Analysis of Non-Linear Non-Stationary Oscillations

Abstract

<p>The behaviour of certain non-linear oscillatory systems are studied analytically. These systems are of the "separable" type i.e. they can be modelled using linear frequency-dependent networks, frequency independent non-linear resistive networks, and non-linear reactive networks.</p> <p>When the time-lags in an oscillatory system are negligibly small, the system may be described by a non-linear differential equation. If the time-lags cannot be ignored, the system may be described by a non-linear difference-differential equation.</p> <p>The exact analytical solutions of non-linear differential or difference-differential equations are not known, except in rare cases. However, with appropriate restrictions, analytical approximations may be found.</p> <p>In this work, analytical approximations are developed for treating second-order, forced or unforced weakly non-linear oscillatory systems, as well as a restricted class of unforced highly non-linear systems. These systems may be of the degenerative or regenerative type. Also, the case when time-lags exist in the system, has been studied analytically.</p> <p>The analytical results are verified either experimentally or by numerical simulation.</p>