Mezheritsky Alex A, Mezheritsky Alex V
The City University of New York, New York, USA.
IEEE Trans Ultrason Ferroelectr Freq Control. 2007 Dec;54(12):2662-77. doi: 10.1109/TUFFC.2007.595.
A theoretical description of the dissipative phenomena in the wave dispersion related to the "energytrap" effect in a thickness-vibrating, infinite thicknesspolarized piezoceramic plate with resistive electrodes is presented. The three-dimensional (3-D) equations of linear piezoelectricity were used to obtain symmetric and antisymmetric solutions of plane harmonic waves and investigate the eigen-modes of thickness longitudinal (TL) up to third harmonic and shear (TSh) up to ninth harmonic vibrations of odd- and even-orders. The effects of internal and electrode energy dissipation parameters on the wave propagation under regimes ranging from a short-circuit (sc) condition through RC-type relaxation dispersion to an opencircuit (oc) condition are examined in detail for PZT piezoceramics with three characteristic T -mode energy-trap figure-of-merit c-(D)(33)/c-(E)(44) values - less, near equal and higher 4 - when the second harmonic spurious TSh resonance lies below, inside, and above the fundamental TL resonanceantiresonance frequency interval. Calculated complex lateral wave number dispersion dependences on frequency and electrode resistance are found to follow the universal scaling formula similar to those for dielectrics characterization. Formally represented as a Cole-Cole diagram, the dispersion branches basically exhibit Debye-like and modified Davidson Cole dependences. Varying the dissipation parameters of internal loss and electrode conductivity, the interaction of different branches was demonstrated by analytical and numerical analysis. For the purposes of dispersion characterization of at least any thickness resonance, the following theorem was stated: the ratio of two characteristic determinants, specifically constructed from the oc and sc boundary conditions, in the limit of zero lateral wave number, is equal to the basic elementary-mode normalized admittance. As was found based on the theorem, the dispersion near the basic and nonbasic TL and TSh resonances reveal some simple representations related to the respective elementary admittance and showing the connection between the propagation and excitation problems in a continuous piezoactive medium.
本文给出了一个理论描述，该描述涉及与具有电阻性电极的厚度振动、无限厚度极化压电陶瓷板中的“能量阱”效应相关的波色散中的耗散现象。利用线性压电性的三维（3-D）方程来获得平面谐波的对称和反对称解，并研究厚度纵向（TL）直至三次谐波以及剪切（TSh）直至九次谐波振动的奇次和偶次本征模式。对于具有三个特征T模式能量阱品质因数c-(D)(33)/c-(E)(44)值（小于、近似相等和大于4）的PZT压电陶瓷，详细研究了内部和电极能量耗散参数在从短路（sc）条件到RC型弛豫色散再到开路（oc）条件的各种状态下对波传播的影响，此时二次谐波杂散TSh共振位于基波TL共振反共振频率区间之下、之内和之上。计算得到的复横向波数色散对频率和电极电阻的依赖性遵循类似于介电特性的通用标度公式。以科尔 - 科尔图形式正式表示时，色散分支基本上呈现出德拜型和修正的戴维森 - 科尔依赖性。通过解析和数值分析证明了改变内部损耗和电极电导率的耗散参数时不同分支之间的相互作用。为了对至少任何厚度共振进行色散表征，陈述了以下定理：在横向波数为零的极限情况下，由oc和sc边界条件专门构建的两个特征行列式的比值等于基本基模归一化导纳。基于该定理发现，基本和非基本TL及TSh共振附近的色散揭示了一些与各自基本导纳相关的简单表示，并显示了连续压电活性介质中传播和激发问题之间的联系。
