Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, Russian Federation.
IEEE Trans Ultrason Ferroelectr Freq Control. 2010 Sep;57(9):2028-34. doi: 10.1109/TUFFC.2010.1650.
Acoustic plate modes of different orders n, having equal velocities v(n) close to that of the longitudinal BAW v(L), are numerically studied in crystals of different symmetries. Three families of the modes with v(n) ≈ v(L), 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 u1, shear-horizontal u2, and shear-vertical u3 displacements, the Anisimkin Jr. (AN) mode with u1 >> u2 and u3, and u1 ≈ constant ≠ 0 at any depth, and the quasilongitudinal (QL) mode with u1 > u2, and u3, but u1 ≠ 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/λ) ~10(3) m/s. The two other modes are characterized by lower dispersion dv(n)/d(h/λ) ≤ 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.
不同阶数 n 的声学板模式，其速度 v(n) 与纵向 BAW v(L) 接近，在不同对称性的晶体中进行了数值研究。在相关板厚 h/λ = (h/λ)n 处，发现了三种具有 v(n) ≈ v(L) 的模式家族：广义兰姆模式，具有相当的纵向 u1、剪切水平 u2 和剪切垂直 u3 位移；阿尼西姆金 Jr.（AN）模式，具有 u1 >> u2 和 u3，以及 u1 在任何深度处均为常数 ≠ 0；准纵向（QL）模式，具有 u1 > u2 和 u3，但在板厚内 u1 不为常数。这些模式家族的存在并不取决于板的各向异性或压电性质，而是取决于模式速度 v(n) 与 BAW 速度 v(L) 的接近程度、在 v(n) = v(L) 和 h/λ = (h/λ)n 处的色散斜率 dv(n)/d(h/λ) 的值，以及支持模式的板厚 (h/λ)n 与提供板表面之间横向 BAW 共振的板厚 (h/λ)R 的接近程度。兰姆模式在远离共振 (h/λ)R 的不规则 (h/λ)n 处以及在较大的色散斜率 dv(n)/d(h/λ)~10(3) m/s 处接近 v(n) = v(L)。另外两种模式的特点是色散较小 dv(n)/d(h/λ) ≤ 10(3) m/s，并且接近共振 (h/λ)R 的规则 (h/λ)n。由于这两种模式在板表面上的垂直位移较小，并且几乎完全在晶体中传播，因此它们对液体传感具有吸引力。
