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Single-mode response and control of a hinged–hinged flexible beam

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Abstract

The problem of suppressing the vibrations of a hinged–hinged flexible beam that is subjected to primary and principal parametric excitations is tackled. Different control laws are proposed, and saturation phenomenon is investigated to suppress the vibrations of the system. The dynamics of the beam are modeled with a second-order nonlinear ordinary-differential equation. The method of multiple scales is used to derive two-first ordinary differential equations that govern the time variation of the amplitude and phase of the response. These equations are used to determine the steady-state responses and their stability. The results of perturbation solution have been verified through numerical simulations, where different effects of the system parameters on the steady-state amplitude and on saturation phenomena at resonance have been reported.

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  1. Department of Mathematics, Faculty of Science, Al-Azhar University, Gaza, Palestine

    U. H. Hegazy

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  1. U. H. Hegazy
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Hegazy, U.H. Single-mode response and control of a hinged–hinged flexible beam. Arch Appl Mech 79, 335–345 (2009). https://doi.org/10.1007/s00419-008-0230-9

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  • DOI: https://doi.org/10.1007/s00419-008-0230-9

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