Stability of three degrees-of-freedom auto-parametric system

He, Ji‐Huan; Amer, T. S.; Abolila, Amany F; Galal, A. A.

doi:10.1016/j.aej.2022.01.064

Cited by 46 publications

(22 citation statements)

References 44 publications

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“…To check the stability of the system, 46–48 we need to obtain the solvability conditions and the modification equations for the acquired solutions. Therefore, we will examine the two cases of the primary external resonance that occurs simultaneously, that is, we consider a combination of p1≈1 and p2≈ ω which describes the nearness of p1 and p2 to 1 and ω, respectively.…”

Section: Resonance Cases and Stability’s Evaluationmentioning

confidence: 99%

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

Amer

Tian

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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This work focuses on vibration alleviation and energy harvesting in a dynamical system of a spring-pendulum. The structure of the pendulum is modified using an independent electromagnetic harvesting system. The harvesting depends on the oscillation of a magnet in a coil. An endeavor has been made to get both the energy harvesting and mitigation of vibration efficacy of the harvester. The governing kinematics equations are derived using Lagrange’s equations and are solved asymptotically using the multiple scales method to achieve the intended outcome as new and precise results. The resonance states are classified, and the influence of various parameters of the studied system is analyzed. Fixed points at steady states are categorized into stable and unstable. The time behavior of the solutions, the modified amplitudes, and phases are examined and interpreted in the light of their graphical plots. Zones of stability and instability are concerned, in which the system’s behavior is stable for a wide range of used parameters. This model has become essential in recent times as it uses control sensors in industrial applications, buildings, infrastructure, automobiles, and transportation.

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Section: Resonance Cases and Stability’s Evaluationmentioning

confidence: 99%

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

Amer

Tian

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

show abstract

“…This section classifies various cases of resonance, investigates two of them, and derives ME in the context of these cases. When the denominators of the foregoing approximate second or third orders solutions tend to zero, resonance cases can be distinguished [35]. Therefore, we can classify them as principal primary external and internal resonances which can be done when 1 ≈ ω 1 and…”

Section: Resonance Requirements and Modulation Equations (Me)mentioning

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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“…The harmonic response analysis of different stiffness, damping, and mass distribution is carried out in ABAQUS [8]. Jihuan He, et.al [9] studied the dynamical response of a vibrating three degrees-of-freedom (DOF) autoparametric system near resonance.…”

Section: Introductionmentioning

confidence: 99%

Research on the effects of raft on vibration isolation

Zhang

Liu

Tan

et al. 2022

J. Phys.: Conf. Ser.

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The floating raft vibration isolation system includes upper and lower isolators and middle raft. As one of the most important parts that affect the performance of vibration isolation, the raft is usually assumed to be an undamped or viscous damping structure in the analysis, which is different from the actual situation. To study the effects of raft with hysteresis damping characteristics, a three-freedom complex stiffness mechanical model was built, and an approach for calculating the raft's force transmission rate was derived from impedance methods. Based on the mechanical model and a large-sized floating raft, we analysed the effects of raft mass, stiffness and damping on vibration isolation through numerical calculation. Results show that increasing raft mass improved vibration isolation over most frequency ranges; increase in raft stiffness contributed to improved isolation performance over frequency ranges near its low-order natural frequencies, while reduced the performance over higher frequency ranges; and greater raft damping led to enhanced vibration isolation at its natural frequencies and higher frequency ranges.

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Stability of three degrees-of-freedom auto-parametric system

Cited by 46 publications

References 44 publications

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

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

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

Research on the effects of raft on vibration isolation

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