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 K´arm´an 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 enab-les the possibility of exciting torsional vibrations by flexural vibrations. This possibility was analyzed for a model problem, when flexural vibrations occur in normal modes.