任意边界下石墨烯增强多孔圆柱壳的振动特性

Vibration Characteristics of Graphene-Reinforced Porous Cylindrical Shells with Arbitrary Boundary Conditions

为了研究任意边界石墨烯增强多孔复合材料(GPLRPC)圆柱壳的振动特性,提出了一种以盖根堡多项式作为容许函数的半解析法.基于Halpin-Tsai微观力学模型和开胞体理论得到GPLRPC圆柱壳的有效材料参数.利用人工弹簧技术模拟了壳体两端的边界条件和壳段之间的连续耦合.然后,基于一阶剪切变形理论,采用Rayleigh-Ritz方法推导出壳体结构的运动方程,求得GPLRPC圆柱壳的无量纲频率.数值算例验证了该方法的有效性和准确性,并讨论了边界条件、孔隙系数、孔隙类型、石墨烯分布模式、石墨烯质量分数、边界弹簧刚度和几何参数等因素对壳体结构振动特性的影响.结果表明:盖根堡多项式作为容许函数具有良好的收敛性和准确性;边界条件对圆柱壳的频率有不同的影响,GPL-A分布模式和孔隙类型Ⅱ的刚度增强效果最好;此外,平移弹簧对频率的影响大于旋转弹簧,圆柱壳长径比的影响较大,但径厚比的影响较小.研究结论可为此类结构的工程设计提供理论参考.

In order to investigate the vibration characteristics of graphene platelet reinforced porous composite(GPLRPC)cylindrical shells under arbitrary boundary conditions,a semi-analytical method using Gegenbauer polynomials as admissible functions is proposed in this paper.First,the effective material properties of the GPLRPC cylindrical shell are derived based on the Halpin-Tsai micromechanical model and closed-cell body theory.Artificial spring technique is utilized to simulate the boundary conditions at both ends of the shell and continuous coupling conditions between shell segments.Then,based on the first-order shear deformation shell theory,the motion equations of the structure are derived and it's dimensionless frequencies are obtained with Rayleigh-Ritz method.Hence,numerical calculations are performed to analyze the effects of boundary conditions,porosity coefficients,porosity types,graphene distribution patterns,graphene mass fractions,boundary spring stiffness,and geometrical parameters on the vibration characteristics of the shell structure.The results show that the Gegenbauer polynomials have excellent convergence and accuracy as admissible functions.It is also found that the boundary conditions have different effects on the frequency of cylindrical shells,and GPL-A and Type II have the best stiffness enhancement effect.Additionally,it is observed that the influence of translational springs on frequency is greater than rotational springs,and the effect of cylindrical shell length-to-diameter ratio is greater,but the effect of diameter-to-thickness ratio is less.Overall,applying graphene to cylindrical shells has a wide range of applications,and the research results can provide data support and theoretical reference for the engineering design.