Modeling and frequency analysis of prestressed functionally graded plates with holes

Materials with complex inhomogeneous structure, including functionally graded composites, are widely used in military and civil engineering, and in modern construction. Due to the peculiarities of the technological process of manufacturing such materials, in many of them a non-uniform initial stress-strain state develops. At the same time, in the production, prestress fields are often embedded in structures to improve their strength characteristics. This paper presents a general linearized formulation of the problem on oscillations of a prestressed elastic body. Using it as a basis, we have formulated the problem on steady-state mixed vibrations of a functionally graded perforated plate in a prestressed state within the framework of Timoshenko deformation hypotheses. A numerical solution to the direct problem was constructed using the finite element method; the effect of the inhomogeneous prestressed state of the plate on its amplitude-frequency characteristics and resonant frequencies was investigated. The results of computational experiments for the functionally graded laws for material modules simulating the W-Cu alloy are given. In the zones of circular plate holes, we used the local condensation of the finite element mesh to increase the accuracy of calculations. The proposed model allows to set an arbitrary type of initial state in the plate, both in the form of analytical dependencies and numerically. We present an example of a numerical experiment, when stress fields were formed in a plate as a result of applying some initial mechanical static load to a part of its boundary. In order to describe such a stress field, the corresponding static problem for the plate under consideration was additionally solved. The possibilities of identifying the parameters of a plane prestressed state based on the acoustic measurement data on the frequency characteristics of the plate are investigated