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Upper and Lower Bounds for the Frequencies of Rectangular Cantilever 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.19670470406
Subject(s) - cantilever , upper and lower bounds , rayleigh–ritz method , mathematics , vibration , mathematical analysis , symmetry (geometry) , geometry , physics , structural engineering , acoustics , engineering , boundary value problem
The authors use a recently developed procedure for lower bounds and the Rayleigh ‐ Ritz procedure for upper bounds to estimate frequencies of free vibration of thin rectangular cantilever plates. The applicability of the lower bound procedure is demonstrated, and calculations are given for a symmetry class of normal modes. The lower bounds seem to be the first rigorously obtained for this problem. The upper bounds are improvements over previously published rigorous results.