{"title":"Natural Vibrations of Composite Cylindrical Shells Partially Filled with Fluid","authors":"S. A. Bochkarev, S. V. Lekomtsev, V. P. Matveenko","doi":"10.1134/s1063454123040052","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper presents the results of studies of natural vibrations of circular vertical layered cylindrical shells completely or partially filled with a quiescent compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells, together with the corresponding geometric and physical relations, are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the generalized differential quadrature method. The formulated boundary-value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of the vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of the lowest vibration frequencies on the ply angle and the fluid level for simply supported, rigidly clamped, and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of lay-up scheme and the ply angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"34 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454123040052","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper presents the results of studies of natural vibrations of circular vertical layered cylindrical shells completely or partially filled with a quiescent compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells, together with the corresponding geometric and physical relations, are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the generalized differential quadrature method. The formulated boundary-value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of the vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of the lowest vibration frequencies on the ply angle and the fluid level for simply supported, rigidly clamped, and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of lay-up scheme and the ply angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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