The information on this site is advisory. It is provided without guarantee of any kind.


This site attempts to provide a central resource for the design of ultrasonic resonators. However, it is neither comprehensive nor is it the last word.

  1. Consult the Contents to find a particular topic.
  2. A topic is released when it contains sufficient information to be useful. Thus, a particular topic may be incomplete. Please contact the site to see if additional information may be available.
  3. If you are unsure of the meaning of a term, please consult the Glossary.
  4. Unless otherwise specified, all resonators are 20 kHz designs. However, all dimensions and mechanical performances can be linearly scaled to other operating frequencies. (Note that the effect of loads, where considered, may not necessarily scale linearly to other frequencies.)
    Where possible, the dimensions of 20 kHz "standard" designs have been chosen so that they scale nicely to other common frequencies (15 kHz, 30 kHz, 35 kHz, and 40 kHz). This avoids some awkward dimensions. For example, for a 20 kHz cylindrical horn, a face diameter of 126 mm scales nicely whereas a diameter of 125 mm does not. (Note: not all dimensions can be chosen to scale nicely, especially to 35 kHz.)
  5. Frequency (kHz) Face diameter
    ("awkward" dimensions)
    Face diameter
    ("nice" dimensions)
    20 125.0
    (scales awkwardly to other frequencies below)
    (scales nicely to other frequencies below)
    15 187.5 189.0
    30 83.333... 84.0
    35 71.429... 72.0
    40 62.5 63.0
  6. When an equation shows a multiplication operation, the multiplication sign "x" (or "*") is not shown. However, adjacent multiplication factors will always be separated by at least a space in order to distinguish the individual factors. For example, Newton's second law of motion would be shown as \( F = m \, \ddot{u} \) rather than \( F = m\ddot{u} \).
  7. Unless otherwise stated:
    1. For experimental tests, all performance data and tuning rates include a transducer that drives the resonator.
    2. For finite element analysis, the transducer is not included (i.e., only the resonator is analyzed).
    3. All systems are linear.
    4. All stress values are von Mises.
    5. All materials are assumed to be isotropic and homogeneous.
    6. All aluminum resonators are made from Al 7075-T6.
    7. All titanium resonators are made from Ti-6Al-4V.
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Primary units are metric. Secondary units are imperial.

Table 1. Units
Parameter Primary units
[Secondary unnits]
General mks -SI
Dimensions mm
Amplitudes microns_peak (μm)
(see below)
[mils, peak]
Temperatures Celcius (°C)
[Fahrenheit, °F]
Surface roughness microns (μm) or ISO Grade Number
[microinches, μin]

In the above table, secondary units (used only occasionally) are shown in brackets [ ].


Important — Amplitudes have traditionally been specified as peak-to-peak values. However, acceleration forces, stresses, and strains are determined from peak amplitudes, rather than peak-to-peak. Thus, peak amplitudes will be used on this site (with a few legacy exceptions). For text where there may be any confusion, the amplitude will be written as "microns_peak". In equations, the amplitude will generally be written simply as \( U \) where peak amplitude is implied.


See here.

Finite element analysis (FEA)


Resonators are generally shown with the output face pointed upward. This orientation has been chosen because the face amplitude distribution is often most important for the application. Drawings use this same orientation.


FEA colors

FEA colors show the relative values of amplitude and stress — hot colors such as red indicate high values whereas cool colors such as blue indicate low values. Unless otherwise indicated, the colors do not indicate any actual values. Hence, the colors generally can't be compared between different resonators. For example, two horns may both show areas of "red" stress. However, these red areas only indicate where the stress is high — they do not indicate that the two horns have equally high stresses ; in fact, one horn could have substantially higher stress than the other.

For actual resonators the amplitudes and stresses vary in a continuous manner (i.e., they don't make sudden stepped jumps). This is shown in the left image below. However, in order to clearly distinguish different performance regions, the FEA models are shown with striated colors (the right image below).

Actual ultrasonic horn - continuous colors
Actual horn - continuous colors
Actual ultrasonic horn - striated colors
FEA horn - striated colors
Figure 1. FEA amplitude coloration

During animation each color remains constant at the same value that it originally had at maximum displacement.

Displaced scale

The vibration displacements in the images are greatly exaggerated in order to be discernable.


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See here.


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