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Upper and Lower Bounds for the Frequencies of Rectangular Clamped Plates
Author(s) -
Bazley N. W.,
Fox D. W.,
Stadter J. T.
Publication year - 1967
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19670470307
Subject(s) - upper and lower bounds , rayleigh–ritz method , symmetry (geometry) , square (algebra) , vibration , mathematics , class (philosophy) , mathematical analysis , rayleigh scattering , ritz method , geometry , physics , computer science , optics , acoustics , boundary value problem , artificial intelligence
The authors apply a recently developed method for lower bounds and the Rayleigh‐Ritz procedure for upper bounds to the estimation of the frequencies of free vibration of clamped rectangular plates. The applicability of the lower bound procedure is demonstrated and calculations are presented for a symmetry class for rectangular plates and for a sub‐symmetry class for square plates. The resulting bounds represent improvements over previously published rigorous results and demonstrate the utility of the lower bound method.