Vibration of angle-ply laminated plates with twist by Rayleigh–Ritz procedure Original Research Article

Considering transverse strain and rotary inertia, an analytical method for vibration of an angle-ply laminated plate with twist is proposed. An accurate strain–displacement relationship of a twisted plate is derived by the Green strain tensor on the general shell theory and the Mindlin plate theory. The equilibrium for free vibration is given out by the principle of virtual work and is solved by using the Rayleigh–Ritz procedure with normalized characteristic orthogonal polynomials generated by the Gram–Schmidt process. The convergence and the accuracy of the present method are investigated. The parametric effects of a fibre angle, a twist angle, a thickness ratio and a stacking sequence on vibration frequencies and mode shapes of laminated plates are studied.