General properties of the Anisimkin jr. plate modes

Acoustic plate modes of different orders n, having equal velocities vn close to that of the longitudinal BAW vL, are numerically studied in crystals of different symmetries. Three families of the modes with v
_n
~ vL, each at relevant plate thickness h/λ = (h/λ)
_n
, are found (h is the thickness, λ is the wavelength): the generalized Lamb mode with comparable longitudinal u
₁
, shear-horizontal u
₂
, and shear-vertical u
₃
displacements, the Anisimkin Jr. (AN) mode with u
₁
≫ u
₂
and u
₃
, and u
₁
~ constant ≠ 0 at any depth, and the quasilongitudinal (QL) mode with u
₁
> u
₂
, and u
₃
, but u
₁
≠ constant over the plate thickness. Existence of the families does not depend on anisotropy or piezoelectric properties of the plate, but on the closeness of the mode velocity v
_n
to the BAW velocity v
_L
, the value of the dispersion slope dv
_n
/d(h/λ) at v
_n
= v
_L
and h/λ = (h/λ)
_n
, and the proximity of the plate thickness (h/λ)
_n
supporting the mode, to the thickness (h/λ)
_R
providing transverse BAW resonance between plate faces. The Lamb modes approach v
_n
= v
_L
at irregular (h/λ)
_n
far from resonance (h/λ)
_R
and at large dv
_n
/d(h/
_n
) ~10
³
m/s. The two other modes are characterized by lower dispersion dv
_n
/d(h/
_n
) <; 10
³
m/s and regular (h/λ)
_n
close to the resonance (h/λ)
_R
. Because both modes have small vertical displacement on plate faces and propagate almost entirely within the crystals, they are attractive for liquid sensing.