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

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.