Guided waves in periodically stratified plates: Deficiency of homogenizations

The problem of dispersion of guided waves propagating in stratified composite plates containing layers with alternating physical properties is analyzed by using combination of sextic formalism Cauchy, exponential fundamental matrices and Thomson - Haskell method for constructing transfer matrices. The developed method is applicable to analyzing stratified media containing homogeneous anisotropic periodic layers with arbitrary elastic anisotropy. It is revealed that the dispersion portraits of guided waves in plates containing even (asymmetric layout) or odd (symmetric layout) number of alternating layers are significantly different, remaining different even at large number of alternating layers. It is also found that the observed discrepancy between even and odd sets should in principle, be persistent for any composite plates with odd and even numbers of alternating layers. The latter circumstance prevents application of the existing methods of homogenization for obtaining dispersion portraits of guided waves in the stratified media with alternating layers.

Automated summary

The dispersion of guided waves in stratified composite plates containing alternating layers with different physical properties was analyzed using a combination of different mathematical methods. The method revealed significant differences in dispersion patterns between plates containing even and odd numbers of alternating layers, which persisted even with a large number of layers. The discrepancy between even and odd sets may prevent the application of existing methods for obtaining dispersion patterns in stratified media with alternating layers.