Vibration Analysis of Inclusion Reinforced Composite Square Plates under Various Boundary Conditions

Abstract

The vibration behavior of E-glass epoxy cross-ply laminated plates containing unidirectionally aligned inclusions was studied under different boundary conditions by using first-order shear deformation theory (FSDT). The effective elastic modulus of composite was expressed by using the Mori-Tanaka mean field approach for unidirectionally aligned inclusions. The governing equations were obtained by means of the Hamilton's principle and solved by using the Navier-type solution and Ritz method. The continuity of transverse shear stress between layers of the symmetric cross-ply laminated plates was satisfied by the use of the shape function incorporated into the theory. The effects of the inclusion volume fraction, the inclusion aspect ratio, and the plate span to thickness ratio on the vibration behavior of the laminated plates were studied. It was found that the dimensionless frequency increases with increasing the aspect ratio of the reinforcements and approaches asymptotically to frequency of the continuous fibers.