Free Vibration Analysis of a Functionally Graded Plate by Finite Element Method

A new category of materials (composite materials) is in full development, both in terms of their manufacture and calculation, in static and dynamic regime. These are Functionally Graded Materials used in the construction of various structural components such as beams and plates. In this paper, the authors present some results regarding the analysis of the free vibrations of a plane, circular plate, clamped on the boundary, made of such a material based on two constituent elements: alumina and aluminum. Two new, original concepts are introduced by the authors: the equivalent plate concept and the multilayer plate concept. The authors also present a study on the influence of the power coefficient of thr material laws on the natural frequencies of the plate. The the using of the multilayer plate concept is based on the replacement of the continuous variation (according to a given law) of the elastic properties with a step variation of them, according to the methodology proposed by the authors. The methodology of modal analysis proposed by the authors is validated by comparison with the results obtained analytically and numerically for homogeneous and isotropic plates. The results of the research undertaken by the authors are presented graphically and tabularly, representing the foundations of the formulated conclusions. These conclusions and especially the models and concepts presented in this paper are useful for the dynamic calculation of different types of structures made of functionally graded materials. The purpose of the work, that of presenting valid and easily accessible models and methodologies for the calculation of FGPs, is also fulfilled by using a widely spread and recognized software product (Ansys), using both common, simple finite elements and special finite elements (multilayer type), without any intervention in the respective stiffness matrices.