具有约束层阻尼旋转复合材料轴的动态特性研究

摘要

复合材料驱动轴在高速旋转下的振动抑制,是先进直升机和汽车传动系统结构设计需要考虑的重要问题.约束层阻尼技术是工程领域内普遍采用的实用有效的阻尼减振设计方法;然而通过采用约束层阻尼处置方式增加复合材料传动轴的阻尼能力的研究报道,目前国内外很少见到.从应力-应变关系、应变-位移关系出发,推导出复合材料Timoshenko轴、约束层与黏弹性层的动能及势能的数学表达式,采用Hamilton原理建立具有约束层阻尼的旋转复合材料轴的运动学方程.采用广义Galerkin法对动力学方程进行了离散化,建立了广义坐标表示的自由振动方程组,通过特征值求解得到系统的固有频率和阻尼比;基于比例阻尼假设和四阶Runge-Kutta数值积分方法求解上述方程,得到系统的自由振动响应曲线.通过数值分析揭示了约束层材料、黏弹性层材料、铺层方式、长径比和转速对具有约束层阻尼的旋转复合材料轴的固有振动特性以及自由振动响应特性的影响.%The vibration suppression of a composite shaft operating at high speeds is an important issue in structural design of advance power transmission of helicopters and automobiles.Constrained layer damping technology is an effective method in engineering field and it is widely used for reducing structural vibration.However,the studies on strengthening damping of a composite shaft by using constrained layer damping treatment are relatively few.Here,a mechanical model was developed for a rotating composite shaft with passive constrained layer damping (PCLD).Based on the constitutive relation of materials and the strain-displacement relation,the kinetic energy and strain energy of the composite shaft,constrained layer and viscoelastic layer were derived.Hamilton's principle was used to derive the motion equations of the shaft with PCLD.The motion equations were discretized by using the general Galerkin method.The natural frequencies and modal damping ratios were obtained by computing a matrix eigenvalue problem.Using the assumption of proportional damping and Runge-Kutta integration algorithm,the time history responses of the system's damped free vibration were gained.The effects of constrained layer material,viscoelastic layer material,stacking sequences,ratio of length to diameter and rotating speed on the natural vibration characteristics and damped free vibration responses of the composite shaft with PCLD were analyzed using numerical simulation.