轴向运动SMA层合梁的主共振分析

Primary resonance analysis of axially moving SMA laminated beam

研究了均布横向载荷作用下轴向运动SMA(形状记忆合金)层合梁的横向非线性振动。考虑轴向运动效应、轴力等因素的综合影响,利用力平衡条件、变形协调方程及SMA多项式函数的本构关系,建立了SMA层合梁在均布横向载荷作用下的动力学方程。针对两端简支边界条件,通过伽辽金积分得到了轴向运动SMA层合梁横向振动微分方程。应用平均法得到了横向载荷作用下系统主共振幅频响应方程,对理论结果进行了数值验证;分析了轴向运动速度、温度、激励参数对系统稳态响应的影响。结果表明:轴向速度、轴向载荷的变化只对系统共振频率产生影响;在外激励幅值较大时,温度增加和SMA层增厚对系统产生了相同的减振效果。

The laterally nonlinear vibration of axially moving SMA(shape memory alloy)laminated beam under the transverse load is analyzed.Considering the influence of the axial motion and the axial force,the dynamic equation of SMA laminated beam is established by comprehensive application of the force equilibrium condition,deformation coordination equation and the SMA polynomial stress-strain model.According to the simply supportedboundary condition,the transverse vibration differential equations of the axially moving SMA laminated beam are obtained through applying Galerkin integral method.Based on the averaging method,the primary resonance amplitude-frequency response equations under transverse load of the system are gained.Then the theoretical results are verified numerically,and the influences of axial velocity,temperature,transverse load on the amplitude of the system resonance are analyzed.The results show that the variation of the axial velocity and axial load only affect the resonance frequency of the system;and the vibration amplitude of the beam can be reduced with increase in temperature and SMA layer film when the amplitude of transverse excitation is large enough.