Resonances in linear one-degree-of-freedom systems with piecewise-constant parameters

A technique based on the composition of elementary phase fluxes double dagger is proposed for investigating parametric resonance in systems with "large" perturbations, described by second-order linear differential equations with periodic piecewise-constant coefficients. A monodromy matrix is given and a parametric resonance criterion is indicated, which takes into account the possibility of multiple multipliers and the action of dissipative forces. When there is a two-stage dependence of the coefficients on time during one period, regions of parametric resonance are obtained for different types of linear mechanical systems with one degree of freedom. (C) 1999 Elsevier Science Ltd. All rights reserved.