This article is focused on a simple approach for determining the natural frequency and mode shape of laminated angle-ply plates with various shapes by rectangular orthotropy. Since the boundary of the domain for all shapes are not natural to the material coordinate axes it seems appropriate to express the plate displacement amplitude in terms of a polynomial and a general shape function multiplication in the x and y coordinates. The boundary conditions considered are clamped and simply supported edges. The effect of the fiber orientation, layer number, and lamination sequence on the natural frequencies of plates is also considered. The natural frequency determinant has been generated using the classical Rayleigh-Ritz method. The algorithm developed can be used for a wide range of different plate shape having an internal hole, internal ring support, and any aspect ratio by simple programming. The natural frequencies and mode shapes of four cases of plate shape are obtained and some results were compared with those existing in the literature and analytical solution for simply supported rectangular plates with especially orthotropy. POLYM. COM-POS., 32:445-454,

In this paper, force vibration of composite laminate plates subjected to low-velocity impacts are investigated semi-analytically and analytically. Symmetrically angle-ply laminated rectangular, circular and elliptical plates are considered. The simply supported edges boundary condition is considered. Plates were studied based on small deflection thin plate theory. A Hertz Contact Theory models the contact forces between the rigid projectile and the laminated plate.A simple and improved model was developed to calculate force vibration of composite plates. A semi-analytical model was obtained for force vibration of composite laminated plates by the method of Rayleigh-Ritz and modal expansion. Calculations of the impact response in composite material structures are important in damage-tolerant design. The results were compared with the results from the available literature and found to be in good agreement.