Novel Asymptotic Solutions for the Planar Dynamical Motion of a Double-Rigid-Body Pendulum System Near Resonance

El-Sabaa, F. M.; Amer, T. S.; Gad, H.M.; Bek, M. A.

doi:10.1007/s42417-022-00493-0

Cited by 16 publications

(7 citation statements)

References 33 publications

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“…In the current section, numerous resonance scenarios will be classified using the achieved approximate solutions, which are considered acceptable in so much as the denominators are not equal to nothing [36].…”

Section: Resonance's Classifications and Modulation Equationsmentioning

confidence: 99%

Dynamical Stability of a 3-DOF Auto-Parametric Vibrating System

Amer

Moatimid

Amer

2022

J. Vib. Eng. Technol.

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Purpose This article concentrates on the oscillating movement of an auto-parametric dynamical system comprising of a damped Duffing oscillator and an associated simple pendulum in addition to a rigid body as main and secondary systems, respectively. Methods According to the system generalized coordinates, the controlling equations of motion are derived utilizing Lagrange's approach. These equations are solved applying the perturbation methodology of multiple scales up to higher orders of approximation to achieve further precise unique outcomes. The fourth-order Runge–Kutta algorithm is employed to obtain numerical outcomes of the governing system. Results The comparison between both solutions demonstrates their high level of consistency and highlights the great accuracy of the adopted analytical strategy. Despite the conventional nature of the applied methodology, the obtained results for the studied dynamical system are considered new. Conclusions In light of the solvability criteria, all resonance scenarios are classified, in which two of the fundamental exterior resonances are examined simultaneously with one of the interior resonances. Therefore, the modulation equations are achieved. The conditions of Routh–Hurwitz are employed to inspect the stability/instability regions and to analyze them in accordance with the solutions in the steady-state case. For various factors of the examined structure, the temporary history solutions, the curves of resonance in terms of the adjusted amplitudes and phases, and the stability zones are graphically presented and discussed. Applications The results of the current study will be of interest to wide range experts in the fields of mechanical and aerospace technology, as well as those working to reduce rotors dynamical vibrations and attenuate vibration caused by swinging structures.

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Section: Resonance's Classifications and Modulation Equationsmentioning

confidence: 99%

Dynamical Stability of a 3-DOF Auto-Parametric Vibrating System

Amer

Moatimid

Amer

2022

J. Vib. Eng. Technol.

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“…More recently, El-Sabaa et al considered the planar motion of a twodegree-of-freedom double rigid body pendulum, where the pivot point is constrained to move in a Lissajous curve [11]. The resonances were classified for this system and solvability conditions were identified for the steady-state solutions.…”

Section: Introductionmentioning

confidence: 99%

A compound double pendulum with friction

Williams

2023

Forces in Mechanics

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“…Numerical computations have validated the quantitative outcomes of this study. This method was used in many works [12][13][14][15] to attain the estimated formulas of various vibrational models. The stability of the parametric DO was investigated [16].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of a Damped Harmonic Forced Duffing Oscillator with Time Delay

Moatimid

Amer

2022

Preprint

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This paper is concerned with a time-delayed controller of a damped nonlinear excited Duffing oscillator (DO). Since time-delayed techniques have recently been the focus of numerous studies, the topic of this investigation is quite contemporary. Therefore, time delays of position and velocity are utilized to reduce the nonlinear oscillation of the model under consideration. A much supplementary precise approximate solution is achieved using an advanced Homotopy perturbation method (HPM). The temporal variation of this solution is graphed for different amounts of the employed factors. The organization of the model is verified through a comparison between the plots of the estimated solution and the numerical one which is obtained utilizing the fourth order Runge-Kutta technique (RK4). The outcomes show that the improved HPM is appropriate for a variety of damped nonlinear oscillators since it minimizes the error of the solution while increasing the validation variety. Furthermore, it presents a potential model that deals with a diversity of nonlinear problems. The multiple scales homotopy technique is used to achieve an estimated formula for the suggested time-delayed structure. The controlling nonlinear algebraic equation for the amplitude oscillation at the steady state is gained. The effectiveness of the proposed controller, the time delays impact, controller gains, and feedback gains have been investigated. The realized outcomes show that the controller performance is influenced by the total of the product of the control and feedback gains, in addition to the time delays in the control loop. The analytical and numerical calculations reveal that for certain amounts of the control and feedback signal improvement, the suggested controller could completely reduce the system vibrations.

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Novel Asymptotic Solutions for the Planar Dynamical Motion of a Double-Rigid-Body Pendulum System Near Resonance

Cited by 16 publications

References 33 publications

Dynamical Stability of a 3-DOF Auto-Parametric Vibrating System

Dynamical Stability of a 3-DOF Auto-Parametric Vibrating System

A compound double pendulum with friction

Dynamical Analysis of a Damped Harmonic Forced Duffing Oscillator with Time Delay

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