Lower Bounds to the Gravest and All Higher Frequencies of Homogeneous Vibrating Plates of Arbitrary Shape

[+] Author and Article Information
D. Pnueli

Department of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

J. Appl. Mech 42(4), 815-820 (Dec 01, 1975) (6 pages) doi:10.1115/1.3423712 History: Received January 01, 1975; Revised June 01, 1975; Online July 12, 2010


A method is presented by which lower bound can be calculated for the gravest and all higher frequencies of both clamped and simply supported plates of arbitrary shape. The results have the form of simple algebraic formulas which depend on the plate’s area only. Numerical examples are presented for rectangular, triangular, and elliptical configurations.

Copyright © 1975 by ASME
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