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

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