旋转运动SMA层合梁动力学建模与非线性自由振动分析  

Dynamic modeling of rotating SMA laminated beam and nonlinear free vibration analysis

作　　者：王航 穆安乐[1] 黄泽波 WANG Hang;MU Anle;HUANG Zebo(Faculty of Mechanical and Precision Instrument Engineering,Xi’an University of Technology,Xi’an 710048,China;School of Mechanical and Electrical Engineering,Xi’an Railway Vocational&Technical Institute,Xi’an 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,陕西西安710026

出　　处：《西安理工大学学报》2022年第1期32-40,共9页Journal of Xi'an University of Technology

基　　金：国家自然科学基金资助项目(51075326)。

摘　　要：层合梁铺层中内嵌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Brinson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、初始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, and the dynamic characteristics of the laminated beam are changed. In order to study the fundamental frequency of rotating SMA laminated beams, the recovery stress and martensite volume fraction are obtained by using Brinson’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 to the laminated beam with large rotation motion. The nonlinear free vibration equation to the laminated beam is obtained by Ritz method. The rotational motion has an obvious effect on the free vibration of SMA laminated beams. The natural frequency at the same rotating speed changes when there existing different SMA volume fractions, pre-strains and angles of laying graphite fiber.

关 键 词：形状记忆合金 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]