Vibration reduction of multi-parametric excited spring pendulum via a transversally tuned absorber

Eissa, M.; Kamel, M.; EL-Sayed, A. T.

doi:10.1007/s11071-009-9635-4

Cited by 19 publications

(3 citation statements)

References 19 publications

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“…The effects of the longitudinal absorber on the system are described through the obtained results. This model is modified in [18] by connecting the spring pendulum to the transverse absorber. So, the motion has three degrees of freedom under multiparametric excitations.…”

Section: Introductionmentioning

confidence: 99%

The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

Amer

2017

Advances in Mathematical Physics

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In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

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Section: Introductionmentioning

confidence: 99%

The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

Amer

2017

Advances in Mathematical Physics

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“…The analytical solutions were verified by comparing them with the numerical ones. From another perspective, the transversal tuned absorber of an exciting spring pendulum was used to control the system vibrations due to the existence of influential excitation forces, e.g., [10,11]. A numerical investigation of the positive impact of the absorber on the dynamical behaviour is presented.…”

Section: Introductionmentioning

confidence: 99%

“…These functions depend only upon the time scale 2 τ . Therefore, we can write them as the following notations of polar forms: ordinates φ and γ according to the hypotheses ( 9) and (10).…”

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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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