Simply supported elastic beams under parametric excitation
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In this paper, the nonlinear characteristics of the parametric resonance of simply supported elastic beams are investigated. Considering a geometrically exact formulation for unsharable and inextensible elastic beams subject to support motions, the integral-partial-differential equation of motion is obtained. The third-order perturbation of the equation of motion is then determined in a form amenable to an asymptotic treatment. The method of multiple scales is used to obtain the equations that describe the modulation of the amplitude and phase of parametric-resonance motions. The stability and bifurcations of the system are investigated considering, in particular, the frequency-response function. Furthermore, experimental results are shown to confirm the theoretically predicted stability and bifurcations.
KeywordsParametric excitation Cosserat theory Nonlinear inertia Nonlinear elastic rod Experimental frequency-response curve Method of multiple scales
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