Free vibration of thick generally laminated cantilever quadrilateral plates

Abstract

Free vibration of plate structures of various material systems has been vastly studied. Transverse shear can play an important role even in thin laminated structures and therefore must be included in the analysis. A method applicable to the study of generally laminated, thick, skew, trapezoidal plates is developed as there appears to be limited information available in this area. Using Chebychev polynomials as displacement functions in the Rayleigh-Ritz method, the first-order shear deformation theory is utilized to account for the transverse shear effects. All appropriate inertia terms are retained. Boundary conditions are enforced by the appropriate use of distributed linear and rotational springs along the edges. Thus, the method is applicable to any supported quadrilateral plate but is applied to cantilever plates in this study. After the validity of the method is established through comparison to published results, an extensive study is made of thick, symmetrically laminated and unsymmetrically laminated, cantilever, skew, trapezoidal plates.