Leclaire Philippe, Goossens Jozefien, Martinez Loïc, Wilkie-Chancelier Nicolas, Serfaty Stéphane, Glorieux Christ
Laboratorium voor Akoestiek en Thermische Fysica, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium.
IEEE Trans Ultrason Ferroelectr Freq Control. 2006 Oct;53(10):1934-43. doi: 10.1109/tuffc.2006.126.
An experimental and theoretical study of bending modes in a partially electroded circular piezoelectric quartz (AT-cut) with free edge is presented. The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane displacements. The classical theory of bending of thin disks is used to describe the flexural modes at frequencies lower than the first thickness shear resonance (6 MHz). A fairly good agreement is found between experimental and theoretical results for the forced mode shapes and for the resonance frequencies. However, it appears that the two springs used to maintain the disk in position introduce extra clamping conditions. Several source shapes were studied, among which a collection of an arbitrary number of forces is particularly useful. The two-dimensional wavenumber representation shows the presence of anisotropy related to the crystallographic axes at higher frequencies, which is not predicted by the model. The experimental phase velocities are compared to those given by the classical theory of disks and to those of Lamb A(0) mode. This study confirms the correspondence at low frequencies between the A(0) mode and the bending eigenmodes of a disk with finite size.
本文呈现了对具有自由边缘的部分电极化圆形压电石英（AT 切型）弯曲模式的实验与理论研究。通过施加在电极上的电压脉冲激发石英，并使用激光测振仪扫描其表面以测量面外位移。在低于第一厚度剪切共振频率（6 MHz）时，采用薄圆盘弯曲的经典理论来描述弯曲模式。在强迫模态形状和共振频率的实验结果与理论结果之间发现了相当好的一致性。然而，用于将圆盘固定在位置上的两个弹簧似乎引入了额外的夹紧条件。研究了几种源形状，其中任意数量力的集合特别有用。二维波数表示表明在较高频率下存在与晶轴相关的各向异性，这是该模型未预测到的。将实验相速度与圆盘经典理论给出的相速度以及兰姆 A(0) 模式的相速度进行了比较。这项研究证实了在低频时 A(0) 模式与有限尺寸圆盘的弯曲本征模式之间的对应关系。
