Comments on ‘vibration analysis of plates with cutouts by the modified Rayleigh-Ritz method’

✍ Scribed by Roberto Gelos; Patricio A.A. Laura

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 41 KB
• Volume: 29
• Category: Article
• ISSN: 0003-682X
• DOI: 10.1016/0003-682x(90)90014-l

✦ Synopsis

Letter to the Editors

COMMENTS ON 'VIBRATION ANALYSIS OF PLATES WITH CUTOUTS BY THE MODIFIED RAYLEIGH-RITZ METHOD'

Dr K. Y. Lam and coworkers must be congratulated for their interesting contribution and useful results. 1 It is felt, however, that a more careful mathematical analysis is needed as the authors refer to their approach as being an 'extension of the Rayleigh-Ritz method'.

It is well known that the Rayleigh-Ritz method yields upper bounds for the eigenvalues. On the other hand, the approximate approach proposed by the authors yields eigenvalues which increase in value as the number of approximation terms is increased, whereas the opposite trend should be observed in a Rayleigh-Ritz formulation.

It would be extremely useful, and it would certainly constitute an important contribution, if the authors could prove that their approach yields lower bounds, as the results shown in Table 3 denote a trend in that respect, in view of the fact that the results contained in the authors' Ref. 8 are accurate.

On the other hand, it is difficult to draw conclusions from the results shown by the authors in Tables 4 and5. REFERENCE I. Lam, K. Y., Hung, K. C. & Chow, S. T., Vibration analysis ofplates with cutouts by the modified Rayleigh-Ritz method. Applied Acoustics, 28 (1989) 49-60.