The phenomenon of parametric resonance in a linear system arising from a periodic modulation of its parameter is investigated both analytically and with the help of a computer simulation based on the educational software package PHYSICS OF OSCILLATIONS (see in the web http://www.aip.org/pas). The simulation experiments aid greatly an understanding of basic principles and peculiarities of parame...

Parametric excitation refers to dynamics problems in which the forcing function enters into the governing differential equation as a variable coefficient. Evolutionary dynamics refers to a mathematical model of natural selection (the “replicator” equation) which involves a combination of game theory and differential equations. In this paper we apply perturbation theory to investigate parametric...

Consider a one-mass system with two degrees of freedom, nonlin-early coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable a stable periodic solution...

This paper investigates the parametric excitation of a micro-pipe conveying fluid suspended between two symmetric electrodes. Electrostatically actuated micro-pipes may become unstable when the exciting voltage is greater than the pull-in value. It is demonstrated that the parametric excitation of a micro-pipe by periodic (ac) voltages may have a stabilizing effect and permit an increase of the...

In this study, synchronization phenomena observed from coupled van der Pol oscillators involving periodically forced capacitors are investigated. Firstly, we confirm effects of parametric excitation on synchronization. Next, we investigate behavior of parametric excitation in coupled system. By carrying out computer calculations for two to five subcircuits cases, various interesting synchroniza...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...

Spin motive force generated by parametrically excited magnetization dynamics is numerically investigated. We calculate spin in a permalloy disk under an ac magnetic field with twice the ferromagnetic resonance frequency parallel to static based on Landau–Lifshitz–Gilbert equation. found that large originating from standing waves driven parametric excitation appears system. The observed time dep...