On the accuracy limits of plate theories for vibro-acoustic predictions

•Analytical expressions of the frequency limits for thin and thick plate theories are derived.•Coincidence and critical frequency expressions are refined from thick plate theory.•Expressions are validated against sound transmission loss simulations for various materials. Several vibro-acoustic models for either single wall or multi-layer constructions are based on classical plate and first order shear deformation theories. The equivalent or condensed plate models employ the thin plate model to extract the dynamic mechanical properties of the multi-layer system considering only flexural and shear motions for the structure under investigation. Since these plate models do not account for the compressional or symmetric motion of the structure, both thin and thick plate theories encounter limitations for mid to high frequency predictions depending on the structures considered. In this work, analytical expressions for the frequency limit of thin and thick plate theories are derived for an elastic layer of isotropic material from the analyses of wavenumbers and admittances. Additionally, refined expressions for coincidence and critical frequencies are presented. Validation of these frequency limits are made by comparing the transmission loss (TL) obtained from both plate theories with the TL computed through the theory of elasticity for a range of thin/thick and soft/stiff materials.