Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method.

In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate.

Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates.

This study aimed to develop series analytical solutions based on the Mindlin plate theory for the free vibrations of functionally graded material (FGM rectangular plates. The material properties of FGM rectangular plates are assumed to vary along their thickness, and the volume fractions of the plate constituents are defined by a simple power-law function. The series solutions consist of the Fourier cosine series and auxiliary functions of polynomials.