Asymptotic analysis of geometrically nonlinear vibrations of long plates

In this paper, we performed an asymptotic analysis for equations of the classical plate theory with the von Kármán strains under the assumption that the width of the plate is small compared with its length. A system of one-dimensional equations, which describes the nonlinear interaction of flexural and torsional vibrations of beams, was derived. This enables the possibility of exciting torsional vibrations by flexural vibrations. This possibility was analyzed for a model problem, when flexural vibrations occur in normal modes.