形状记忆合金(SMA)层合梁动力学分岔分析  

Bifurcation analysis of shape memory alloy laminated beam

作　　者：张夏辉[1] 吴志强[1] 

机构地区：[1]天津大学机械工程学院,天津300072

出　　处：《应用力学学报》2017年第3期397-403,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11172198);国家973项目(2014CB046805)

摘　　要：针对有形状记忆合金的层合梁系统,分析了形状记忆合金层与梁中间基体的厚度比相关参数、激励强度对系统的振动幅频响应的影响。采用形状记忆合金多项式本构模型,建立层合梁的量纲归一化的运动方程,用Galerkin方法离散得到任意阶模态动力学方程,再由平均法求得幅频响应方程。利用奇异性理论计算转迁集和不同类型的幅频响应图。结果表明,一阶模态非线性振动幅频响应可分为类线性和硬特性两种类型。响应为类线性时,厚度比和激励强度在类线性区取值,形状记忆合金层对系统几乎没有减振效果;响应为硬特性时,激励幅值越大,形状记忆合金层越厚,SMA层对系统的减振效果越明显。在不同的激励及SMA层厚度下,二阶和三阶模态非线性振动幅频响应定性相同,其类型可分为:类线性、硬特性、软特性、软硬特性。The influence of thickness ratio(a parameter related with the thickness ratio of SMA layer and the intermediate layer)and excitation intensity on SMA(shape memory alloy)laminated beam are analyzed.With SMA continuous polynomial stress-strain model,the dimensionless vibration equation is established.Using Galerkin method,the dynamic equation of arbitrary order mode can be solved and the amplitude-frequency response equation can be solved by the average method.The transition sets and different types of amplitude-frequency response figures are calculated on the basis of singularity theory.Results show that,there are two types of nonlinear amplitude-frequency response of first-order mode:near-linear,hard spring type.When the amplitude-frequency response is near-linear,the values of thickness ratio and excitation intensity are in the near-linear region,there is nearly no vibration attenuation effect;when the amplitude-frequency response is nonlinear,vibration attenuation effect is more obvious when excitation amplitude is bigger and SMA layer is thicker.Nonlinear amplitude-frequency responses of second-order and third-order modal are qualitatively identical,there are four types of nonlinear amplitude-frequency response:near-linear,hard spring,soft spring,soft-hard spring.These results provide a theoretical basis for the design and control of the laminated beams.

关 键 词：形状记忆合金层合梁 SMA多项式本构模型 转迁集 分岔 

分 类 号：O322[理学—一般力学与力学基础]