Eissa, M.Kamel, M.El-Sayed, A. T.2019-12-282019-12-282011Cited References in Web of Science Core Collection: 170025-6455https://doi.org/10.1007/s11012-010-9311-2https://link.springer.com/article/10.1007/s11012-010-9311-2Accession Number: WOS:000287856000006The vibration of a ship pitch-roll motion described by a non-linear spring pendulum system (two degrees of freedom) subjected to multi external and parametric excitations can be reduced using a longitudinal absorber. The method of multiple scale perturbation technique (MSPT) is applied to analyze the response of this system near the simultaneous primary, sub-harmonic and internal resonance. The steady state solution near this resonance case is determined and studied applying Lyapunov's first method. The stability of the system is investigated using frequency response equations. Numerical simulations are extensive investigations to illustrate the effects of the absorber and some system parameters at selected values on the vibrating system. The simulation results are achieved using MATLAB 7.0 programs. Results are compared to previously published work.enUniversity of Passive vibration control; Spring pendulum; Multi-excitation; StabilityINTERNAL RESONANCE; SYSTEMArticlehttps://doi.org/10.1007/s11012-010-9311-2