Analyzing the motion of a forced oscillating system on the verge of resonance

Ghanem, Sewalem; Amer, T. S.; Amer, W. S.; Elnaggar, Shimaa; Galal, A. A.

doi:10.1177/14613484221142182

Cited by 9 publications

(9 citation statements)

References 39 publications

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“…Referring to the plotted curves of the amplitudes h j ðτÞ ðj ¼ 1; 2; 3Þ and the modified phases θ j ðτÞ, one can present the projection of these curves in the planes θ j h j for the same considered values of the damping and frequency parameters, as seen in Figures 14,15,16,17,18,and 19. Decay waves are noted for the graphed curves in Figures 14, 15, 16, 17, periodic waves are observed in Figure 18(a) and (b), while spiral curves heading towards one point are drawn in Figures 18(a) and 19.…”

Section: Evaluation Of Resonancementioning

confidence: 99%

On the influence of an energy harvesting device on a dynamical system

Amer,

Arab,

Galal

2024

Journal of Low Frequency Noise, Vibration and Active Control

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This article studies the motion of a three degrees-of-freedom (DOF) dynamical system, which consists of two parts, a dynamic part, and an electromagnetic harvesting device. The composition of the system depends on the magnet oscillating in the coil of this device. An electric potential is exerted because of the electromotive force to obtain energy harvesting (EH). Lagrange's equations (LE) are used to derive the system’s equations of motion (EOM), which are solved analytically up to a third-order of approximation using the multiple-scales method (MSM). These solutions are considered novel, in which the mentioned method is applied to a novel dynamical system. The gained are confirmed through comparison with the numerical solutions of the EOM to reveal a high degree of consistency. To establish the system’s solvable conditions and modulation equations (ME), three scenarios of primary external resonance are investigated simultaneously. Certain diagrams of time histories for the amplitudes and phases of the examined dynamical system are plotted to show their behaviors at any given instance of time. The Routh–Hurwitz criteria (RHC) are used to establish the stability and instability regions in light of the graphs of resonance response curves. The presence of an energy harvester in dynamic devices helps us to convert vibrational motion into electrical energy that can be exploited in several applications in a variety of daily tasks, including structural and environmental monitoring, military applications, space exploration, and remote medical sensing.

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Section: Evaluation Of Resonancementioning

confidence: 99%

On the influence of an energy harvesting device on a dynamical system

Amer,

Arab,

Galal

2024

Journal of Low Frequency Noise, Vibration and Active Control

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“…9,10 Vibrational motions can be studied by transforming the motion into equations that may be solved, studying their stability areas and the responsibilities of various parameters of the solution to find the best possible solutions. [11][12][13] The vibrational motions are noted in the movement of some pendulums on various trajectories and many other examples in daily life. [14][15][16][17][18] It should be highlighted that many researchers have become interested in the movement of damped elastic pendulums along various pathways.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the stability of a two degrees-of-freedom dynamical system

Amer

Ismail

Amer

2023

Journal of Low Frequency Noise, Vibration and Active Control

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This work studies a two degrees-of-freedom (DOF) dynamical system whose governing system is solved analytically using the multiple scales approach (MSA). The solvability requirements are obtained in light of the elimination of secular terms. All resonance states are classified to understand the equilibrium of the dynamical system. Two of them are examined in parallel to get the associated equations for the system’s modulation. All probable fixed points are identified at the states of stability and instability using the criteria of Routh-Hurwitz (RH). The curves of resonance and the system’s behavior during the motion are plotted and analyzed. The numerical solutions (NS) of the governing system are obtained using the method of Runge-Kutta fourth-order, and they are compared with the analytical solutions (AS). The comparison reveals high consistency between them and proves the accuracy of the MSA. To determine the positive effects of different parameters on the motion, stability zones are studied from the perspective of their graphs. The applications of such works are very important in our daily lives and were the reason for the development of several things, including protection from earthquakes, car shock absorbers, structure vibration, human walking, television towers, high buildings, and antennas.

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“…In [34], RHC are used to explore the stability and instability zones, which are subsequently studied in terms of steady-state solutions. In [35], the authors obtained analytical solutions of an oscillating 2DOF dynamical system using MSA. All possible FP are determined in view of the examined resonance cases, while the stability of the triple pendulum is investigated using the nonlinear stability analysis approach in [36].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a forced vibrating planar motion of a spring pendulum

Amer

Galal

2023

Preprint

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This work studies the nonlinear movement of a two degrees-of-freedom (DOF) spring pendulum that is dampened and affected by a torque and harmonic force externally. It is presumed that the spring’s pivot point travels along an elliptic route. Lagrange's equations are utilized to generate the regulating system of motion. The multiple-scales approach (MSA) is used to gain the system’s analytic solutions up to the third approximation. Therefore, all resonance cases that have emerged are categorized, wherein two of them are scrutinized at once. As a result of the removal of secular terms, the solvability constraints are attained and then the steady-state solutions are investigated. The examined motion's temporal evolution, the resonance response curves, and the solutions at the steady-state are all depicted graphically. In compliance with the Routh-Hurwitz criteria (RHC), all possible fixed points (FP) for the cases of steady and unsteady are found and displayed. The stability zones are examined and analysed to estimate the effect of various factors on the system’s behavior. This model has gained prominence recently due to its industrial uses in fields including construction, infrastructure, transportation, and vehicles.

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Analyzing the motion of a forced oscillating system on the verge of resonance

Cited by 9 publications

References 39 publications

On the influence of an energy harvesting device on a dynamical system

On the influence of an energy harvesting device on a dynamical system

Evaluation of the stability of a two degrees-of-freedom dynamical system

Dynamical analysis of a forced vibrating planar motion of a spring pendulum

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