Konsantre kütleli Timoshenko kirişlerinin titreşim analizi

Nonlinear vibrations of beams carrying a concentrated mass on an arbitrary point have been investigated. It is assumed that the beam is of Timoshenko type, and both ends of it have simply supports. According to these assumption, the extensions of the beam under vibration are taken into account since the end points of these beams are immovable. This system is formulated mathematically by using Hamilton Principle based on Energy Approach and then forcing and damping terms are added to the derived equations of motion. To find out approximately solutions of the problem, Method of Multiple Scale(Perturbation Method) have been used. In case of primary resonance, analytical solutions have been derived. First terms of the perturbation series construct the linear problem. By means of New Symplectic Approach, coupled differential equations constructing linear problem have been solved and natural frequencies and mode shapes have been obtained. The other terms of perturbation series appear as corrections to the linear terms. Amplitude-Phase modulation equations including these correction terms have been derived by using New Symplectic Approach. From these equations, vibrational characteristic specify of the beam have been investigated in the region of steady-state during the vibrations. Thus, nonlinear frequencies for free vibrations are calculated first. Then, external excitation versus amplitude graphs have been obtained by including forcing. Therefore, effects of the position and magnitude of the concentrated mass on nonlinear vibrations have been analysed.