Vibration reduction of a nonlinear spring pendulum under multi-parametric excitations via a longitudinal absorber

Abstract

The vibration of a ship is a disadvantage for safety operation. It should be reduced to the minimum. In this paper, the vibration of a ship pitch-roll motion described by a nonlinear spring pendulum (three degrees of freedom) subjected to multi-parametric excitation forces can be reduced using a longitudinal absorber. The theoretical results are obtained by applying the multiple scale perturbation technique (MSPT). The stability of the system near the simultaneous sub-harmonic resonance is studied by using frequency response equations. The numerical solution needs extensive investigations to illustrate the effects of the absorber and some system parameters at selected values on the vibrating system. Optimum working conditions of the system are extracted applying passive control methods. A threshold value of the linear damping coefficient can be used directly for vibration suppression of both vibration modes. Comparison with the available published work is reported.