Shi Dongyan, He Dongze, Wang Qingshan, Ma Chunlong, Shu Haisheng
College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China.
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China.
Materials (Basel). 2020 Feb 17;13(4):884. doi: 10.3390/ma13040884.
A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton's principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants.
采用一种半解析方法来分析具有任意经典和弹性边界条件的中等厚度复合材料层合圆柱壳的自由振动特性。通过哈密顿原理和一阶剪切变形理论，可以建立复合材料壳的控制方程。将位移变量转换为波函数形式以确保控制方程的正确性。基于位移变量与内力之间的动力学关系，建立了与任意边界条件相关的最终方程。采用二分法计算复合材料壳的固有频率。为了验证本方法的正确性，将本方法的结果与具有各种边界条件的文献中的结果进行了比较。此外，还计算了一些数值例子来研究几个参数对复合材料壳的影响，如长径比、厚径比和弹性约束常数。
