Hybrid-Galerkin perturbation method for forced oscillations of the Duffing equation

✍ Scribed by Robert J. Telban; James F. Geer; James M. Pitarresi

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 298 KB
• Volume: 14
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/0895-7177(90)90159-k

✦ Synopsis

Perturbation approximations with the "small" coefficient e are developed for the Duffing equation ij + 2&plJ + w:lJ + calJ3 = &F sin Ot, e>O, by the method of multiple time scales. Solutions are generated for the problem of nonresonant excitation (n not near w,) and for the problem of resonant excitation (n near w,). A two term expansion is derived for the case of nonresonant excitation, with both one and two term expansions resulting for the case of resonant excitation. The Hybrid-Galerkin perturbation method is then applied to each of the perturbation solutions derived. In each case the resultant Hybrid-Galerkin solution is compared to its corresponding perturbation solution for various values of E and R. Both methods are also compared to a fourth-order Runge-Kutta solution of the given differential equation.