Geodesic
Oscillations of a circular three-layer plate under external linear in time load
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2023), pp. 49-63

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The problem of dynamic deformation of a circular three-layer plate with a step-variable thickness of the outer layers is considered. The plate deformation model is based on the zig-zag theory. The approach to the consideration of the problem relies on the method of decomposition of the plate geometry. According to this, we represent the equations of motion for each section of the plate with a constant thickness. The derivation of these equations predicated on Hamilton’s variational principle. A particular analytical solution is obtained for forced plate vibration induced by linear in time external action. The represented solution is based on a superposition of quasi-static and dynamic components of the displacement appearing in the plate during vibrations. To test the obtained solution, numerical studies were performed for various materials.
Keywords: dynamic deformation of a three-layer plate; quasi-static deformation of a three-layer plate; circular three-layer stepped plate. 
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D. V. Leonenko; M. V. Markova. Oscillations of a circular three-layer plate under external linear in time load. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2023), pp. 49-63. http://geodesic.mathdoc.fr/item/BGUMI_2023_1_a4/