On the Calculus of the Natural Frequencies of Functionally Graded Plates by Using the Concepts of Multilayer and Equivalent Material

Functionally graded materials represent a relatively new class of materials, which can be attributed to the broad category of composite materials. The specificity of functionally graded materials consists in the fact that in one of the directions (usually the smallest in a given body) the elastic, physical, mechanical, electrical, etc. constants vary according to a continuous and monotonic function, between two values assigned to the two materials, which are the basis for the realization of the functionally graded material. The paper presents a method for calculating the natural frequencies of functionally graded plates using two concepts of approaching the calculation of structures made of functionally graded materials, multilayer material and equivalent material. With the help of these concepts, the shapes and natural frequencies of a plate can be determined, using the theoretical foundations of plates made of homogeneous and isotropic materials.