Isogeometric Analysis for Free Vibration of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

Abstract

This paper presents a novel quasi-three-dimensional shear deformation theory called the spectral displacement formulation (SDF) for analyzing the free vibration of functionally graded plates. The SDF expresses the unknown displacement field as a unique form of the Chebyshev series in the thickness direction. By increasing the truncation number in the Chebyshev series, the bending analysis results can approach the three-dimensional elasticity solution and satisfy the traction-free boundary conditions without requiring a shear correction factor. The SDF is an extension of the classical plate theory, thereby naturally avoiding the shear-locking phenomenon. These characteristics enable the SDF to apply to plates of arbitrary thickness while maintaining accuracy. The nonuniform rational B-spline-based isogeometric approach is employed to enhance the applicability of this theory to free vibration analysis of functionally graded plates with complex geometries and different boundary conditions. Numerical examples are presented to demonstrate the accuracy and reliability of the proposed method in analyzing the free vibration of functionally graded plates.