Free vibration analysis of in-plane functionally graded plates using a refined plate theory and isogeometric approach.

This paper investigates the free vibration behaviors of functionally graded (FG) plates considering in-plane material inhomogeneity. Isogeometric analysis (IGA) in conjunction with a refined plate theory (RPT) is employed for fulfilling the investigation. In RPT, the displacement field is described only with four unknown variables and shear correction factor is not necessary any more. A new transverse shear stress function is proposed by combining linear function with cosine function and the shear stress has parabolical distribution through the plate thickness. The governing and discretized equations are solved using IGA rooted in non-uniform rational B-splines (NURBS) basis functions, which have high-order continuous derivatives and facilely satisfy the C 1 - continuity condition of the RPT. The excellent efficiency and accuracy of the current method are testified in the analysis of skew and elliptical plates by comparison with other researchers’ solutions. Furthermore, the influence of the geometric parameter, boundary condition and material inhomogeneity on dynamic characteristics is discussed in detail. [ABSTRACT FROM AUTHOR]