Construction of simplified equations of nonlinear dynamics of plates and shallow shells by the averaging method (Q1821602)

A sequential procedure for deriving of equations of Berger type is described that relies upon the method of averaging for rectangular and circular isotropic plates and isotropic and sandwich shallow shells. It is shown that the smallness of the second invariant of the strain tensor is random in nature. The Berger hypothesis holds in pure form only for isotropic single-layer and transversely-isotropic sandwich plates, while the averaging idea is necessary for the sequential construction of a simplified Berger theory.