Extensive Elastic Compliance and Mechanical Loss in the k31 Mode PZT Plate: New Methodology and Comprehensive Analysis

Restricted (Penn State Only)
Majzoubi, Maryam
Graduate Program:
Electrical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 07, 2017
Committee Members:
  • Kenji Uchino, Thesis Advisor
  • Direct loss measurement
  • intensive and extensive parameters
  • resonance vibration mode
  • mechanical loss
  • PZT
  • mechanical quality factor
  • non-electrode sample
Dielectric, elastic, and piezoelectric constants, and their corresponding losses in piezoelectric materials are defined under constant conditions of two categories; namely, intensive (i.e., E, electric field or T, stress), and extensive (i.e., D, dielectric displacement or x, strain) ones because of the electromechanical coupling effect. In the conventional IEEE Standard methods, only the intensive loss factors can be measured directly in the piezoelectric k31 mode rectangular plate specimen, while only the extensive loss factors can be measured directly in the k33 mode rod specimen. Then, the corresponding extensive or intensive parameters were derived indirectly from the coupling factor k31 or k33, and the so-called “K” matrix. However, the extensive loss parameters, calculated through this indirect method, could have large uncertainty, due to the error propagation in the calculation. In order to overcome this problem in lead-zirconate-titanate (PZT) k31 mode rectangular plate ceramics, extensive losses should be measured separately from the measurable intensive ones. We propose a new mechanical-excitation methodology, using a non-destructive testing approach by means of a partial electrode configuration of the PZT specimen, instead of the conventional full electrode configuration. For this purpose, a non-electrode (NE) sample was prepared, where the electrode covered only 10% of the top and bottom surfaces at the center to actuate the whole sample, and also monitor the responding vibration. The admittance spectrum of this sample corresponds to PZT properties under dielectric displacement D constant condition. Furthermore, ceramics with partial-electrodes (PE) were also prepared to create short and open circuit boundary conditions, attributing to resonance and anti-resonance modes. In the proposed way, we were able to measure both intensive and extensive elastic compliances and mechanical losses directly for the first time. The accuracy of this new method is compared with the conventional measurements by use of indirect calculations. The preliminary results (by neglecting the 10% actuator part difference at this point) were obtained, which were in good agreements (less than 3% difference) with the previous indirect method. Furthermore, we derive the exact analytical solution by considering the actuator part for calculating the resonance vibration mode and mechanical quality factors in a partial non-electrode sample, parametrically, with respect to “a”, the portion of the middle electrode. This is achieved by solving the dynamic and constitutive equations in a composite bar with both electrode (intensive losses) and non-electrode (extensive losses) boundary conditions. The result suggests that the almost accurate value of the extensive elastic compliance and mechanical loss can be obtained even for a specimen up to a = 0.4 (i.e., 40% covered by the electrode). This analytical solution for the partial electrode samples has the benefit of being more precise and simple to use, comparing with the other ones, such as finite element simulation and equivalent circuit approach. Some parts of this thesis are reproduced from “M. Majzoubi, H. N. Shekhani, A. Bansal, E. Hennig, T. Scholehwar, and K. Uchino, “Advanced Methodology for Measuring Elastic Compliance and Mechanical Loss Directly in k31 Mode Piezoelectric Ceramic Plates,” J. Appl. Phys., vol. 120, no. 22, pp. 225113, 2016,” with the permission of AIP Publishing.