Use of asymptotic solutions from a modified bolotin method for obtaining natural frequencies of clamped rectangular orthotropic plates

✍ Scribed by K. Vijayakumar; G.K. Ramaiah

• Book ID: 104154005
• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 677 KB
• Volume: 59
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(78)80002-9

✦ Synopsis

Solutions of the problem of flexural vibration of clamped rectangular orthotropic plates are initially obtained by a modified Bolotin's asymptotic method and these solutions are then used as admissible functions in the Rayleigh-Ritz method. Estimates of frequencies obtained by the (i) modified Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are presented. Accuracies of these estimates are discussed in detail. It is shown that the percentage difference between the Bolotin and Rayleigh estimates decreases to zero with H]v/-ff~Dy tending to zero as well as tending to infinity. It is found that the maximum error is under 4"870 in the Bolotin estimates whereas it is under 0"3270 only in the Rayleigh estimates. The present Rayleigh estimates are found to be always lower than those obtained from Hearmon's formula. In fact, it is shown that, for large values of H/Dvt-D-~D~, the least eigenvalue obtained from Hearmon's formula is more than 5070 higher than the true value.