材料内阻对旋转复合材料轴动力学稳定性的影响研究

摘要

由于复合材料与金属材料相比,具有更为突出的阻尼耗散能力,超临界旋转复合材料轴在材料内阻的作用下更容易产生不稳定自激振动.从复合材料本构关系、应变-位移关系基本方程出发,基于Bernoulli-Euler梁理论,并考虑复合材料的黏弹性阻尼耗散特性,在导出旋转复合材料轴的动能、势能和内阻耗散能的基础上,采用Hamilton原理建立了转子系统的运动微分方程,采用Galerkin法对复数形式的弯曲方程进行求解,导出转子系统的特征方程.通过数值分析得到固有频率-转速曲线和阻尼-转速曲线,求得了临界转速和失稳阈.研究了铺层角、长径比和铺层方式的影响.模型结果的正确性,通过与文献结果对比,得到了验证.%As composite material has a higher damping capacity than metallic materials,a supercritical rotating composite shaft under the action of material's internal damping is easier to have an unstable self-excited vibration.Here,based on the basic equations for constitutive relations and strain-displacement relations of composite material,the kinetic energy,the potential energy,and the internal damping dissipative energy of the rotor system including the rotating composite shaft were derived with Bernoulli-Euler beam theory and considering dissipative characteristics of viscoelastic damping.The rotor system's equations of motion were deduced using Hamilton principle.Galerkin method was used to solve the rotor system's equations of motion in complex coordinates to derive the characteristic equations of the rotor system.The rotor system's natural frequency versus rotating speed curve and damping versus rotating speed curve were obtained through numerical analysis.From these curves,the critical rotating speed and instability threshold of the system were gained.The effects of ply angle,stacking sequences,and ratio of length to outer radius on the system's critical rotating speed and instability threshold were analyzed.The correctness of the dynamic model built here for the rotor system was verified by comparing the calculated results of critical speedand damping of the rotor system with those available in literatures.