Dynamics and Stability of a Two Degree of Freedom Oscillator With an Elastic Stop

[+] Author and Article Information
Madeleine Pascal

Laboratoire Systèmes Complexes, Université d’Evry Val d’Essonne et CNRS FRE 2494, 40 rue du Pelvoux, 91020 Evry cedex, Francempascal@iup.univ-evry.fr

J. Comput. Nonlinear Dynam 1(1), 94-102 (May 16, 2005) (9 pages) doi:10.1115/1.1961873 History: Received April 19, 2005; Revised May 16, 2005

A two degree of freedom oscillator with a colliding component is considered. The aim of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes to a finite value to an infinite one. Several cases are considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are found in analytical form. In the case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Double oscillator

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Figure 2

Actual periodic impact solution (rigid impact, unforced system)

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Figure 3

Stability of the periodic solution (rigid impact, unforced system)

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Figure 4

Bifurcation value of the period (rigid impact, unforced system)

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Figure 5

Actual periodic solution (rigid impact, forced system)

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Figure 6

Bifurcation values of the period T=2π∕ω (rigid impact, forced system)




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