Influence of the Motion of a Spring Pendulum on Energy-Harvesting Devices

Abohamer, M.K.; Awrejcewicz, Jan; Starosta, R.; Amer, T. S.; Bek, M. A.

doi:10.3390/app11188658

Cited by 52 publications

(28 citation statements)

References 44 publications

(65 reference statements)

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“…Since the detuning parameters are known as the distances from the oscillations to the strict resonance [35,36], we can use the small parameter ε to express these parameters as follows:…”

Section: The Perturbation Techniquementioning

confidence: 99%

The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

et al. 2022

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This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three degrees of freedom. It consists of a damped Duffing oscillator as a primary system attached to a damped spring pendulum as a secondary system. Lagrange’s equations are utilized to acquire the equations of motion according to the number of the system’s generalized coordinates. The perturbation technique of multiple scales is applied to provide the solutions to these equations up to a higher order of approximations, with the aim of obtaining more accurate novel results. The categorizations of resonance cases are presented, in which the case of primary external resonance is examined to demonstrate the conditions of solvability of the steady-state solutions and the equations of modulation. The time histories of the achieved solutions, the resonance curves in terms of the modified amplitudes and phases, and the regions of stability are outlined for various parameters of the considered system. The non-linear stability, in view of both the attained stable fixed points and the criterion of Routh–Hurwitz, is investigated. The results of this paper will be of interest for specialized research that deals with the vibration of swaying buildings and the reduction in the vibration of rotor dynamics, as well as studies in the fields of mechanics and space engineering.

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“…Since the detuning parameters are known as the distances from the oscillations to the strict resonance [35,36], we can use the small parameter ε to express these parameters as follows:…”

Section: The Perturbation Techniquementioning

confidence: 99%

The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

et al. 2022

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“…Table 1 Demonstrates the positions of the PFP and the CFP for the response curves at σ 2 0 and ω 1 (1.2, 1.5, 1.7)for the curves of Fig. 5.1 (40) However, the essential prerequisites of the stability for specific solutions at the case of steady-state based on the Routh-Hurwitz criterion [42,43] are…”

Section: Data Availabilitymentioning

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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“…In this section, we will demonstrate the properties of nonlinear amplitude for the system of Equations (37) and investigate their stabilities [28][29][30]. Then, the transformations below are taken into account…”

Section: Non-linear Analysismentioning

confidence: 99%

Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

et al. 2021

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This work looks at the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity. These pendulums have different lengths and are attached with different masses. Lagrange’s equations are employed to derive the governing kinematic system of motion. The multiple scales technique is utilized to find the desired approximate solutions up to the third order of approximation. Resonance cases have been classified, and modulation equations are formulated. Solvability requirements for the steady-state solutions are specified. The obtained solutions and resonance curves are represented graphically. The nonlinear stability approach is used to check the impact of the various parameters on the dynamical motion. The comparison between the attained analytic solutions and the numerical ones reveals a high degree of consistency between them and reflects an excellent accuracy of the used approach. The importance of the mentioned model points to its applications in a wide range of fields such as ships motion, swaying buildings, transportation devices and rotor dynamics.

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Influence of the Motion of a Spring Pendulum on Energy-Harvesting Devices

Cited by 52 publications

References 44 publications

The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

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

Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

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