|
MATHEMATICS
Method of reference problems for obtaining approximate analytical solution of multiparametric Sturm–Liouville problems
Valeriy D. Luk'yanova, Lyudmila V. Nosovab a Joint-Stock Company "Avangard", St. Petersburg, Russia
b Mozhaisky Military Space Academy, St. Petersburg, Russia
Аннотация:
Approximate analytical formulas are obtained for the eigenfrequencies of longitudinal oscillations of an elastic rod with different mechanical fixings of the ends. The eigenfrequencies are found by solving Sturm–Liouville problems with the third kind boundary conditions as roots of transcendental equations. Homogeneous boundary conditions contain one or more parameters whose values are calculated through the indices of mechanical system. Approximate expression for analytical dependencies of the eigenfrequencies on the single parameter are obtained for one-parametric problems, which are called reference ones. We propose a method for obtaining approximate analytical expression for dependencies of the eigenfrequencies on several parameters in boundary conditions by sequentially solving the reference problems. The two-parametric Sturm–Liouville problem is solved by the proposed method.
Ключевые слова:
Sturm–Liouville problem, elastic rod, longitudinal oscillations, eigenfrequencies, approximation, least-squares method.
Поступила в редакцию: 12.04.2023 Исправленный вариант: 29.05.2023 Принята в печать: 30.05.2023
Образец цитирования:
Valeriy D. Luk'yanov, Lyudmila V. Nosova, “Method of reference problems for obtaining approximate analytical solution of multiparametric Sturm–Liouville problems”, Наносистемы: физика, химия, математика, 14:3 (2023), 321–327
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nano1195 https://www.mathnet.ru/rus/nano/v14/i3/p321
|
Статистика просмотров: |
Страница аннотации: | 72 | PDF полного текста: | 29 |
|