Non-linear Vibrations of Beams with Attached Spring-mass System

概要

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A study is made of the coupled non-linear vibrations of a simply supported beam, with ends restrained elastically in the direction of length of beam, carrying a concentrated mass to which a spring-mass system is attached, and subjected to a transverse periodic force at an arbitrary point under the influence of gravity. The solution is derived for the steady-state vibration in the first mode resonance region with first approximation. Numerical results of the amplitude responses of the concentrated mass on the beam and the mass of the spring-mass system are presented for the principal resonance and the second and third order higherharmonic resonances, and then the occurrence of these resonances, and especially the effect of damping in the spring-mass system on the higherharmonic resonances are investigated. The stability of the steady-state solutions is also investigated for the case of no-damping.
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