Труды Института механики им. Р.Р. Мавлютова

ISSN 2542–0380

Электронный научный журнал | Electronic Scientific Journal

Proceedings of the Mavlyutov Institute of Mechanics

Akhtyamov A.M., Muftakhov A.V. On the problem of finding the parameters of elastic fastening of the edges of a rectangular plate Proceedings of the Institute of Mechanics of Ufa Branch of RAS. 4 (2006). 11–22.

2006. Vol. 4. Issue 1, Pp. 11–22
URL: http://proc.uimech.org/uim2006.1.001,en
DOI: 10.21662/uim2006.1.001

On the problem of finding the parameters of elastic fastening of the edges of a rectangular plate

A.M. Akhtyamov^∗, A.V. Muftakhov^∗∗

^∗Mavlyutov Institute of Mechanics, Ufa
^∗∗Bashkir State University, Ufa

Abstract

A rectangular plate is considered, in which two opposite edges are freely supported, while the other two are supported by elastic beams. In this paper, we prove the duality of the solution of the problem of finding the rigidities of elastic beams by all natural oscillation frequencies of a plate. It is also shown that if the rank of a certain matrix is equal to 9, then both solutions of the problem of finding the rigidities of elastic beams can be found from 9 natural frequencies.

Keywords

natural frequencies,
rectangular plate,
elastic fastening