This document summarizes the design and simulation of a stacked horn transducer. It describes a skewed grid model used to represent curved surfaces more accurately. The horn consists of a 6-disc PZT4D stack with a steel backing and titanium tapered tip. Simulation outputs show tip displacement over time and spectra, electrical impedance spectra, and modal displacements at key frequencies. Peak displacement was 540 nm/V at 13.9 kHz resonance. Modal displacements provide insight into device operation at resonant frequencies. The model used 1,680 elements and ran in 1 minute 18 seconds using 4 MB of memory.

1. Stacked Horn Transducer
CONFIDENTIAL

2. Introduction
This example makes use of a skewed grid to create a
model or a high power ultrasonic horn

3. Skewed Grid
Skewed elements used to
create smooth circular
grid
Created in specific grid generation
software
Can be useful for more accurate
representation of curved surfaces
Small geometrical advantages over
Standard Partition, comes with
computational overhead
Attempt Standard Partition first before
deciding to move to Skew

4. Horn Design
6 disc PZT4D stack connected electrically in
parallel
Steel backing mass
Titanium tip with logarithmic taper
Dimensions
Length = 175 mm
Disc Radius = 15 mm
Tip Radius = 5 mm

5. Model Outputs
Tip displacement vs time
Tip displacement spectra in m/V
Electrical impedance spectra
Modal displacements at frequencies of
interest
13.9 kHz
22.6 kHz
33.8 kHz
Free boundary conditions

6. Tip Displacement vs Time

7. Tip Displacement Spectra

8. Electrical Impedance

9. Modal Displacements
13.9 kHz
22.6 kHz
33.8
kHz
Displacement Scale

10. Conclusions
The main resonant modes are apparent in
both the impedance and displacement
results
A peak displacement of 540 nm/V was
achieved at the fundamental resonance
Modal displacements provide additional
insight into device operation at its resonant
frequencies

11. Simulation Metrics
Model 2D Axisymmetric
Elements 1,680
Runtime* 1 min 18 s
Memory (RAM) 4 MB
* Run on dual core Intel i7 3517U Laptop