Finite element analysis of non linear coupled oscillator

Large flexible structures and aerospace structures can be studied by building a model flexible beam with an appendage. The appendage can be used as a passive or an active vibration absorber for a structure under sinusoidal and random excitation. In this study, a cantilever beam-tip mass-pendulum system is investigated by using Finite Element method (FEM). Dynamical behaviour of the model has been investigated under sinusoidal excitation in the neighbourhood of autoparametric region which is the condition of that the natural frequency of the beam is twice the natural frequency of the pendulum (Ω=ωb=2ωp). The autoparametric interaction between the beam and the pendulum (absorber) has been exhibited. Hence, the maximum energy transfer between the beam and the pendulum was observed when the autoparametric resonance condition was satisfied. Detailed analysis has been performed for different mass ratios (pendulum mass/tip mass) and excitation amplitudes. Results show that the pendulum can be used as a passive vibration absorber for flexible structures having low natural frequency.