Abstract: In this paper, we studied a method of averaging which decide a uniform valid solution for nonlinear equation and got the, modified forms for KB, method (Krylov-Bogoliubov method)and KBM method (Krytov-Bogoliubov-Mitropolski method). Through the comparison of two examples with the method of multiple scales it can be shown that the modifies averaging methods here are uniformly valid and thereby the applied area of the methodof averaging are extended.

Key words: composite, shear deformation plates, Kármán equations, KB method, KBM method, method of multiple scales, uniformlyvalid solution