功能梯度三相复合材料圆柱壳的非线性振动研究

Nonlinear Vibration Study of Functionally Graded Three-Phase Composite Cylindrical Shell

论文研究了一种由环氧树脂、石墨烯纳米片、碳纤维制成的功能梯度三相复合材料圆柱壳的非线性振动响应.基于一阶剪切变形理论和von-Karman几何非线性关系,考虑到温湿效应、气动力和外激励的共同作用,利用Hamilton原理建立了两端固支圆柱壳的非线性偏微分运动方程.利用Galerkin法将非线性偏微分运动方程离散成一组相互耦合的二阶非线性常微分方程,利用伪弧长延拓法求解非线性常微分方程组,给出对应的幅频响应曲线.本论文中仅考虑湿度和外激励等参数的变化对新型三相复合材料圆柱壳结构非线性振动响应的影响,分析了湿度和外激励的变化对功能梯度三相复合材料圆柱壳共振响应的影响.

We study the nonlinear vibration response of functionally graded three-phase composite cylindrical shell,which is made of epoxy resin,Graphene NanoPlatelets and carbon fibers.Based on the first-order shear deformation theory and the von-Karman geometric nonlinear relation,the nonlinear partial differential equations of motion of the clamped cylindrical shell at both ends are established by Hamilton principle,taking into account the interaction of hygrothermal environment,aerodynamic force and external excitation.The nonlinear partial differential equations of motion are discreteted into a set of coupled second-order nonlinear ordinary differential equations by Galerkin method.The nonlinear ordinary differential equations are solved by pseudo-arc length extension method,and the corresponding frequency-response curves are given.We only consider the influence of moisture and external excitation on the nonlinear vibration response of the new three-phase composite cylindrical shell,and the resonance response of functionally graded three-phase composite cylindrical shell under the influence of moisture and external excitation is analyzed.