โ Scribed by Yu.F. Golubev
No coin nor oath required. For personal study only.
A technique based on the composition of elementary phase fluxes~; 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.
๐ SIMILAR VOLUMES
Free oscillations of a non-linear system having two weakly coupled degrees of freedom in which an internal resonance may occur are treated with a modified version of the K-B-M averaging method. The method presented permits one to obtain a first approximation of the solution very easily in comparison
The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving th