具有形状记忆合金丝的复合材料轴转子系统的振动与稳定性

Vibration and stability of a composite shaft-rotor system with SMA wires

提出具有SMA丝的复合材料轴-盘-刚性支承转子系统的数学模型,研究转子系统的振动与稳定性。将轴视为一个平行于轴线方向埋入SMA丝的薄壁复合材料空心梁,盘为各向同性刚性圆盘,轴位于刚性轴承上。基于变分渐进法(VAM)描述复合材料薄壁梁的变形,基于Brinson热力学本构方程计算SMA丝的回复应力,采用Hamilton原理推导出系统的运动方程,采用Galerkin法进行模型离散化和近似数值计算。着重分析SMA丝含量和初始应变对复合材料轴振动固有频率和转子系统临界转速的影响。研究结果表明,所建立的动力学模型能够用于揭示SMA对转子系统的振动与稳定性的影响机理。

A dynamical model of a rotor system containing a composite shaft with shape memory alloy （SMA）wires parallel to the shaft axis embedded,isotropic rigid disks and flexible bearings considered as linear springs and viscous dampers was presented and then used to predict the natural frequencies and dynamical stability of the rotor system.A composite thin-walled beam based on variational asymptotically approach（VAM）was employed to describe the deformation of the shaft.A thermo-mechanical constitutive equation of SMA proposed by Brinson et al.was used to calculate the recovery stress of the constrained SMA wires.Hamilton＇s principle was used to derive the dynamic equations of the rotor system,they were discretized and solved with Galerkin＇s method.The influcences of SMA wire content and initial strain on the natural frequencies and critical speeds of the rotor system were analyzed.Results showed that the proposed model can be used to reveal the effects of SMA on the dynamic characteristics of the rotor system.