Page 350 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

330 SURFACE ACOUSTIC WAVES IN SOLIDS

10.5.3 Love Modes

Ewing and co-workers (1957) were one of the first to point out from long-period seismo-
graphs that in addition to measuring the characteristic horizontal motion during the main
disturbance of the earthquake, the seismographs also showed a large amount of transverse
components. This early established fact in seismology was explained in 1911 by Love,
and he easily showed that there could be no SH surface wave on the free surface of a
homogeneous elastic half-space (Love 1934). Hence, this simple model could not explain
the measurements. Love, however, showed subsequently that the waves involved were
SH waves, confined to a superficial layer of an elastic half-space and the layer having
a different set of properties from the rest of the half-space. Following Love's treatment
here, Love waves can be considered as SAWs that propagate along a waveguide made
of a layer of a given material M 2 (e.g. glass) deposited on a substrate made of another
material M 1, (e.g. stable temperature (ST)-cut quartz), with different acoustic properties
and, effectively, an infinite thickness when compared with the original layer.
These waves are transverse and they bring only shear stresses into action. The displace-
ment vector of the volume element is perpendicular to the propagation direction O-x 1 and
axis. Because the Love wave is a surface wave, the
is oriented in the direction of the O-x 2
propagating energy is located in the layer and in that part of the substrate that is close to
the interface. Its amplitude decreases exponentially with depth. However, it should also
be noted that materials should have appropriate properties to propagate and carry a Love
wave, as shall be discussed in the section hereby.

10.5.3.1 Existence conditions of Love waves dispersion equation

The case in which the two propagating media are isotropic is examined first. The coor-
dinate origin is chosen on the interface; the O-x 1 axis is oriented in the direction of
propagation and the jcs-axis is oriented vertically upwards (see Figure 10.7). The plane

SiO, Direction of propagation
v 3 Shear velocity in waveguide

Region of propagation of Love waves
ST cut quartz
M 2 layer
v. Shear velocity in substrate

Figure 10.7 Structure of a Love waveguide: M 1 is the substrate; M 2 is the guiding layer