Exact analytical solutions for forced undamped duffing oscillator

Publikationstyp
Journal Article
Publikationsdatum
2016-06-22
Sprache
English
Author
Starossek, Uwe 
Institut
Baustatik B-4 
TORE-URI
http://hdl.handle.net/11420/5462
Enthalten in
International journal of non-linear mechanics 
Volume
85
Start Page
197
End Page
206
Citation
International Journal of Non-Linear Mechanics (85): 197-206 (2016-10-01)
Publisher DOI
10.1016/j.ijnonlinmec.2016.06.008
Scopus ID
2-s2.0-84981277915
Publisher
Elsevier Science
The steady-state response of an undamped Duffing oscillator to periodic external forces is studied. The forcing functions are chosen such that the time course of the displacement can be described by exact analytical expressions. The displacement and forcing functions are governed by Jacobi elliptic functions and thus are periodic but generally non-harmonic. The parameter of the elliptic functions is deliberately chosen. For certain parameter choices, exact analytical expressions are found for the frequency–amplitude relation.
Schlagworte
Exact analytical frequency–amplitude relation
Jacobi elliptic functions
Non-harmonic periodic loading
Nonlinear oscillator
DDC Class
720: Architektur