Upper and Lower Bounds for the Frequencies of Rectangular Cantilever Plates
- 1 January 1967
- journal article
- research article
- Published by Wiley in ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- Vol. 47 (4) , 251-260
- https://doi.org/10.1002/zamm.19670470406
Abstract
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.Keywords
This publication has 7 references indexed in Scilit:
- A method for finding the m smallest values of a monotonic function defined on ordered sets of positive integersCommunications of the ACM, 1966
- Methods for lower bounds to frequencies of continuous elastic systemsZeitschrift für angewandte Mathematik und Physik, 1966
- Lower bounds to eigenvalues using operator decompositions of the form B*BArchive for Rational Mechanics and Analysis, 1962
- Householder's Method for the Solution of the Algebraic EigenproblemThe Computer Journal, 1960
- The Vibration of Rectangular PlatesProceedings of the Institution of Mechanical Engineers, 1954
- Vibration of Rectangular and Skew Cantilever PlatesJournal of Applied Mechanics, 1951
- Vibration of Rectangular Plates by the Ritz MethodJournal of Applied Mechanics, 1950