Three-Dimensional Analysis of the Free Vibrations of Layered Composite Plates Based on the Semianalytic Finite-Element M
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International Applied Mechanics, Vol. 56, No. 4, July, 2020
THREE-DIMENSIONAL ANALYSIS OF THE FREE VIBRATIONS OF LAYERED COMPOSITE PLATES BASED ON THE SEMIANALYTIC FINITE-ELEMENT METHOD
A. V. Marchuk, S. V. Reneiskaya, and O. N. Leshchuk
The spatial theory of elasticity is used to develop two variants of the semianalytic finite-element method for studying the frequencies of free vibrations and modes of distribution of displacements in them. The calculation by the two methods serves as a proof of the reliability of the analysis. The frequencies of free vibrations and the corresponding modes of distribution of displacements in a layered composite plate with two opposite boundaries free and the other two hinged are analyzed. A plate with a free lower surface, which is clamped to the lower surface and leaning on an elastic layer with finite thickness and inertial properties is considered. The high accuracy of the proposed models in these problems is demonstrated. It is pointed out that the inertial properties of the foundation should not be neglected. Keywords: 3D analysis, semianalytical finite-element method, sandwich ñomposite panel, free vibrations Introduction. The use of structural composite systems, in particular layered ones that are substantially orthotropic and have constituent materials with essentially different moduli of elasticity has been increasing. They are in complicated deformation conditions, have different boundary and interface conditions, and are subject to dynamic loads close to resonance. These features can lead to three-dimensional dynamic deformation. The use of direct exact methods of the spatial theory of elasticity for studying the free vibrations of such structures is significantly complicated and limited to the consideration of hinged plates. In particular, such problems were considered in [2, 26, 29]. Classical approaches based on simplified Kirchhoff–Love hypotheses can lead in certain cases to significant errors in the characteristics of free vibrations. Therefore, various refined versions of theories for studying the dynamic behavior of layered structures continue to be developed [2, 11–14, 17, 20, 33, 36–38, etc.]. Different refined models were used in [2, 4–10, 18, 19, 22, 23, 25, 33–37, 39–42, etc.] to study dynamic deformation. Various numerical-analytical methods of three-dimensional analysis of layered structures continue to be developed [1, 3, 9, 11, 12, 15, 16, 21, 24, 30–32, 43]. Despite the abundance of studies on the dynamic deformation of layered plates, we failed to find three-dimensional analyzes of the free vibrations of plates with two opposite boundaries free and the other two hinged on an elastic layer with finite thickness and inertial properties, and also on a perfectly rigid foundation. Such a case can be an integral part of a design model of transport facilities. Problem Statement. The goal of this paper is to develop two versions of the semianalytical finite-element method that allow analyzing the free vibrations of layered composite plates. In the first ver
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