On the Vibrational Analysis for the Motion of a Rotating Cylinder

Bek, M. A.; Amer, T. S.; Abohamer, M.K.

doi:10.1007/978-3-030-77306-9_1

Cited by 2 publications

(1 citation statement)

References 5 publications

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“…The parametric form of the quickest-descent directrix for the algebraic equation is obtained. On the other hand, the vibrational motion of a rolling cylinder in a circular curve is examined in [32]. The governing EOM are derived and solved using the MMS.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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

2022

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The dynamical motion of a rolling cylinder and its stability analysis: analytical and numerical investigation

Amer

2022

Arch Appl Mech

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The present paper addresses the dynamical motion of two degrees-of-freedom (DOF) auto-parametric system consisting of a connected rolling cylinder with a damped spring. This motion has been considered under the action of an excitation force. Lagrange's equations from second kind are utilized to obtain the governing system of motion. The uniform approximate solutions of this system are acquired up to higher order of approximation using the technique of multiple scales in view of the abolition of emerging secular terms. All resonance cases are characterized, and the primary and internal resonances are examined simultaneously to set up the corresponding modulation equations and the solvability conditions. The time histories of the amplitudes, modified phases, and the obtained solutions are graphed to illustrate the system's motion at any given time. The nonlinear stability approach of Routh–Hurwitz is used to examine the stability of the system, and the different zones of stability and instability are drawn and discussed. The characteristics of the nonlinear amplitude for the modulation equations are investigated and described, as well as their stabilities. The gained results can be considered novel and original, where the methodology was applied to a specific dynamical system.

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On the Vibrational Analysis for the Motion of a Rotating Cylinder

Cited by 2 publications

References 5 publications

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

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

The dynamical motion of a rolling cylinder and its stability analysis: analytical and numerical investigation

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