One mechanism of hard excitation of oscillations in nonlinear flutter systems

Abstract

In this paper, we consider so-called finite-dimensional flutter systems, i.e., systems of ordinary differential equations that come about, first, from the Galerkin approximation of certain boundary value problems of the aeroelasticity theory and, second, in a number of radiophysics applications. Small parametric oscillations of these equations in the case of 1: 3 resonance are studied. By combining analytical and numerical methods, it is found that this resonance can cause the hard excitation of oscillations. Namely, for flutter systems, there is shown the possibility of emerging, in parallel with the stable equilibrium zero state, both stable invariant tori of arbitrary finite dimension and chaotic attractors.