考虑不可伸长和材料内阻的旋转复合材料轴的非线性自由振动分析

Nonlinear free vibration analysis of an in-extensional rotating composite shaft with material internal damping

建立了考虑材料内阻的旋转复合材料轴的非线性动力学模型,研究材料内阻对旋转轴非线性自由振动的影响。模型包括转动惯量和陀螺效应,但剪切变形不予考虑。基于不可伸长假设,采用曲率和惯性非线性描述复合材料轴的大振幅振动。基于复合材料的黏弹性描述阻尼耗散特性。基于扩展的Hamilton原理,导出旋转复合材料轴的弯-弯耦合非线性振动偏微分方程组。采用Galerkin法将偏微分方程进行离散化,采用多尺度法对常微分方程进行摄动分析,导出非线性自由振动解的分析表达式,针对铺层角、长径比、铺层方式和旋转速度进行数值分析,研究材料内阻对旋转复合材料轴的非线性固有频率的影响。将多尺度法求解的结果与数值积分的结果进行了比较,验证了模型与方法的正确性。

An dynamical model of an inextensible rotating composite shaft with internal damping is presented and analyzed to investigate the effects of the internal damping on the nonlinear free vibration of the shaft.The rotating composite shaft is modeled as an Euler Bernoulli beam which includes the rotary inertia and gyroscopic effects while negelects the shear deformation.Nonlinearities are due to the inextensiblity in the shaft which lead to nonlinearities in curvature and inertia.The damping property is described by the dissipative behavior of viscoelastic composites.The extended Hamilton principle is employed to derive the nonlinear equations of bending-bending vibration of the rotating composite shaft.The partial differential equations of motion are discretized by Galerkin method.The solution of nonlinear free vibration is derived by using the method of multiple scales.The nonlinear natural frequencies are examined for different parameters such as ply angle,ratio of length over outer radius,stacking sequence and rotating speed,the effects of the internal damping of the composite are evaluated.The results of multiple scales for free vibration responses are compared with the numerical simulations.