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Fundamental tones and buckling loads of clamped plates. (English) Zbl 0891.73028

The authors present lower bounds on the critical buckling load of the plate, the fundamental frequency of the plate and that of the membrane, along with a relevant proof. The estimates reported in this paper do not improve on the known bounds, but they are of the right-order of magnitude, as claimed by the authors. Further, it is claimed that “we would be surprised if they were the best known for any intensively studied particular shape”.
In this context, the authors are advised to refer to the papers by K. Vijayakumar and G. K. Ramaiah [J. Sound Vibration 56, No. 1, 127-135 (1978; Zbl 0379.70024) and ibid. 59, No. 3, 335-347 (1978; Zbl 0381.70027)]. These two papers contain some of the best data heretofore reported on upper and lower bounds for vibration of clamped rectangular isotropic and orthotropic plates.

MSC:

74G60 Bifurcation and buckling
74K20 Plates
74H45 Vibrations in dynamical problems in solid mechanics
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