DELTA-OPERATOR TECHNIQUE TO IMPROVE THE THOMSON-HASKELL-METHOD STABILITY FOR PROPAGATION IN MULTILAYERED ANISOTROPIC ABSORBING PLATES

A modified version of the transfer-matrix method that models propagation of heterogeneous plane waves through immersed multilayered plates made of anisotropic absorbing layers is presented. Since this method suffers from numerical instabilities, the so-called delta matrix operator is applied. As for propagation through isotropic media, the case of propagation in the principal plane of anisotropic media requires us to define sixth-order delta matrices. This method eliminates numerical difficulties. The same technique is used for propagation out of the principal plane. Fifteenth-order delta matrices are necessary to get improved results. However, numerical problems persist with computational data corresponding to the usual experimental situations. Then, a modified version of the delta matrix operator is proposed. From the reflection and transmission coefficients expressions, both 15th- and 20th-order delta matrices are necessary to get reliable numerical results, whatever the computational data may be.