Periodically Forced Duffing's Equation

✍ Scribed by B. Mehri; M. Ghorashi

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 195 KB
• Volume: 169
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1994.1019

✦ Synopsis

Sufficient conditions are established for an equation of the type (x^{\prime \prime}+\alpha x+\beta x^{3}=p(t)) to have periodic solutions, where (p(t)) is periodic. The results are applied to analyze forced vibrations of a mass supported by a non-linear spring. To verify sufficiency of the conditions, a computer program has been prepared, and used to provide results for some examples. The program searches for periodic solutions of the generalized problem of non-linear, non-autonomous, second order differential equations, and draws (x-t) and phase trajectory diagrams for the periodic solutions obtained. These numerical results are in agreement with theoretical expectations.