IDENTIFICATION OF THE COEFFICIENTS OF EQUATION FOR A VIBRATING ROD IN ACOUSTIC DIAGNOSTICS
AbstractThe work is devoted to the study solving some inverse problem of identifying the coefficients of Sturm-Liouville operator. Inverse problems in vibration are concerned with constructing a vibrating system of a particular type, e.g., a string, a rod, that has specified properties. During the operation of the technical design, the dynamic characteristics can be changed by changing the boundary connection. Often these compounds are not directly accessible and their states can be judged from indirect information. In acoustic diagnostics, often the available information is the natural frequencies. Thus, by the set of natural frequencies it is necessary to estimate the state of the boundary connections. In this work an algorithm for constructive determination of coefficients of Sturm-Liouville operator is given. A straightforward solution of the inverse problem for Sturm-Liouville equation in a rod is presented.
doi: 10.1007/BF02545749. https://projecteuclid.org/euclid. acta/1485890008
 Hald O. H. "The inverse Sturm-Liouville equation and the Rayleigh-Ritz method" 32 (294) (1978): 687-705.
 Hochstadt H., "The inverse Sturm-Liouville problem", Communic. on Pure and Appl. Math. Vol. XXVI (1973): 715-729.
 Ahtyamov A. M., Ayupova A. R. "Diagnostirovanie dvuh mass, sosredotochennyih na balke [Diagnosing two masses focused
on a beam]", Priboryi i sistemyi. Upravlenie, kontrol, diagnostika (2010): 42-44.
 Vatulyan A.O., Obratnyie zadachi v mehanike deformiruemogo tverdogo tela [Inverse preblems in the mechanics of a
deformable solid] (M.: Fizmatlit, 2007): 224.
 Gladwell G. M.L., Inverse problem in vibration Second Edition. (New York: Kluwer Academic Publishers, 2004): 456.
 Gladwell G. M. L. and Movahhedi M., "Reconstruction of a massspring system from spectral data I: Theory", 1(84) (1995):
 Golub G. H. and Boley D., "Inverse eigenvalue problems for band matrices" in G. A. Watson (Ed. ) Numerical Analysis
Heidelberg, New York: Springer Verlag 70 (1977): 23-31.
 Kayyirbek Zh.A., Nurmetova A.T., "Vossozdanie kusochao-odnorodnogo sterzhnya po sobstvennyim chastotam [Recon-
struction piecewise homogeneous rod of eigenfrequencies]" Traditsionnaya mezhdunarodnaya nauchnaya aprelskaya kon-
ferentsiya, Almaty (2018): 55-56.
 Sobolev S.L., Vvedenie v teoriyu kubaturnyih formul [Introduction to the theory of cubature formulas| (M.: Nauka, 1974):