An efficient higher order non-polynomial Quasi 3-D theory for dynamic responses of laminated composite plates

In this work, a new simple Quasi 3-D theory based on linear variation of transverse displacement along the thickness of plate is proposed for free and forced vibration of laminated composite plates. The theory satisfies both zero transverse shear stress conditions at top and bottom surfaces of the plate and non-linear distribution of transverse shear stresses across the thickness of plate. Therefore, the necessity of shear correction factor can be avoided. The governing equations of motion are obtained by using Lagrange equation. The finite element discretization of the plate is presented by considering an eight noded serendipity element. The forced vibration of the plate under different time dependent loads is also illustrated. The Newmark's time integration techniques is employed to obtain the forced response of laminated plate. The adaptability of the proposed theory is demonstrated by solving several numerical examples and validated with available results. The effect of various parameters like thickness ratio, aspect ratio, modulus ratio and temperature on fundamental frequency of plate is investigated through several examples. The results shows that, the free vibration regime of the plate is greatly affected by the duration of blast load on plate. The theory gives an excellent agreement with available literature.