旋转运动SMA层合梁动力学建模与非线性自由振动分析  

DynamicModeling of Rotating SMA Laminated Beam and Nonlinear Free Vibration Analysis

作　　者：王航 穆安乐[1] 黄泽波 WangHang;Mu Anle;Huang Zebo(School of Mechanical and Precision Instrument Engineering,Xi'an University of Technology,Xi'an,Shaanxi 710048;School ofMechanical and Electrical Engineering,Xi'an Railway Vocational and Technical Institute,Xi'an,Shaanxi 710026,China)

机构地区：[1]西安理工大学机械与精密仪器工程学院,陕西西安710048 [2]西安铁路职业技术学院机电工程学院机电一体化教研室,陕西西安710026

出　　处：《西安轨道交通职业教育研究》2022年第3期12-20,共9页Xi'an Rail Transit Vocational Education Research

摘　　要：层合梁敷层中内嵌SMA丝时,可以有效改变层合梁旋转运动时的动态特性。为了研究旋转运动SMA层合梁的振动特性,使用Brison一维SMA本构模型获得温度变化时的恢复应力与马氏体体积分数。使用坐标变换建立层合梁质点在惯性系下的位移。基于Euler-Bernoulli梁和Von Karman大变形理论,建立了位移场与应变之间的关系。使用Hamilton变分原理,获得大范围旋转运动层合梁的动力学方程。并用Ritz法获得内嵌SMA丝层合梁的非线性自由振动方程。旋转运动对SMA层合梁的自由振动有明显的影响。研究了同一转速下,不同SMA体积分数、预应变对固有频率的影响。而且研究了石墨层纤维铺设角度对层合梁基频的影响。When SMA wires are embedded in the laminated beam,the dynamic characteristics of the laminated beam is changed.In order to study the fundamental frequency of rotating SMA laminated beams,the recovery stress and martensite volume fraction are obtained by using Brison’s one-dimensional SMA constitutive model.Based on Euler-Bernoulli beam and von Karman large deformation theory,the relationship between displacement and strain is obtained.The displacement of laminated beam is established by coordinate transformation.The Hamilton principle is used to obtain the dynamic equation of the laminated beam with large rotation motion.The nonlinear free vibration equation of the laminated amount of SMA wire is obtained by Ritz method.The rotational motion has an obvious effect on the free vibration of SMA laminated beams.The influence of different SMA volume fraction and pre strain on the natural frequency at the same speed is studied.Moreover,the influence of graphite fiber laying angle on the fundamental frequency of laminated beam is studied.

关 键 词：记忆合金丝 非线性自由振动 旋转层合梁 

分 类 号：O327[理学—一般力学与力学基础]