STUDY OF A NON-LINEAR OSCILLATOR UNDER PARAMETRIC IMPULSIVE EXCITATION USING A NON-SMOOTH TEMPORAL TRANSFORMATION

✍ Scribed by V.N. Pilipchuk; S.A. Volkova; G.A. Starushenko

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 262 KB
• Volume: 222
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.2067

✦ Synopsis

Solutions of dierential equations of motion for mechanical systems with periodic impulsive excitation are represented in a special form which contains a standard pair of non-smooth periodic functions and possesses the structure of an algebra without division. This form is also suitable in the case of excitation with a periodic series of discontinuities of the ®rst kind. All transformations are illustrated on the Dung oscillator under a parametric non-equidistant pulsed forcing with a dipole-like shift of the impulses, although the technique can be applied to more general cases. An explicit form of analytical solutions has been obtained for periodic regimes. These solutions and numerical simulations indicate a principal role of the impulses' shift. Namely, the system performs periodic, multiperiodic and stochastic-like dynamical regimes if varying a parameter of the shift. The analytical approach is based on the limit of linear system under equidistant distribution of the impulses and asymptotically takes into account the dipole-like shift and non-linearity.