Influence of geometrical nonlinearity on the waves propagating through a thin, free plate : PMM vol. 43, no. 6, 1979, pp. 1089–1094

Exact wave solutions of the equations of motion of a thin plate are obtained for the one-dimensional case of a first approximation model. The dependence of the velocity of propagation of flexural-longitudinal waves on their frequency is computed for different values of the amplitude of the bending components. The nonlinear character of the relation connecting the deformations and displacements in the theory of thin shells may give rise to effects which cannot be described in terms of the linear approximation even in those cases when the Hooke's law still holds [1]. The estimation of the magnitude of the displacements at which the effects caused by the geometrical nonlinearity become apparent, is of interest.