Sound transmission through periodically inhomogeneous anisotropic thin plates: Generalizations of Cremer's thin plate theory

摘要

Cremer's treatment of the sound transmission through thin homogeneous and elastically isotropic plates is generalized in several aspects: (i) the plate may be periodically inhomogeneous, (ii) the bending stiffness may be anisotropic, (iii) the fluids on both sides of the plate may be different. A formal solution of the problem is given in terms of an infinite system of linear equations for the transmission coefficients of the diffracted waves. Explicit analytical solutions are available for some limiting cases. Numerical results for several simple examples show various new features of the transmission loss curve due to the existence of radiating and non-radiating diffraction orders. Most conspicuous is a 'spike' in the transmission loss curve below the cut-on frequency of the first non-zero diffraction order. [References: 20]