石墨烯增强泡沫圆柱壳的自由振动分析

Free Vibration Analysis of Graphene Reinforced Foam Cylindrical Shells

基于一种半解析区域分解法,对石墨烯增强泡沫圆柱壳的自由振动进行分析。该方法沿旋转轴将壳体分解成若干个壳段,采用改进的变分原理和最小二乘加权残差法将壳段界面势能引入到壳体的能量泛函,使壳体的自由振动分析问题归结为无约束泛函变分问题。壳段位移变量采用Fourier级数和Chebyshev多项式函数展开,对运动控制方程进行离散并求其自由振动频率,将计算结果与已有成果进行了对比,验证了本文计算方法的正确性,并分析了孔隙系数、石墨烯质量分数以及几何参数对圆柱壳自由振动固有频率的影响。

Free vibration of a porous graphene-enhanced cylindrical shell is analyzed based on a semi- analytical domain decomposition method. According to this method, the shell is decomposed into several shell segments along the axis of rotation. The improved variational principle and the least square weighted residual method are used to introduce the shell interface potential energy into the energy functional of the shell so that the free vibration analysis of the shell is reduced to an unconstrained functional variational problem. The shell displacement variable is expanded by the Fourier series and Chebyshev polynomial function. The motion control equation is discretized and the free vibration frequency is calculated. The calculation results are compared with the existing results to verify the correctness of the calculation method in this paper, and the influence of po-rosity, graphene mass fraction and geometric parameters on the natural frequency of the free vi-bration of a cylindrical shell is analyzed.