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...