A four unknown non-polynomial theory for the free vibration of angle-ply plates

Abstract

This research evaluates a non-polynomial type plate theory with four unknowns for the frequency analysis of angle-ply laminated plates. By incorporating exponential functions in terms thickness coordinates, this theory does not need correction factor in order to account for shear deformation effects. A significant advancement of this theory is its ability to satisfy zero shear conditions at the top and bottom surfaces of the plate, streamlining the analysis with only four-unknown variables compared to the five required by traditional first-order plate theory. Equations of motion and boundary conditions are derived using Hamilton’s principle. Utilizing Navier’s approach, the study focuses on the free vibration analysis of laminated plates with simple end conditions. Several numerical examples of angle-ply laminated plates are solved in this paper to verify the accuracy of the proposed theory. The natural frequencies predicted by the proposed theory are rigorously compared against those derived from other established theories and exact solutions to validate the proposed theory. This comparative analysis reveals that the natural frequencies calculated from the developed theory are in remarkable agreement with those obtained from the exact elasticity approach. This research contributes to the field vibration analysis of plates by offering a more efficient and accurate method for estimating the frequencies of angle-ply laminated plates.