简谐激励下黏弹性分数阶模型研究  

Research on Viscoelastic Fractional Order Model Under Harmonic Excitation

作　　者：石玉文 李雪梅 马瑞群 SHI Yuwen;LI Xuemei;MA Ruiqun(Nanjing Bridge Machinery Co.,Ltd.,Nanjing Jiangsu 211101,China;School of Intelligent Manufacturing,Nanjing Polytechnic Institute,Nanjing Jiangsu 210048,China)

机构地区：[1]南京大桥机器有限公司,江苏南京211101 [2]南京科技职业学院智能制造学院,江苏南京210048

出　　处：《盐城工学院学报（自然科学版）》2024年第2期55-61,共7页Journal of Yancheng Institute of Technology:Natural Science Edition

基　　金：2022年南京科技职业学院“科研北斗计划”青年资助项目(NJPI-2022-12)。

摘　　要：基于简谐激励(正弦)研究了黏弹性分数阶本构模型。由于正弦函数的分数阶导数与整数阶导数具有相同的形式,据此将线性模型表示为单项分数阶导数项的形式,并进行复模量计算及响应特性分析;将分数阶非线性模型表达成谐波形式,可以很容易地进行非线性参数识别;最后将分数阶非线性模型转化为整数阶非线性形式,并以参考文献[17]中的4 Hz试验数据用五阶谐波形式进行参数拟合验证。结果表明:在10%的小应变时,ADF模型比分数阶模型更贴合试验数据;随着应变的增大,分数阶模型比ADF模型越来越贴合试验数据。The viscoelastic fractional order constitutive model is studied based on harmonic excitation(sine).Because the fractional order derivative of sine function has the same form as the integer order derivative,the linear model is expressed as a single fractional order derivative term,and the complex modulus is calculated and the response characteristics are analyzed.The nonlinear parameters can be easily identified by expressing the fractional order nonlinear model in harmonic form.Finally,the fractional order nonlinear model is transformed into integer order nonlinear form,and the parameters are fitted and verified with the 4 Hz test data in refdrence[17]in the form of fifth-order harmonic.The results show that the ADF model fits the test data better than the fractional-order model at a small strain of 10%.With the increase of strain,the fractional order model fits the test data more and more than ADF model.

关 键 词：简谐激励 分数阶微积分 黏弹性 

分 类 号：O345[理学—固体力学]