Nonlinear Dynamics

, Volume 91, Issue 4, pp 2485–2502 | Cite as

On the vibrational analysis for the motion of a harmonically damped rigid body pendulum

Original Paper


The present work outlines the investigation of a damped harmonically excited spring pendulum which moves in an elliptic path with constant angular velocity. A rigid body is attached with a damped spring and has a linear force acted along the pendulum arm. The multiple scales technique was utilized to obtain the asymptotic solutions for the governing equations of motion up to the third approximation. Some resonance cases have been classified in view of the attained modulation equations. The solvability conditions for the steady-state solutions are obtained. The time history of the attained solutions is represented graphically and compared with the numerical solutions of the governing equations of motion for suitable physical parameters of the considered dynamical model. Moreover, the resonance curves for these solutions are plotted for the same parameters.


Harmonically excitation Resonances Perturbation methods Poincaré map 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceTanta UniversityTantaEgypt
  2. 2.Department of Physics and Engineering Mathematics, Faculty of EngineeringTanta UniversityTantaEgypt
  3. 3.School for Marine Science and TechnologyUniversity of MassachusettsNew BedfordUSA

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