E. E. Perepelkin, A. E. Verkhoglyadov, I. V. Kushnir, M. V. Klimenko
{"title":"Natural Frequencies and Eigenfunctions of a Composite Rod","authors":"E. E. Perepelkin, A. E. Verkhoglyadov, I. V. Kushnir, M. V. Klimenko","doi":"10.1134/s1547477124020092","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">\n<b>Abstract</b>—</h3><p>The problem of finding the natural frequencies and eigenfunctions of the fuel element of a nuclear reactor is considered. A rod with a piecewise constant material density in the longitudinal direction is used as a model. The frequency equation is explicitly derived, and the natural frequencies of the first twelve harmonics are determined numerically and analytically. Analytical expressions for eigenfunctions are obtained, which are in good agreement with calculations made using the Galerkin method and numerical calculations in the ANSYS program. The results will be used to simulate the dynamics of the NEPTUN pulsed reactor for examining the stability of its operation.</p>","PeriodicalId":730,"journal":{"name":"Physics of Particles and Nuclei Letters","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Particles and Nuclei Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1547477124020092","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract—
The problem of finding the natural frequencies and eigenfunctions of the fuel element of a nuclear reactor is considered. A rod with a piecewise constant material density in the longitudinal direction is used as a model. The frequency equation is explicitly derived, and the natural frequencies of the first twelve harmonics are determined numerically and analytically. Analytical expressions for eigenfunctions are obtained, which are in good agreement with calculations made using the Galerkin method and numerical calculations in the ANSYS program. The results will be used to simulate the dynamics of the NEPTUN pulsed reactor for examining the stability of its operation.
期刊介绍:
The journal Physics of Particles and Nuclei Letters, brief name Particles and Nuclei Letters, publishes the articles with results of the original theoretical, experimental, scientific-technical, methodological and applied research. Subject matter of articles covers: theoretical physics, elementary particle physics, relativistic nuclear physics, nuclear physics and related problems in other branches of physics, neutron physics, condensed matter physics, physics and engineering at low temperatures, physics and engineering of accelerators, physical experimental instruments and methods, physical computation experiments, applied research in these branches of physics and radiology, ecology and nuclear medicine.