Spatially complex localization in twisted elastic rods constrained to an elliptic cylinder

4th Symposium on the Mechanics of Slender Structures

物理学;力学

Feng, Jingjing^1,2 ; Zhang, Qichang^1,2 ; Wang, Wei^1,2

Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, China^1

Tianjin Key Labortory of Nonlinear Dynamics and Chaos Control, Tianjin University, Tianjin, China^2

关键词: 3d configurations;    Analytical method;    Analytical results;    Distributed forces;    Elliptic cylinder;    Heteroclinic orbit;    Heteroclinic solutions;    Numerical integrations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/448/1/012005/pdf
DOI  :  10.1088/1742-6596/448/1/012005

学科分类：力学，机械学

来源: IOP

【 摘 要 】

In molecular biology, the elastic rod is wound on the elliptic cylinder can be used as a simplified model of the DNA and protein molecules, in which the elliptic cylinder is used to simulate the heterogeneity of the protein molecules. The problem can be described as a long thin weightless rod constrained, by suitable distributed forces, to lie on an elliptic cylinder while being held by end tension and twisting moment. The Cosserat director theory is used to formulate this problem. More complicated shaped are possible and special attention is given to localized configurations described by homoclinic and heteroclinic orbits of the oscillator. The analytical results of homoclinic and heteroclinic boundary conditions are obtained from Pade´ approximation. By using the analytical results of homoclinic and heteroclinic solution, both internal force and 3D configuration are discussed in detail. The results of analytical and numerical integration are compared to verify the effectiveness and feasibility of the analytical method.