A General Mode Approach to Nonlinear Flexural Vibrations of Laminated Rectangular Plates

This paper is concerned with an analytical investigation of free flexural large-amplitude vibrations of rectangular composite plates. Solutions of the dynamic von Karman-type equations of these plates in conjunction with different boundary conditions are obtained by use of generalized double Fourier series and the method of harmonic balance. Numerical calculations for multimode vibrations of unsymmetric cross-ply and angle-ply plates having various material properties and lamination geometry were performed for all-clamped and all-simply supported stress-free edges. The present results indicate that the effect of coupling of vibrating modes on nonlinear frequencies is not appreciably significant for isotropic plates but considerably significant for composite plates, especially for clamped high-modulus laminates.