Response of parametrically excited one degree of freedom system with non-linear damping and stiffness

The behavior of one-degree-of-freedom system with different quadratic damping and cubic stiffness non-linearities simulating the axial vibration of a cantilever beam under multi-parametric excitation forces is studied. The approximate solution of the given system up to and including the third order approximation is determined applying the multiple time scale perturbation technique. The steady state solution and its stability tire investigated. The theoretical resonance conditions are confirmed applying numerical techniques. The stability of the numerical solution is studied using the phase-plane method. Effects of the different parameters on the system behavior and jump phenomenon on the frequency response curves are also investigated. A comparison with other similar published works is reported.