Non-Linear Transverse Vibrations of A Simply Supported Multi-Stepped Beam

Non-Linear Transverse Vibrations of A Simply Supported Multi-Stepped Beam

Özkaya, Erdoğan
Tekin, Ayla

In this study, the nonlinear vibrations of Euler-Bernoulli multiple-stepped beam are investigated. The beam is simply supported at both ends. The equations of motions are obtained using Hamilton’s principle and made non-dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms are also included in the equations. A perturbation method is applied to the equations of motions. The first terms of the perturbation series led to the linear problem. Natural frequencies for the linear problem are calculated exactly for different step cases. Second order non-linear terms of the perturbation series behaved as corrections to the linear problem. Amplitude and phase modulation equations are obtained. Non-linear free and forced vibrations are investigated in detail. These analyses are repeated for different step ratios and step numbers.

Conference or Workshop Item
PeerReviewed

2010-06

625