ISSN 2542–0380
Труды Института механики им. Р.Р. Мавлютова
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Proceedings of the Mavlyutov Institute of Mechanics





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Utyashev I.M., Akhtyamov A.M. Identification of the string boundary conditions using natural frequencies Proceedings of the Mavlyutov Institute of Mechanics. 2016. 11(1). 38–52.
2016. Vol. 11. Issue 1, Pp. 38–52
URL: http://proc.uimech.org/uim2016.1.007,en
DOI: 10.21662/uim2016.1.007
Identification of the string boundary conditions using natural frequencies
Utyashev I.M., Akhtyamov A.M.
Mavlyutov Institute of Mechanics, Ufa

Abstract

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

Keywords

spectral problem,
boundary conditions identification,
string,
Plucker condition,
eigenvalues