Resonances in linear one-degree-of-freedom systems with piecewise-constantparameters

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