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

Sayed, M.; Hamed, Y. S.

doi:10.1007/s11071-010-9841-0

Cited by 52 publications

(17 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Rolling is also a crucial reason of overturning accidents [4][5][6][7]. In the nineteenth century, Krylov and Froude put forward early classical movement theories on ship longitudinal and transverse motion, respectively.…”

Section: Introductionmentioning

confidence: 99%

Research on chaos and nonlinear rolling stability of a rotary-molded boat

Qi-guo

Liu

2016

Nonlinear Dyn

View full text Add to dashboard Cite

On the basis of nonlinear features analysis of restoring torque, damping torque and especially hull deformation, a nonlinear roll equation of rotary-molded boats has been established. The equation includes elastic deformation term which makes the equation different from existing ones for steel boats. This paper dissected its dynamic characteristic of rolling motion from different aspects by using time domain diagram, phase graph, Poincare map, as well Lyapunov exponential spectrum. And then, an exact feedback linearization controller was designed using closed-loop gain shaping algorithm to make the boat get rid of chaotic state. Through numerical simulation, it is found that the roll frequency and velocity increase when elastic deformation occurs; i.e., the roll stability margin shrinks, and the chaos phenomenon is much more remarkable. This conclusion laid the foundation for controlling or restraining the boat's rolling and can be used as the basis of how to amend the evaluation criteria on rotarymolded boat stability.

show abstract

Section: Introductionmentioning

confidence: 99%

Research on chaos and nonlinear rolling stability of a rotary-molded boat

Qi-guo

Liu

2016

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…Amer et al [26] dealt with the dynamical system of a twin-tail aircraft under different controllers. They used two simple active control laws based on the linear negative velocity and acceleration feedback Sayed and Hamed [27] obtained the analytical and numerical solutions of coupled nonlinear differential equations describing the motion of pitch roll under parametric and harmonic excitations using multiple scale method. Sayed and Kamel [28,29] investigated the effects of different controllers on the vibrating system and the saturation control to reduce vibrations due to rotor blade flapping motion.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Mousa

Sayed

Eldesoky

et al. 2014

Int. J. Dynam. Control

Self Cite

View full text Add to dashboard Cite

The aim of this paper is to investigate the stability of a simply supported laminated composite piezoelectric rectangular plate under combined excitations. Analysis of the amplitude and phase modulation equations with the associated nonlinear interaction coefficients, as provided by the multiple scale analyses of various 1:1 internal resonance conditions and primary resonance case, where ω 2 ∼ = ω 1 and 3 ∼ = ω 1 is considered. The method of multiple time scale is applied to solve the non-linear differential equations describing the system up to the second-order approximation. All possible resonance cases at this approximation order are extracted. The stable/unstable periodic solutions are determined and are presented through frequency response plots. The analytical results are verified by comparing them with those of numerical integration of the modal equations. The influence of different parameters on the dynamic behavior of the composite laminated piezoelectric rectangular plate is studied. Variation of the some parameters leads to multivalued amplitudes and hence to jump phenomena. A comparison with the available published work is reported.

show abstract

“…The stability of the system is investigated using both phase-plane method and frequency response curves. Sayed and Hamed [20] studied the response of a two-degreeof-freedom 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.…”

Section: Introductionmentioning

confidence: 99%

Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

Sayed

Mousa

2013

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

An analytical investigation of the nonlinear vibration of a symmetric cross-ply composite laminated piezoelectric rectangular plate under parametric and external excitations is presented. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations describing the system up to and including the second-order approximation. All possible resonance cases are extracted at this approximation order. The case of 1 : 1 : 3 primary and internal resonance, whereΩ3≅ω1,ω2≅ω1, andω3≅3ω1, is considered. The stability of the system is investigated using both phase-plane method and frequency response curves. The influences of the cubic terms on nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate are studied. The analytical results given by the method of multiple time scale is verified by comparison with results from numerical integration of the modal equations. Reliability of the obtained results is verified by comparison between the finite difference method (FDM) and Runge-Kutta method (RKM). It is quite clear that some of the simultaneous resonance cases are undesirable in the design of such system. Such cases should be avoided as working conditions for the system. Variation of the parametersμ1,μ2,α7,β8,ω1,ω2,f1,f2leads to multivalued amplitudes and hence to jump phenomena. Some recommendations regarding the different parameters of the system are reported. Comparison with the available published work is reported.

show abstract

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

Cited by 52 publications

References 11 publications

Research on chaos and nonlinear rolling stability of a rotary-molded boat

Research on chaos and nonlinear rolling stability of a rotary-molded boat

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

Contact Info

Product

Resources

About