Single-frequency oscillations of non-linear systems with distributed parameters

✍ Scribed by L.D. Akulenko; S.V. Nesterov

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 772 KB
• Volume: 62
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(98)00088-4

✦ Synopsis

A weakly non-linear oscillatory system with distributed parameters is investigated. An asymptotic method of consu'ucting a solution, which describes the oscillatory motions of the single-mode (single-frequency) approximation, which is usually implemented in practical problems, is described and justified. Constructive suff~ent conditions are formulated and the closeness of the approximate single-frequency solution to the exact solution in an asymptotically long time interval is proved. Poss~le extensions of the structure of the perturbing functions are considered and the case of the fmite-mode approximation is investigated. Solutions of specific problems, which are of practical interest, are constructed to illustrate the effectiveness of the single-frequency approximation method.