Abstract
The progress in numerical methods and simulation tools promotes the use of inverse problems in material characterisation problems. A newly developed procedure can be used to identify the behaviour of piezoceramic discs over a wide frequency range using a single specimen via fitting simulated and measured impedances by optimising the underlying material parameters. Since there is no generally accepted damping model for piezoelectric ceramics, several mechanical damping models are examined for the material identification. Three models have been chosen and their ability to replicate the measured impedances is evaluated. On the one hand, the common Rayleigh model is considered as a reference. On the other hand, a Zener model and a model using complex constants are extended to model the transversely isotropic material. As the Rayleigh model is only valid for a limited frequency range, it fails to model the broadband behaviour of the material. The model using complex constants leads to the best fit over a wide frequency range while at the same time only adding three additional parameters for modelling damping. Thus, damping can be assumed approximately frequency-independent in piezoceramics.
Zusammenfassung
Die Verwendung inverser Verfahren im Kontext von Materialcharakterisierung wird durch die Entwicklung numerischer Verfahren und Simulationswerkzeugen vorangetrieben. Ein neu entwickeltes Verfahren kann dazu verwendet werden, das Verhalten von piezokeramischen Scheiben über einen weiten Frequenzbereich unter Verwendung einer einzelnen Probe zu identifizieren, indem simulierte Impedanzen durch Variation der Materialparameter so optimiert werden, dass gemessene Impedanzen möglichst gut nachgebildet werden. Da es kein allgemein akzeptiertes Dämpfungsmodell für piezoelektrische Keramiken gibt, werden mehrere mechanische Dämpfungsmodelle untersucht. Dazu werden drei Modelle ausgewählt und evaluiert. Zum einen wird das gängige Rayleigh-Modell als Referenz betrachtet. Zum anderen werden ein Zener-Modell und ein Modell mit komplexen Konstanten erweitert, um das transversal isotrope Material zu modellieren. Da das Rayleigh-Modell nur für einen begrenzten Frequenzbereich gültig ist, kann es das Breitbandverhalten des Materials nicht modellieren. Das Modell mit komplexen Konstanten führt über einen weiten Frequenzbereich zur besten Anpassung und benötigt gleichzeitig nur drei zusätzliche Parameter für die Modellierung der Dämpfung. Somit kann bei Piezokeramiken eine annähernd frequenzunabhängige Dämpfung angenommen werden.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 321120716
Funding statement: The authors would like to thank the German Research Foundation (DFG) for financial support of the research project 321120716.
About the authors
Nadine Feldmann, M. Sc. is a research associate at the Measurement Engineering Group at the Faculty of Electrical Engineering, Computer Science and Mathematics at Paderborn University, Germany. Her field of research includes inverse measurement procedures and the characterisation of piezoelectric ceramics.
Veronika Schulze, M. Sc. is a research associate at the Department of Mathematics at Humboldt-Universität zu Berlin. Her research includes the simulation and theory of partial differential equations describing piezoelectric behaviour and corresponding optimization of piezoelectric problems.
Leander Claes, M. Sc. completed his studies in electrical engineering in 2014. Since 2015, he has been a research associate and, starting mid-2016, deputy head of the Measurement Engineering Group at Faculty of Electrical Engineering, Computer Science and Mathematics at Paderborn University, Germany. His research includes the development of acoustic measurement procedures, with a focus on material and fluid characterisation applications.
Dr. Benjamin Jurgelucks is a postdoctoral research associate at the Department of Mathematics at Humboldt-Universität zu Berlin. His main area of research is nonlinear optimization, parameter identification and inverse problems especially in an engineering context.
Lars Meihost completed his studies in electrical engineering in 2018. He then worked as a hardware engineer and programmer at Meinberg Funkuhren GmbH & Co. KG. In late 2020, he joined the Measurement Engineering Group at Paderborn University as a laboratory engineer.
Prof. Dr. Andrea Walther has been full professor for Mathematical Optimization at the Department of Mathematics at the Humboldt-Universität zu Berlin since 2019. Her main research interests are nonlinear optimization and scientific computing.
Prof. Dr.-Ing. Bernd Henning is head of the Measurement Engineering Group at Faculty of Electrical Engineering, Computer Science and Mathematics at Paderborn University, Germany. His main areas of research are acoustic measurement procedures, ultrasonic and optical measurement engineering as well as biomedical measurement techniques.
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