2008/01/12 by A. M. Akhtymov, Akhtymov, A. M., Artour Mouftakhov +5
Business, Management and Accounting · Computer Science · Engineering · Mathematics · #34A55 #65L09 #74H45 #FOS: Mathematics #Mathematical Control Systems and Analysis #Optics and Image Analysis #Physics and Engineering Research Articles #Spectral Theory (math.SP) #math.SP #msc:34A55 #msc:65L09 #msc:74H45
paper · pdf · doi:10.48550/arxiv.0801.1867
arxiv created 2008/01/12 · openalex publication_date 2008/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of finding boundary conditions for fastening of a ring membrane, which are inaccessible for direct observation from the natural frequencies of its flexural oscillations, is considered. Two theorems on the uniqueness of this problem are proved, and a method for establishing the unknown conditions for fastening of the membrane to the walls is indicated. An approximate formula for determining the unknown conditions is obtained, using first three natural frequencies. The method of approximate calculation of unknown boundary conditions, is explained with the help of an example. Keywords: Boundary conditions, inverse spectral problem, membrane, natural frequencies, Plucker coordinates, Plucker relation.