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Exact analytical solutions for forced cubic restoring force oscillator
Publikationstyp
Journal Article
Date Issued
2015-11-12
Sprache
English
Author(s)
Starossek, Uwe
Institut
TORE-URI
Journal
Volume
83
Issue
4
Start Page
2349
End Page
2359
Citation
Nonlinear Dynamics 4 (83): 2349-2359 (2016-03-01)
Publisher DOI
Scopus ID
Publisher
Springer Science + Business Media B.V
A strongly nonlinear oscillator is considered in which the restoring force is a purely cubic function of the displacement variable. Its forced undamped oscillation response to non-harmonic periodic loading is studied. The loading function is derived from the free oscillation response whose time course follows a Jacobi elliptic function. It is chosen such that exact analytical solutions are obtained for the steady-state response and the amplitude–frequency relation. The equation describing the amplitude–frequency relation is a cubic polynomial equation. Its solutions are presented and further discussed by means of diagrams that illustrate the equilibrium of dynamic forces. Furthermore, results of a numerical study are presented concerning the stability of the identified analytical steady-state solutions. The numerical study also reveals the existence of a subharmonic steady-state response with a period three times the period of the loading function. The general approach of using non-harmonic loading functions is transferable to other types of nonlinear oscillators.
Subjects
Amplitude–frequency relation
Jacobi elliptic functions
Non-harmonic periodic loading
Nonlinear oscillator
DDC Class
600: Technik
620: Ingenieurwissenschaften
690: Hausbau, Bauhandwerk