On the solution of the unforced damped duffing oscillator with no linear stiffness term

Panayotounakos, DE; Panayotounakou, AD; Vakakis, AF

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Panayotounakou, AD	en
dc.contributor.author	Vakakis, AF	en
dc.date.accessioned	2014-03-01T01:18:10Z
dc.date.available	2014-03-01T01:18:10Z
dc.date.issued	2002	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14833
dc.subject	Asymptotic solutions	en
dc.subject	Duffing oscillator	en
dc.subject	Nonlinear ordinary differential equations	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Approximation theory	en
dc.subject.other	Asymptotic stability	en
dc.subject.other	Bessel functions	en
dc.subject.other	Damping	en
dc.subject.other	Integral equations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Oscillators (electronic)	en
dc.subject.other	Stiffness	en
dc.subject.other	Abel equations	en
dc.subject.other	Duffing oscillator	en
dc.subject.other	Emdem-Fowler equations	en
dc.subject.other	Functional transformations	en
dc.subject.other	Mathematical transformations	en
dc.title	On the solution of the unforced damped duffing oscillator with no linear stiffness term	en
heal.type	journalArticle	en
heal.identifier.primary	10.1023/A:1014925032022	en
heal.identifier.secondary	http://dx.doi.org/10.1023/A:1014925032022	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	Using a series of functional transformations we reduce the unforced, damped Duffing oscillator to equivalent equations of the Abel and Emden-Fowler classes. Taking into account the known exact analytic solutions of these equivalent equations we prove that there does not exist an exact analytic solution of the damped, unforced Duffing oscillator in terms of known (tabulated) analytic functions. It follows that a new class of solutions must be defined for solving this problem 'exactly'. Finally, a new approximate solution of the intermediate integral of the damped Duffing oscillator with weak damping is constructed.	en
heal.publisher	KLUWER ACADEMIC PUBL	en
heal.journalName	Nonlinear Dynamics	en
dc.identifier.doi	10.1023/A:1014925032022	en
dc.identifier.isi	ISI:000174762100001	en
dc.identifier.volume	28	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	16	en