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 Steel and Composite Structures   Volume 26, Number 4, February25 2018, pages 473-484 DOI: https://doi.org/10.12989/scs.2018.26.4.473 Free vibration of cross-ply laminated plates based on higher-order shear deformation theory Saira Javed, K.K. Viswanathan, M.D. Nurul Izyan, Z.A. Aziz and J.H. Lee Abstract     [Buy Article] Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs. Key Words free vibration; higher-order theory; spline; composite plates; cross-ply Address (1) Saira Javed, K.K. Viswanathan, M.D. Nurul Izyan, Z.A. Aziz: UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu Sina Institiute for Scientific & Industrial Research, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia; (2) K.K. Viswanathan: Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box 27235, Safat 13133, Kuwait; (3) J.H. Lee: Department of Naval Architecture & Ocean Engineering, Inha University, 100 inharo, Nam-gu Incheon 22212, South Korea.

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