轴向运动形状记忆合金层合梁的参强联合共振  

The resonance of parametric vibration with forced vibration of the axially moving shape memory alloy laminated beam

作　　者：郝颖[1,2] 李哲 胡宇达[1,2] HAO Ying;LI Zhe;HU Yuda(School of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao 066004,China;Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学建筑工程与力学学院,河北秦皇岛066004 [2]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,河北秦皇岛066004

出　　处：《振动与冲击》2023年第10期1-7,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(11902287,12172321);河北省自然科学基金(A2020203007,A2022203044)。

摘　　要：该研究探讨了轴向变速运动形状记忆合金(shape memory alloy,SMA)层合梁在简谐激励下的参强联合共振问题。基于SMA的Falk多项式本构模型,结合Timoshenko梁理论推导了轴向运动SMA层合梁的非线性振动方程。利用伽辽金积分法对其进行时间变量和空间变量的离散,用多尺度法以及坐标变换的方法推导系统参强联合共振的幅频响应方程。通过算例分析,得到不同物理参数变化时的幅频响应曲线图和振幅-参数曲线图,分析了轴向速度、温度及强迫激励对系统参强联合共振特性的影响。结果表明,系统呈现典型的非线性振动特征和复杂的动力学行为。In this paper,the resonance of parametric vibration with forced vibration of the axially variable-velocity moving shape memory alloy(SMA) laminated beam under harmonic excitation was investigated.Based on the Falk polynomial constitutive model of SMA and the Timoshenko beam theory,the nonlinear vibration equation of the axially moving SMA laminated beam was derived.The time and space variables of the equation were discretized by using Galerkin integral method,then the amplitude-frequency response equation of resonance by the combined parametric and forced excitations was derived by multiscale method and coordinate transformation method.According to the example analysis,the amplitude-frequency response and amplitude-parameter curves of different physical parameters were obtained,and the effect of axial velocity,temperature and forced excitations on the resonance characteristics were analyzed.The results show that the system exhibits typical nonlinear vibration characteristic and complex dynamic behavior.

关 键 词：轴向变速运动 形状记忆合金(SMA)层合梁 参强联合共振 多尺度法 

分 类 号：O442[理学—电磁学] O322[理学—物理]