Abstract
Abstract
Purpose
This article concentrates on the oscillating movement of an auto-parametric dynamical system comprising of a damped Duffing oscillator and an associated simple pendulum in addition to a rigid body as main and secondary systems, respectively.
Methods
According to the system generalized coordinates, the controlling equations of motion are derived utilizing Lagrange's approach. These equations are solved applying the perturbation methodology of multiple scales up to higher orders of approximation to achieve further precise unique outcomes. The fourth-order Runge–Kutta algorithm is employed to obtain numerical outcomes of the governing system.
Results
The comparison between both solutions demonstrates their high level of consistency and highlights the great accuracy of the adopted analytical strategy. Despite the conventional nature of the applied methodology, the obtained results for the studied dynamical system are considered new.
Conclusions
In light of the solvability criteria, all resonance scenarios are classified, in which two of the fundamental exterior resonances are examined simultaneously with one of the interior resonances. Therefore, the modulation equations are achieved. The conditions of Routh–Hurwitz are employed to inspect the stability/instability regions and to analyze them in accordance with the solutions in the steady-state case. For various factors of the examined structure, the temporary history solutions, the curves of resonance in terms of the adjusted amplitudes and phases, and the stability zones are graphically presented and discussed.
Applications
The results of the current study will be of interest to wide range experts in the fields of mechanical and aerospace technology, as well as those working to reduce rotors dynamical vibrations and attenuate vibration caused by swinging structures.
Publisher
Springer Science and Business Media LLC
Subject
Microbiology (medical),Immunology,Immunology and Allergy
Reference41 articles.
1. J. P, Den Hartog, Mechanical vibrations, Courier Corporation (1985).
2. Pars LA (1965) A treatise on analytical mechanics. John Wiley and Sons, New York
3. Koloušek V, Pirner M, Fischer O, Naprstek J (1984) Wind effects on civil engineering, structures. Elsevier, Amsterdam
4. Wu S (2009) Active pendulum vibration absorbers with a spinning support. J Sound Vib 323(1–2):1–16
5. Eissa M, Kamel M, El-Sayed AT (2011) Vibration reduction of a nonlinear spring pendulum under multi external and parametric excitations via a longitudinal absorber. Meccanica 46:325–340
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献