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Piezoelectric Coupled Field Analysis

July 5, 2016 By: Patrick Cunningham

Coupled Field is a term used in the engineering analysis world to describe models that include the interaction of more than one physical phenomenon. Examples commonly discussed include thermal-structural, fluid-thermal, and fluid-structural interactions, but there are other combinations that can be evaluated.

I was recently asked to demonstrate how the finite element method can be used to analyze a piezoelectric transducer. I have some experience in this area, having worked in the ultrasonics industry back in the previous century, and was excited to revisit this lesser known capability of the coupled field tool set.

For anyone unfamiliar with the term, a piezoelectric material is one that will experience mechanical strain when exposed to a voltage, and consequently, develop an electric charge when mechanically strained. Piezoelectric materials are everywhere. They are well suited whenever precise mechanical sensing or actuation needs to be electronically controlled. They can operate over a wide frequency range and have an impressive power density capacity. Frankly, I’m surprised that no one has ever come up with a piezoelectric superhero such as the PZT-Avenger or the Ultrasonic Man. (Stan Lee, if you’re reading this, give me a call!)

Ultrasonic Man – The Inaudible Crime Stopper


The biggest challenge in setting up a piezoelectric model is in the definition of the material properties. The piezoelectric material is typically defined with dielectric constants and a piezoelectric matrix of terms relating the electric field to mechanical strain.  

Piezo materials are usually poled in a primary direction. A deformation will occur in response to a voltage differential across the piezo in the poled direction.  When setting up your model, the geometry must be consistent with the polarity of the material coefficients. With all of these terms to supply, it is always a good idea to evaluate your material model with a simple test case to confirm that that the piezo elements are performing as expected. The good news is that tools like the ANSYS Workbench PiezoAndMEMS ACT extension have made it much easier to input the piezoelectric material coefficients and align them with the poled direction.

The Material Interface from the ANSYS Workbench PiezoAndMEMS ACT Extension


With your materials set up you are ready to go - whether it’s welding spouts on milk containers, sensing enemy submarines or fighting crime. Piezos are often designed for dynamic applications, so your first task is determining the natural frequencies of the piezo enabled structure. This can be done in either open circuit or closed circuit mode with the voltage shunted across the piezo. The open circuit mode is referred to as the parallel (electric) resonance frequency, and the closed circuit mode is known as the series (mechanical) resonance frequency. With a harmonic sweep of the voltage input, the series and parallel resonances can be identified by plotting the piezoelectric charge.   Sensing applications often target the parallel resonance, as it will display a high level of charge sensitivity to a small degree of deformation. Mechanical applications target the series resonance to obtain the benefit of a higher mechanical output to a lesser electrical input.


This information is also important for the design of the electronics of the piezo system. The sharpness of the resonant response is referred to as the Q of the system. Systems with a high Q factor will have a high output to loss ratio with a narrower frequency band over which they can excited effectively. Since the Q is a function of the geometry of the transducer, finite element models can be very useful for transducer design. The finite element model can also be used to evaluate the separation between vibration modes, which will give you confidence that you are exciting or sensing the mode you intended. 

Is anyone out there using finite elements to model piezoelectric components?  If so, we would like to hear your comments.