E. E. Perepelkin, N. G. Inozemtseva, M. V. Klimenko, R. V. Polyakova, M. B. Sadovnikova
{"title":"Numerical-Analytical Method for Finding the Natural Frequencies and Eigenfunctions of a Four-Component Rod System","authors":"E. E. Perepelkin, N. G. Inozemtseva, M. V. Klimenko, R. V. Polyakova, M. B. Sadovnikova","doi":"10.1134/S1063779624701247","DOIUrl":null,"url":null,"abstract":"<p>An analytical method for finding the natural frequencies and eigenfunctions of transverse vibrations of a four-component fuel element (rod) for the designed NEPTUNE pulse reactor is proposed. As a model, a rod with a piecewise constant material density in the longitudinal direction is used. The frequency equation is explicitly obtained via Krylov functions, and the natural frequencies of the first eight modes are determined using a numerical and analytical method. To find higher modes, an exponential analytical extrapolation is proposed. Analytical expressions for eigenfunctions providing a good agreement with numerical calculations in the ANSYS environment are obtained.</p>","PeriodicalId":729,"journal":{"name":"Physics of Particles and Nuclei","volume":"56 1","pages":"88 - 103"},"PeriodicalIF":0.6000,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Particles and Nuclei","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1063779624701247","RegionNum":4,"RegionCategory":"物理与天体物理","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
An analytical method for finding the natural frequencies and eigenfunctions of transverse vibrations of a four-component fuel element (rod) for the designed NEPTUNE pulse reactor is proposed. As a model, a rod with a piecewise constant material density in the longitudinal direction is used. The frequency equation is explicitly obtained via Krylov functions, and the natural frequencies of the first eight modes are determined using a numerical and analytical method. To find higher modes, an exponential analytical extrapolation is proposed. Analytical expressions for eigenfunctions providing a good agreement with numerical calculations in the ANSYS environment are obtained.
期刊介绍：
The journal Fizika Elementarnykh Chastits i Atomnogo Yadr of the Joint Institute for Nuclear Research (JINR, Dubna) was founded by Academician N.N. Bogolyubov in August 1969. The Editors-in-chief of the journal were Academician N.N. Bogolyubov (1970–1992) and Academician A.M. Baldin (1992–2001). Its English translation, Physics of Particles and Nuclei, appears simultaneously with the original Russian-language edition. Published by leading physicists from the JINR member states, as well as by scientists from other countries, review articles in this journal examine problems of elementary particle physics, nuclear physics, condensed matter physics, experimental data processing, accelerators and related instrumentation ecology and radiology.
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