Bounded natural frequencies of completely free rectangular plates

Abstract

This paper presents dimensionless natural frequency parameters for completely free rectangular plates, calculated using the superposition method (SM) and the finite difference method (FDM). The convergence tests show that while the SM gives upper bound results the FDM gives lower bound results. The results obtained using the FDM appears to be the best lower bound results available to date. Together with the upper bound results from the SM, the maximum possible error in the first 12 non-zero natural frequency parameters for completely free rectangular plates of various aspects ratios ranging from 1:1 to 3:1 can be determined from the results presented here.