功能梯度石墨烯增强阶梯圆柱壳的振动特性分析

Analysis of Vibration Characteristics of Functionally Graded Graphene-reinforced Stepped Cylindrical Shells

基于Rayleigh-Ritz法分析功能梯度石墨烯增强复合材料(Functionally Graded Graphene Platelets Reinforced Composite,FG-GPLRC)阶梯圆柱壳的振动特性。首先,采用改进的Halpin-Tsai微观力学模型和复合材料夹杂理论,确定FG-GPLRC的等效材料属性。其次,基于微元法思想和1阶剪切变形理论建立每一子段的基本方程。最后,建立Lagrange动力学能量泛函方程,通过Rayleigh-Ritz法求解FG-GPLRC阶梯圆柱壳的固有频率,并验证方法的有效性。研究表明,FG-GPLRC阶梯圆柱壳的固有频率随层数的增加变化趋势减小,石墨烯质量分数和分布模式会影响圆柱壳的固有频率;弹性边界条件下弹簧刚度系数越大,FG-GPLRC阶梯圆柱壳的第一阶固有频率越大。

The vibration characteristics of functionally gradient graphene platelets reinforced composite(FG-GPLRC)of stepped cylindrical shells were analyzed based on Rayleigh-Ritz method.Firstly,the modified Halpin-Tsai micromechanical model and composite inclusion theory were used to determine the equivalent material properties of the FG-GPLRC.Secondly,the basic equations of each subsegment were established based on the theory of the micro-element method and the first-order shear deformation theory.Finally,the Lagrange dynamic energy functional equation was established,and the natural frequencies of FG-GPLRC stepped cylindrical shells were solved by Rayleigh-Ritz method,and the effectiveness of the method was verified.The results show that the natural frequency of FG-GPLRC stepped cylindrical shell decreases with the increase of the number of layers.The mass fraction and distribution pattern of graphene can affect the natural frequency of the cylindrical shell.Under the elastic boundary condition,the larger the spring stiffness coefficient,the greater the first natural frequency of the FG-GPLRC stepped cylindrical shell.