Title

The Nonstationary Effects On A Softening Duffing Oscillator

Authors

Authors

C. H. Lu;R. M. Evaniwanowski

Comments

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Abbreviated Journal Title

Mech. Res. Commun.

Keywords

Period-Doubling Bifurcations; Chaotic Motion; Transition; Responses; Pendulum; Mechanics

Abstract

This paper presents a numerical study for the bifurcations of a softening Duffing oscillator subjected to stationary and nonstationary excitation. The nonstationary inputs used are linear functions of time. The bifurcations are the results of either a single control parameter or two control parameters that are constrained to vary in a selected direction on the plane of forcing amplitude and forcing frequency. The results indicate: 1. Delay (memory, penetration) of nonstationary bifurcations relative to stationary bifurcations may occur. 2. The nonstationary trajectories jump into the neighboring stationary trajectories with possible overshoots, while the stationary trajectories transit smoothly. 3. The nonstationary penetrations (delays) are compressed to zero with an increasing number of iterations. 4. The nonstationary responses converge through a period-doubling sequence to a nonstationary limit motion that has the characteristics of chaotic motion. The Duffing oscillator has been used as an example of the existence of broad effects of nonstationary (time dependent) and codimensional (control parameter variations in the bifurcation region) inputs which markedly modify the dynamical behavior of dynamical systems.

Journal Title

Mechanics Research Communications

Volume

21

Issue/Number

6

Publication Date

1-1-1994

Document Type

Article

Language

English

First Page

555

Last Page

564

WOS Identifier

WOS:A1994PN36700003

ISSN

0093-6413

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