Upper and Lower Bounds for the Frequencies of Rectangular Clamped Plates

摘要

The authors apply a recently developed method for lower bounds and the Rayleigh-Ritz procedure for upper bounds to the estimation of the frequencies of free vibration of clamped rectangular plates. The applicability of the lower bound procedure is demonstrated and calculations are presented for a symmetry class for rectangular plates and for a sub-symmetry class for square plates. The resulting bounds represent improvements over previously published rigorous results and demonstrate the utility of the lower bound method. (Author)