变速度轴向运动粘弹性梁的动态稳定性  

Dynamic Stability of Axially Moving Viscoelastic Beams With Pulsating Speed

作　　者：杨晓东[1] 陈立群[2] 

机构地区：[1]沈阳航空工业学院工程力学系,沈阳110034 [2]上海市应用数学和力学研究所

出　　处：《应用数学和力学》2005年第8期905-910,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472060);上海市自然科学基金资助项目(04ZR14058)

摘　　要：研究速度变化的轴向运动粘弹性梁在亚谐波共振及组合共振范围内的参数振动.通过平均法,在运动参数激励频率为2倍固有频率或为两阶固有频率之和附近时得到了自治的常微分方程组.在参数激励频率和激励振幅平面上,可以找到由于共振而产生的失稳区域,并应用数值方法验证了理论推导结果的正确性.分析了粘弹性阻尼,速度和预紧张力对失稳区域的影响.粘弹性阻尼使得共振失稳区域减小,而速度和预紧张力使共振失稳区域在频率_振幅平面上发生漂移.Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonstrated. It's found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.

关 键 词：亚谐波共振 平均法 振动稳定性 轴向运动梁 

分 类 号：O317[理学—一般力学与力学基础]