Free vibration of advanced composite plates using a new higher order shear deformation theory
This paper presents a new Higher Order Shear Deformation Theory (HSDT) for free vibration analysis of simply-supported Functionally Graded Material (FGM) plates. One novelty of this paper is the use of two transverse shear strain functions in which the classical trigonometric and parabolic shear strain shape functions are reformulated with a very small exponential perturbation. The present transverse shear strain functions give a more accurate distribution of the transverse shear stress in the thickness direction without using any transverse shear correction factors. Another novelty of this study is the use of the integral format of the displacement field, which is developed to reduce the differential operations and probability of errors during the derivation of equations. The equations of motion are derived based on Hamilton's principle and Navier's procedure. The non-dimensional fundamental frequencies of FGM plates are obtained by solving an eigenvalue problem. The accuracy of the proposed HSDT is verified by comparing the obtained numerical results with other results in the existing literature. Extensive numerical results are presented for different cases both in tabular form and graphical form. These results can be directly used by design engineers. However, there is a need to verify the data by carefully conducting experiments.
scientific article; zbMATH DE number 7362900
scientific article