阻尼力干扰下超弹性球体中预存微孔的混沌运动分析  

Analyses of Chaotic Motion of Pre-Existing Microvoid in Hyperelastic Sphere Under Damping Force Interference

作　　者：陈威屹 许杰 袁学刚 CHEN Wei-yil;XU Jie;YUAN Xue-gang(College of Mathematics and Information,North Minzu University,Yinchuan 750021,China;College of Mechanical and Electronic Engineering,Dalian Minzu University,Dalian 116600,China;School of Science,Dalian Minzu University,Dalian 116600,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]大连民族大学机电工程学院,辽宁大连116600 [3]大连民族大学理学院,辽宁大连116600

出　　处：《数学的实践与认识》2024年第5期141-152,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12172086)。

摘　　要：针对一类径向横观各向同性不可压缩Varga超弹性材料构成的球体,研究了中心处预存微孔的动力学特性;特别地,根据平衡微分方程建立了描述微孔径向对称运动的数学模型,并通过微分方程的初边值条件考虑了作用于球体表面的载荷与阻尼力.给出了如下的分析与结论:1)在常值载荷作用下,对系统进行了定性分析,重点讨论了材料参数与结构参数对系统的平衡点与非线性响应的影响;且由于系统的强非线性,超弹性球体的微孔运动存在着非对称“∞”型同宿轨道.2)在周期载荷与阻尼力作用下,通过相轨迹曲线、幅频曲线、Melnikov方法、分岔图和Poincaré截面等方法,揭示了系统的超谐波共振、拟周期运动、混沌运动等动力学现象。This paper investigated the dynamic characteristics of pre-existing microvoid in the center of sphere composed of a class of transversely isotropic incompressible Varga hyperelastic materials.A mathematical model is established based on the equilibrium differential equation to describe the radially symmetric motion of the microvoid,and considers the load and damping force acting on the surface of the sphere through the initial and boundary conditions of the differential equations.The analyses and conclusions are as follows:1)Under the effect of constant load,qualitative analyses are conducted on the system,with a focus on discussing the impact of material parameters and structural parameters on system's equilibrium points and nonlinear response.Owing to the the strong nonlinearity of the system,the microvoid motion within the hyperelastic sphere exhibites asymmetric"∞"homoclinic orbits.2)Under the infuence of periodic load and damping force,using methods like the phase trajectory curves,amplitude-frequency curves,Melnikov method,bifurcation diagrams,and Poincare sections,the paper reveals dynamic phenomena such as superharmonic resonance,quasi-periodic motion,and chaotic motion of the system.

关 键 词：预存微孔 横观各向同性 阻尼力 MELNIKOV方法 

分 类 号：TB34[一般工业技术—材料科学与工程]