We study a hard regime of stimulation of two-frequency oscillations in the main resonance equation with a fast oscillating external force: εiψ ′ + |ψ| 2 ψ = exp (it 2 /(2ε)), 0 < ε ≪ 1. This phenomenon is caused by resonance between an eigenmode and the external force. The asymptotic solution before, inside and after the resonance layer is studied in detail and matched.

We study the stability of a thin membrane (of zero bending rigidity) with vortex sheet as nonlinear eigenvalue problem in parameter space mass (${R}_{1}$) and pretension (${T}_{0}$). With both ends fixed light membranes become unstable by divergence instability heavy lose flutter for ${T}_{0}$ that increases ${R}_{1}$. leading edge trailing free, or edges eigenmodes transition shape across boun...

A number of approximations have been proposed to estimate basic hydrodynamic quantities, in particular the frequency a limit cycle. One these, RZIF (for Real Zero Imaginary Frequency), calls for linearizing governing equations about mean flow and estimating as imaginary part leading eigenvalue. further reduction, SCM Self-Consistent Model), approximates well, resulting only from nonlinear inter...