Geodesic
Method of reference problems for obtaining approximate analytical solution of multiparametric Sturm--Liouville problems
Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 3, pp. 321-327

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: elastic rod, eigenfrequencies, approximation, least-squares method.
Mots-clés : Sturm–Liouville problem, longitudinal oscillations 
@article{NANO_2023_14_3_a3,
     author = {Valeriy D. Luk'yanov and Lyudmila V. Nosova},
     title = {Method of reference problems for obtaining approximate analytical solution of multiparametric {Sturm--Liouville} problems},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {321--327},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a3/}
}
TY  - JOUR
AU  - Valeriy D. Luk'yanov
AU  - Lyudmila V. Nosova
TI  - Method of reference problems for obtaining approximate analytical solution of multiparametric Sturm--Liouville problems
JO  - Nanosistemy: fizika, himiâ, matematika
PY  - 2023
SP  - 321
EP  - 327
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a3/
LA  - en
ID  - NANO_2023_14_3_a3
ER  - 
%0 Journal Article
%A Valeriy D. Luk'yanov
%A Lyudmila V. Nosova
%T Method of reference problems for obtaining approximate analytical solution of multiparametric Sturm--Liouville problems
%J Nanosistemy: fizika, himiâ, matematika
%D 2023
%P 321-327
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a3/
%G en
%F NANO_2023_14_3_a3
Valeriy D. Luk'yanov; Lyudmila V. Nosova. Method of reference problems for obtaining approximate analytical solution of multiparametric Sturm--Liouville problems. Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 3, pp. 321-327. http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a3/