Bifurcation analysis of a nonlinear coupled pitch–roll ship

Kamel, M.

doi:10.1016/j.matcom.2006.04.003

Cited by 32 publications

(18 citation statements)

References 14 publications

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“…6. The reported results are in good agreement with [10,11] regarding the reduction of vibrations and occurrence of saturation phenomena.…”

Section: Discussionsupporting

confidence: 87%

“…In this paper, we consider a ship model with nonlinear coupled pitch and roll modes subjected to a sinusoidal harmonic excitation [10][11][12] and parametric excitations. The nonlinear system can be written as:…”

Section: Mathematical Analysismentioning

confidence: 99%

“…Substituting (16), (11), and (13) into (15) and equating the real and imaginary parts we obtain the following equations describing the modulation of the amplitudes and phases of the roll and pitch response:…”

Section: Stability Of Motionmentioning

confidence: 99%

“…In comparison with the previous work [10,11], the response and stability of the pitch-roll system under external excitation force from the first order approximation are studied. The method of multiple scale perturbation technique is applied to obtain the bifurcation response equation near the combination resonance case in the presence of 2:1 internal resonance and the stability of the linear solution is only investigated.…”

Section: Comparison With Previously Published Workmentioning

confidence: 99%

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Stability and response of a nonlinear coupled pitch-roll ship model under parametric and harmonic excitations

Sayed

Hamed

2010

Nonlinear Dyn

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The present study deals with the response of a two-degree-of-freedom (2DOF) system with quadratic coupling under parametric and harmonic excitations. The method of multiple scale perturbation technique is applied to solve the nonlinear differential equations and obtain approximate solutions up to and including the second order approximations. All resonance cases are extracted and investigated. Stability of the system is studied using frequency response equations and phase-plane method. Numerical solutions are carried out and the results are presented graphically and discussed. The effects of the different parameters on both response and stability of the system are investigated. The reported results are compared to the available published work.

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“…6. The reported results are in good agreement with [10,11] regarding the reduction of vibrations and occurrence of saturation phenomena.…”

Section: Discussionsupporting

confidence: 87%

Section: Mathematical Analysismentioning

confidence: 99%

Section: Stability Of Motionmentioning

confidence: 99%

Section: Comparison With Previously Published Workmentioning

confidence: 99%

See 2 more Smart Citations

Stability and response of a nonlinear coupled pitch-roll ship model under parametric and harmonic excitations

Sayed

Hamed

2010

Nonlinear Dyn

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“…Empirical estimates of characteristic multipliers in four-dimensional state space are obtained by examining transient behavior after perturbations; the Karhunen-Loeve decomposition is used to identify dominant local modes in these transients. Kamel [18] and Zhou and Chen [19] investigated the response and stability of two modes of ship model under sinusoidal harmonic excitation. They obtained the bifurcation response equation near the combination resonance case in the presence of internal resonance of this system.…”

Section: Introductionmentioning

confidence: 99%

Vibration reduction of multi-parametric excited spring pendulum via a transversally tuned absorber

2009

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The use of passive control strategy is a common way to stabilize and control dangerous vibrations in a nonlinear spring pendulum which is describing the ship's roll motion. In this paper, a tuned absorber in the transversal direction is connected to a spring pendulum with multi-parametric excitation forces to control the vibration due to some resonance cases on the system. The method of multiple scale perturbation technique (MSPT) is applied to study the periodic solution of the given system near simultaneous sub-harmonic and internal resonance case. The stability of the steady-state solution near the resonance case is investigated and studied using frequency response equations. The effects of the absorber and some system parameters on the vibrating system are studied numerically. Optimal working conditions of the system are extracted when applying passive control methods. Comparison with the available published work is reported.

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Numerical analysis of pitch and rolling motions of trimaran in oblique waves

Gong

et al. 2021

J Mar Sci Technol

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Bifurcation analysis of a nonlinear coupled pitch–roll ship

Cited by 32 publications

References 14 publications

Stability and response of a nonlinear coupled pitch-roll ship model under parametric and harmonic excitations

Stability and response of a nonlinear coupled pitch-roll ship model under parametric and harmonic excitations

Vibration reduction of multi-parametric excited spring pendulum via a transversally tuned absorber

Numerical analysis of pitch and rolling motions of trimaran in oblique waves

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