Controlling the kinematics of a spring-pendulum system using an energy harvesting device

He, Chun‐Hui; Amer, T. S.; Tian, Dan; Abolila, Amany F; Galal, A. A.

doi:10.1177/14613484221077474

Cited by 96 publications

(34 citation statements)

References 45 publications

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“…The most famous nonlinear oscillators include the pendulum systems [11,12], van der Pol oscillator and Duffing oscillator [13]. The spring-pendulum systems have many applications in satellites, submarines, aircraft, and energy harvesting device [14]. The recent research frontier in the nonlinear vibration theory is the fractal vibration; hence the description of a vibrating system in a fractal space [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

2022

FU Mech Eng

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The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation. This paper gives a systematical analysis of the formulation, and two simplified formulations are suggested. The cubic-quintic Duffing oscillator is used as an example to show extremely simple calculation and remarkable accuracy. It can be used as a paradigm for many other applications, and the one-step solving process has cleaned up the road of the nonlinear vibration theory.

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Section: Introductionmentioning

confidence: 99%

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

2022

FU Mech Eng

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“…It is clear that the functions A j ðj ¼ 1; 2; 3Þ can be determined using the forgoing criteria (41)- (46) which can be represented in the following polar form [40]…”

Section: Resonance Requirements and Equations Of Modulationmentioning

confidence: 99%

“…(48) as well as exhibiting its characteristics. Therefore, the following transformations are considered [45,46]…”

Section: Nonlinear Analysismentioning

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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“…This section's main purpose is to look at the vibrations at steady-state of the studied system. This case is known to occur when transitory processes disappear owing to damping [39,40]. Therefore, we evaluate the left sides in Eqs.…”

Section: Oscillations At the Case Of Steady-statementioning

confidence: 99%

On the solutions and stability for an auto-parametric dynamical system

2022

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The main goal of this study is to look at the motion of a damped two degrees-of-freedom (DOF) auto-parametric dynamical system. Lagrange’s equations are used to derive the governing equations of motion (EOM). Up to a good desired order, the approximate solutions are achieved utilizing the method of multiple scales (MMS). Two cases of resonance, namely; internal and primary external one are examined simultaneously to explore the solvability conditions of the motion and the corresponding modulation equations (ME). These equations are reduced to two algebraic equations, through the elimination of the modified phases, in terms of the detuning parameters and the amplitudes. The kind of stable or unstable fixed point is estimated. In certain plots, the time histories graphs of the achieved solutions, as well as the adjusted phases and amplitudes are used to depict the motion of the system at any instant. The conditions of Routh–Hurwitz are used to study the various stability zones and their analysis. The achieved outcomes are considered to be novel and original, in which the used strategy is applied on a particular dynamical system. The significance of the studied system can be observed in its applications in a number of disciplines, such as swaying structures and rotor dynamics.

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Controlling the kinematics of a spring-pendulum system using an energy harvesting device

Cited by 96 publications

References 45 publications

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

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

On the solutions and stability for an auto-parametric dynamical system

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