具有分数导数本构关系的粘弹性浅拱的非线性动力学行为.PDFVIP

具有分数导数本构关系的粘弹性浅拱的非线性动力学行为 1，2 3 李媛萍 ，张卫 (1. “重大工程灾害与控制”教育部重点实验室 （暨南大学），广州510632; 2. 暨南大学力学与土木工程系，广州510632; 3.暨南大学信息科学技术学院电子工程系，广州510632) Dynamic Characteristics of Viscoelastic Shallow Arch With Fractional Derivative Constitutive Relation 1 2 3 LI Yuan-p ing ZHAN G Wei ( 1.Key Lab of Disaster Forecast and Control in Engineering, Ministry of Education of the People s Republic of China (Jinan University) ; 2. Department of Mechanics and Civil Engineering, Jinan University; Guangzhou 510632, China 3. Department of Electronic Engineering, Jinan University; Guangzhou 510632, China ） 摘要:利用分数导数本构模型描述材料的粘弹性特性，建立了粘弹性浅拱在横向荷载作用下的动力学方程。利用 Galerkin 截断法并结合边界条件分别得到了一阶和二阶Galerkin 系统的控制微分方程。通 数值计算，分析了简谐 激励下一阶Galerkin 系统的非线动力学行为。研究表明：随着外激励幅值的变化，粘弹性浅拱系统可以通 倍周期 分岔或阵发性两条路径进入混沌；另外，固定外激励幅值、频率以及阻尼系数等状态参数，不同初始条件下，系统 可以出现多周期解共存、周期解与混沌解共存的现象。 关键词:分数导数本构关系；粘弹性浅拱；分岔；混沌；多解共存 中图分类号：O322 文献标识码：A Abstract: The dynamics equation of a viscoelastic shallow arch under lateral loads, in which fractional derivative model introduced to simulate the materials characteristics, is proposed. The simplified differential equations of the first and second order Galerkin systems are developed combined Galerkin method with boundary conditions. Dynamic behaviors of the first order Galerkin system with harmonic loads are discussed by numerical calculations. The results show that: the system may lead to chaotic motion via period-doubling bifurcations or intermittent routes; In addition, the coexistences of multiple periodic solutions and the coexistences of periodic solutions