Stability and primary simultaneous resonance of harmonically excited non-linear spring pendulum system

Eissa, M.; El-Serafi, S. A.; El-Sheikh, M. M. A.; Sayed, M.

doi:10.1016/s0096-3003(02)00496-4

Cited by 26 publications

(13 citation statements)

References 9 publications

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“…In ship's motion, the nonlinearity brings a whole range of phenomena that are not found in linear analysis. These include multiple solutions, jumps, frequency entrapment, period multiplying bifurcation, dynamic chaos and different resonance cases such as, internal, primary, combination, sub-harmonic and super-harmonic resonance are often occur [4,5,8,11,12].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of a nonlinear coupled pitch–roll ship

Kamel

2007

Mathematics and Computers in Simulation

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Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of a nonlinear coupled pitch–roll ship

Kamel

2007

Mathematics and Computers in Simulation

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“…On the other hand, the chaotic motion of 2-DOF weakly nonlinear spring pendulum system for a fixed and moving suspension point is examined in [4] and [5], respectively, to reveal their chaotic behaviors near resonance with respect to the used parameters. The ASM [6] is used in [7] to explore the stability of a nonlinear spring pendulum, in which the improvement of this work is investigated in [8] when the pendulum is subjected to an external force.…”

Section: Introductionmentioning

confidence: 99%

The stability of 3-DOF triple-rigid-body pendulum system near resonances

et al. 2022

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In this article, the motion of three degree-of-freedom (DOF) dynamical system consisting of a triple rigid body pendulum (TRBP) in the presence of three harmonically external moments is studied. In view of the generalized coordinates of the system, Lagrange's equations are used to obtain the governing system of equations of motion (EOM). The analytic approximate solutions are gained up to the third approximation utilizing the approach of multiple scales (AMS) as novel solutions. The solvability conditions are determined in accordance with the elimination of secular terms. Therefore, the arising various resonances cases have been categorized and the equations of modulation have been achieved. The temporal histories of the obtained approximate solutions, as well as the resonance curves, are visually displayed to reveal the positive effects of the various parameters on the dynamical motion. The numerical results of the governing system are achieved using the fourth-order Runge–Kutta method. The visually depicted comparison of asymptotic and numerical solutions demonstrates high accuracy of the employed perturbation approach. The criteria of Routh–Hurwitz are used to investigate the stability and instability zones, which are then analyzed in terms of steady-state solutions. The strength of this work stems from its uses in engineering vibrational control applications which carry the investigated system a huge amount of importance.

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“…Furthermore, they illustrated the unstable motion zone of the system which gotten from the 3 rd -order approximation to become completely coordinated with which acquired from numeral computation. Eissa et al [7][8][9][10] and Sayed [11] applied diversified controllers on the simple and the spring pendulums which showing the sway motion of the ship then; they studied the effects of them. They subjected the two procedures under single-harmonic-stimulation force then they studied the action of the transversal and linear toned absorbed controllers on the existing vibrations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Saturation Controllers for Suppression the Vibration of Nonlinear Spring Pendulum

Amer

EL-Sayed

Younis

et al. 2018

ARJOM

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In this work, we apply the Averaging Method to obtain the theoretical results. The Nonlinear Saturation Controller (NSC) is proposed to decrease the vacillations of the spring pendulum. We investigate the stability of the system nigh the resonance condition by applying the frequency response equations. Numerically, the effects of diversified controller's parameters on the basic system behaviour are studied. The emulation results are attained by utilising Matlab and Maple programs.

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Stability and primary simultaneous resonance of harmonically excited non-linear spring pendulum system

Cited by 26 publications

References 9 publications

Bifurcation analysis of a nonlinear coupled pitch–roll ship

Bifurcation analysis of a nonlinear coupled pitch–roll ship

The stability of 3-DOF triple-rigid-body pendulum system near resonances

Nonlinear Saturation Controllers for Suppression the Vibration of Nonlinear Spring Pendulum

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