Free vibration, buckling, and static deflections of functionally graded plates

This article considers the problems of free vibrations, buckling, and static deflections of functionally graded plates in which material properties vary through the thickness. It is shown that, all other parameters remaining the same, the natural frequencies of functionally graded plates are always proportional to those of homogeneous isotropic plates and that the proportionality constant can be easily be predicted. Similar results are obtained for buckling and static deflection cases. Therefore, one can predict the behavior of functionally graded plates knowing that of similar homogeneous plates. Extensive results available in the literature can be used as well as solutions and software developed for isotropic materials, thereby greatly reducing the need for a direct analysis of such problems for functionally graded plates.