Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure

• Published in: Acta mechanica Sinica 2010-12, Vol.26 (6), p.967-976
• Main Authors: Cao, Dong-Xing, Zhang, Wei, Yao, Ming-Hui
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; Computational Intelligence; Engineering; Engineering Fluid Dynamics; Research Paper; Theoretical and Applied Mechanics; 数值模拟; 梁结构; 混沌动力学; 混沌运动; 结构运动方程; 非线性特性
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-010-0385-9

This paper focuses on theoretical and experimental investigations of planar nonlinear vibrations and chaotic dynamics of an L-shape beam structure subjected to fundamental harmonic excitation,which is composed of two beams with right-angled L-shape.The ordinary differential governing equation of motion for the L-shape beam structure with two-degree-of-freedom is firstly derived by applying the substructure synthesis method and the Lagrangian equation.Then,the method of multiple scales is utilized to obtain a four-dimensional averaged equation of the L-shape beam structure.Numerical simulations,based on the mathematical model,are presented to analyze the nonlinear responses and chaotic dynamics of the L-shape beam structure.The bifurcation diagram,phase portrait,amplitude spectrum and Poincare map are plotted to illustrate the periodic and chaotic motions of the L-shape beam structure.The existence of the Shilnikov type multi-pulse chaotic motion is also observed from the numerical results.Furthermore, experimental investigations of the L-shape beam structure are performed,and there is a qualitative agreement between the numerical and experimental results.It is also shown that out-of-plane motion may appear intuitively.