalty method about spring stiffness technique, the general edge conditions of doubly curved paraboloidal shell can be easily simulated. The solutions about doubly curved paraboloidal shell were solved by approach of Rayleigh⁻Ritz. Convergence study about boundary parameters, Jacobi parameters et al. are carried out, respectively. The comparison with published literatures, FEM and experiment results show that the present method has good convergence ability and excellent accuracy.
本文介绍了一种半解析方法，用于分析具有一般边界条件的阶梯功能梯度抛物面壳的自由振动特性。该解析模型基于多段划分策略和一阶剪切变形理论建立。沿轴向的位移分量由雅可比多项式表示，傅里叶级数用于表示圆周方向的位移分量。基于弹簧刚度技术的罚函数法，可以很容易地模拟双曲抛物面壳的一般边界条件。双曲抛物面壳的解通过瑞利-里兹法求解。分别对边界参数、雅可比参数等进行了收敛性研究。与已发表文献、有限元法和实验结果的比较表明，本文方法具有良好的收敛能力和优异的精度。
