Love waves in a coated vertically periodic substrate

• We study the spectrum of Love SH waves in coated vertically periodic substrates.
• The dispersion equation is cast as an equality of scalar impedance functions.
• The dispersion branches in the Floquet stopbands are proved to be monotonic.
• The number of branches per stopband is related to the number of coating resonances.
• The criterion for existence of the fundamental Love branch is derived.

We study the dispersion spectrum of Love shear horizontal (SH) waves in coated vertically periodic substrates. The analysis is based on the properties of the scalar SH impedances of substrate and coating layer. The dispersion branches, which lie in the Floquet stopbands, are proved to be monotonic. They may have the form of broken segments truncated at the stopband edges and connected by non-monotonic dispersion curves of ’non-physical’ waves (increasing into depth). In contrast to the SH surface waves in a free periodic substrate, there may be more than one Love wave per stopband due to coating. Their number is related to the number of resonances of the coating layer. The criterion for existence of the fundamental Love branch is derived. Examples are provided where coating of periodically layered or functionally graded substrates drastically enriches their SH spectrum.