Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV 26506, USA.
Ultrasonics. 2010 Mar;50(3):347-56. doi: 10.1016/j.ultras.2009.08.006. Epub 2009 Aug 13.
In this study, we present a model study of guided wave dispersion and resonance behavior of an array of piezoelectric plates with arbitrary cross-sections. The objective of this work is to analyze the influence of the geometry of an element of a 1D-array ultrasound transducer on generating multi-resonance frequency so as to increase the frequency bandwidth of the transducers. A semi-analytical finite-element (SAFE) method is used to model guided wave propagation in multi-layered 1D-array ultrasound transducers. Each element of the array is composed of LiNbO3 piezoelectric material with rectangular or subdiced cross-section. Four-node bilinear finite-elements have been used to discretize the cross-section of the transducer. Dispersion curves showing the dependence of phase and group velocities on the frequency, and mode shapes of propagating modes were obtained for different geometry consurations. A parametric analysis was carried out to determine the effect of the aspect ratio, subdicing, inversion layer and matching layers on the vibrational behavior of 1D-array ultrasound transducers. It was found that the geometry with subdiced cross-section causes more vibration modes compared with the rectangular section. Modal analysis showed that the additional modes correspond to lateral modes of the piezoelectric subdiced section. In addition, some modes have strong normal displacements, which may influence the bandwidth and the pressure field in front of the transducer. In addition, the dispersion curves reveal strong coupling between waveguide modes due to the anisotropy of the piezoelectric crystal. The effect of the matching layers was to cluster extensional and flexural modes within a certain frequency range. Finally, inversion layer is found to have a minor effect on the dispersion curves. This analysis may provide a means to analyze and understand the dynamic response of 1D-array ultrasound transducers.
在这项研究中，我们提出了一个模型研究，研究了具有任意横截面的压电板阵列的导波色散和共振行为。这项工作的目的是分析 1D 阵列超声换能器中元件的几何形状对产生多共振频率的影响，以增加换能器的频率带宽。使用半解析有限元（SAFE）方法对多层 1D 阵列超声换能器中的导波传播进行建模。阵列的每个元件都由具有矩形或亚分割横截面的 LiNbO3 压电材料组成。四节点双线性有限元被用于对换能器的横截面进行离散化。得到了不同几何构型下相位和群速度随频率的变化的色散曲线以及传播模式的模态形状。进行了参数分析，以确定纵横比、亚分割、反转层和匹配层对 1D 阵列超声换能器振动行为的影响。结果表明，与矩形截面相比，亚分割截面的几何形状会导致更多的振动模式。模态分析表明，附加模式对应于压电亚分割部分的横向模式。此外，一些模式具有很强的法向位移，这可能会影响换能器前方的带宽和压力场。此外，色散曲线揭示了由于压电晶体的各向异性，波导模式之间存在很强的耦合。匹配层的作用是将伸缩模式和弯曲模式聚类在一定的频率范围内。最后，发现反转层对色散曲线的影响较小。这项分析可以提供一种分析和理解 1D 阵列超声换能器动态响应的方法。
