Li Zhen, Hu Shuangwei, Zhong Rui, Qin Bin, Zhao Xing
College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China.
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China.
Materials (Basel). 2022 Sep 5;15(17):6177. doi: 10.3390/ma15176177.
This paper provides a numerical solution to the vibration of a rotating cross-ply laminated combined conical-cylindrical shell in the thermal environment. Its numerical discrete solution method uses the meshless method. The combined shell assumed the temperature independence of material property is divided to the fundamental conical and cylindrical shell substructures, and the theoretical formulation for each substructure is derived based on the first order shear deformation theory (FSDT) and Hamilton's principle. The effects of the initial hoop tension and temperature change are considered through the kinetic energy reflecting the effects of centrifugal and Coriolis forces and additional strain energy by the nonlinear part of the Green-Lagrange strains. The substructures are then assembled according to the continuity conditions. The boundary and continuity conditions are simulated by introducing artificial virtual spring technology. The displacement component in the theoretical formulation is approximated using a meshless Chebyshev-RPIM shape function. The reliability of the method is verified by comparing with mature and reliable results. The free vibration characteristics of the rotating combined conical-cylindrical shell structure under various sizes, speeds and temperatures are given by numerical examples.
本文给出了热环境下旋转正交铺设层合组合圆锥 - 圆柱壳振动的数值解。其数值离散求解方法采用无网格法。假定材料属性与温度无关的组合壳被划分为基本圆锥壳和圆柱壳子结构，并基于一阶剪切变形理论（FSDT）和哈密顿原理推导了每个子结构的理论公式。通过反映离心力和科里奥利力效应的动能以及格林 - 拉格朗日应变非线性部分产生的附加应变能来考虑初始环向张力和温度变化的影响。然后根据连续性条件对子结构进行组装。通过引入人工虚拟弹簧技术模拟边界条件和连续性条件。理论公式中的位移分量采用无网格切比雪夫 - 再生核质点法（RPIM）形函数进行近似。通过与成熟可靠的结果进行比较验证了该方法的可靠性。数值算例给出了不同尺寸、转速和温度下旋转组合圆锥 - 圆柱壳结构的自由振动特性。
