Comparison of classical plate theory, Timoshenko-Midlin plate theory, and exact elasticity theory for calculation of transmission loss through fluid-loaded plates

Abstract

Two approximate plate theories, “classical” (CP) and Timoshenko-Midlin (TM), are commonly used in computing radiation and scattering from submerged structures. These models have previously been compared with an exact elasticity theory calculation of the phase velocity of the first antisymmetric mode of an unloaded plate. On this basis, CP is limited to frequencies below 0.7 times critical for steel in water. No indication of the limitations of TM is, however, found by this calculation. A more appropriate problem for underwater applications is transmission loss through the plate. We have calculated this quantity versus frequency-thickness product and angle of incidence using both the plate models and the exact theory. This approach shows that CP agrees well up to 1.5 times critical frequency. TM correctly predicts the first and second flexural mode transmission peaks but fails in other ways at frequencies greater than 4.0 times critical. In particular, no effects of symmetric modes are included, and an incorrect limit is reached at grazing incidence.