Research Information System
Journal of Sound and Vibration, vol.257, no.3, pp.413-424, 2002 (SCI-Expanded, Scopus)
An Euler-Bernoulli beam carrying concentrated masses is considered to be a beam-mass system. The beam is simply supported at both ends. The non-linear equations of motion are derived including stretching due to immovable end conditions. The stretching introduces cubic non-linearities into the equations. Forcing and damping terms are also included. Exact solutions for the natural frequencies are given for the linear problem. For the nonlinear problem, an approximate solution using a perturbation method is searched. Nonlinear terms of the perturbation series appear as corrections to the linear problem. Amplitude and phase modulation equations are obtained. Non-linear free and forced vibrations are investigated in detail. The effect of the positions, magnitudes and number of the masses are investigated.