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

作　　者：Dong-Xing Cao·Wei Zhang·Ming-Hui Yao College of Mechanical Engineering,Beijing University of Technology, Beijing 100124,China 

出　　处：《Acta Mechanica Sinica》2010年第6期967-976,共10页力学学报（英文版）

基　　金：supported by the National Science Foundation for Distinguished Young Scholars of China(10425209);the National Natural Science Foundation of China(10732020,10802001,11072008 and 10872010);the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality and the Ph.D.Programs Foundation of Beijing University of Technology(X0001015200801).

摘　　要：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.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.

关 键 词：MULTI-BEAM Structure BIFURCATION CHAOS EXPERIMENT 

分 类 号：O322[理学—一般力学与力学基础]