Theoretical and Experimental Investigation of an L-Shape Beam Structure

Flexible multi-beam structures are significant components of large space station, architecture engineering and other structural systems. The understanding of the dynamic characteristics of these structures is essential for their design and control of vibrations. In this paper, the planar nonlinear vibrations and chaotic dynamics of an L-shape flexible beam structure will be investigated using theoretical and experimental methods. The L-shape beam structure considered here is composed of two flexible beams with right-angle. The governing equations of motion for the L-shape beam structure are established firstly. Then, the method of multiple scales is utilized to obtain a four-dimensional averaged equation. Numerical method is used to analyze the nonlinear dynamic responses and chaotic motions. Finally, The experimental apparatus and schemes for measuring the amplitude of nonlinear vibrations for the L-shape beam structure are introduced briefly. Then, the detailed analysis for experimental data and signals which represent the nonlinear responses of the beam structure are given.