轴向运动层合薄壁圆柱壳内共振的数值分析

Internal resonance of axially moving laminated thin cylindrical shells

以轴向运动复合材料薄壁圆柱壳为研究模型,考虑其弹性模量随振动频率变化(动态弹性模量),据Donnell非线性扁壳理论及经典层合壳理论获得模型非线性振动微分方程。采用含四个广义模态坐标的位移展开式,利用Galerkin方法对振动微分方程离散化;用变步长四阶Runge-Kutta法对非线性模态方程组进行数值积分,研究复合材料圆柱壳1:1:1:1的内共振现象;讨论圆柱壳轴向运动速度、阻尼系数及外激励幅值对系统1:1:1:1内共振响应作用。

A thin composite circular cylindrical shell moving in axial direction was investigated. Based on the Donnell＇s nonlinear shallow-shell theory,together with the classical laminated shell theory,a nonlinear vibration equation of the system was derived,in which the effects of dynamic Young＇s modulus,damping and geometric large deformation were considered.The modal expansion with four generalized modal coordinates was adopted,and the vibration equation was discretized by using the Galerkin method.Applying variable step-size four-order Runge-Kutta method,the nonlinear modal equations of the system was solved,and the nonlinear frequency response curves,which show 1：1：1：1 internal resonance phenomenon in the system were obtained.The effects of moving speed,damping coefficients and amplitudes of external force on the nonlinear vibration response of the shell were also analysed.