Dynamic analysis of a cantilever beam excited by a non ideal source / Análise dinâmica de uma viga engastada excitada por uma fonte não ideal

AUTOR(ES)
DATA DE PUBLICAÇÃO

2009

RESUMO

Studies about the dynamic behaviour of nonlinear structures have been to this date subject of extensive research all around the world. Since the beginning of the development of the nonlinear oscillation theory one has tried to understand the basic mechanisms, like disruptions that would cause complex answers on flexible structures. This paper presents a theoretical and practical study of the dynamic behaviour of a semi-wing of an airplane installed on a turbine with unbalanced propellers; this system is represented through a cantilever beam excited by a non-ideal source located at the end opposite to the coupling. As a non-ideal system we mean the one that considers that the excitement is influenced by the systems response itself. For non-ideal dynamic systems, one must add an equation that describes how the non-ideal source interacts with the system. Only the first vibrating mode is considered in the systems equation. The numeric simulation results shown are obtained by using the Matlab® 8.0 software and the control parameter to be analyzed is the motor torque. The results that show the dynamic behaviour of the system are time history, phase plan, FFT and to identify the chaotic behaviour the Lyapunovs indexes are calculated. The graphic that shows the presence of the Sommerfeld effect (jump) in the system is also presented. In the experimental part, all the practical procedure is presented, as well as experimental results, like, for example: Time history, phase plan reconstruction, FFT, Lyapunov exponents and the analyses that illustrate the presence of the Sommerfeld effect on the experiment.

ASSUNTO(S)

efeito sommerfeld non ideal systems sommerfeld effect sistema não ideal nonlinear systems lyapunov exponents sistema não linear expoentes de lyapunov

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