Natural Vibrations of Laminated and Sandwich Plates

Abstract

An exact analytical solution based on the propagator matrix method and a semianalytical solution based on a higher-order mixed approach (displacement and stress interpolation) have been presented in this paper to evaluate the natural frequencies as well as the stress and displacement mode shapes of simply supported, cross-ply laminated and sandwich plates. Continuity of the transverse stresses and displacements has been maintained at the laminae interfaces. Results have been presented for orthotropic plates, symmetric as well as nonsymmetric cross-ply composite and sandwich laminates. Results from the propagator matrix agree well with the published results for frequencies as well as displacement and stress mode shapes. Furthermore, the frequencies and displacement and stress eigenvectors obtained from the proposed layerwise mixed method are in excellent agreement with those obtained by three-dimensional elasticity theory. Results obtained from the present equivalent single layer theory are in good agreement with those obtained from the displacement based higher order methods. The high accuracy of the present methods is further confirmed by comparing the response of a sandwich plate with significantly different layer properties for which the conventional displacement based formulations yield inaccurate solutions.