Analytical studying the group velocity of three-partial Love (type) waves in both isotropic and anisotropic media

Impossibility to observe the non-dispersive Zakharenko type waves (ZTW) for the three-partial Love type waves (LTW3) is analytically shown for layered systems consisting of a layer on a substrate, in case either isotropic or anisotropic materials with the anisotropy factor alpha(f) = (C44C66 - C-46(2))(1/2) /C-44. The other solutions of new dispersive waves were also considered in addition to the LTW3-waves. The interesting structures Au/Muscovite and Au/Biotite were numerically investigated concerning the LTW3-waves. Monoclinic crystal Muscovite is likely for substrates with the speed V-t4 = (C-44/p)(1/2) = 5053 m/s and alpha(f) similar to 2.08 that gives beta(M) = V-t4 alpha f = 10,510 m/s similar to V-t([100])(Diamond) = 12,800 m/s. Possibility to find supersonic LTW-waves in piezoelectric crystals with beta similar to 20,000 m/s is also discussed. Such the P will be greater than the speed V-l similar to 17,500 m/s of the bulk longitudinal wave for Diamond. Also, the first- and second-order derivatives of the group velocity V-g, as well as the first-, second- and third-order derivatives of the phase velocity V-ph were analytically obtained and shown in dependence on the layer thickness kh, where k is the wavenumber in the wave propagation direction. The obtained results of the derivative calculations of the group velocity V-g could be useful for finding inflexion points in dependence of the group delay time tau(kh) = L/V-g (L is a gone distance) in dispersive delay lines, as well as for production automation of different filter and sensor on dispersive waves.