Modal Analysis

Modal analysis is a computer-assisted "acoustic tool" that is used by the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING in the process of making instruments. Modal analysis makes it possible to analyze and animate the mode shapes of a violin. This is a way of visualizing the main sources of the sound and playability of the instrument.

Modal Analysis of a Violin by Pietro (II) Guarneri

How it works

Modal analysis is an acoustic tool which can be used to display the vibration behavior of any given structure. It has its origin in the fields of aviation and space travel. It was first used to analyze the vibration behavior of airplane wings and satellites, for example. Today, the vibration behavior of the structure is only of secondary importance in many technical applications such as vehicle construction. But in violinmaking, it's a different story: The eigenmodes of vibration of a violin represent the instrument's primary function. It's a fact: The eigenmodes of vibration determine how the instrument sounds and how well it plays. In other words, they control the functioning of the instrument.

This makes it all the more amazing that so far the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING is the only violinmaking shop in the world in which modal analysis is used on a daily basis as a tool for the optimization, tonal adjustment and construction of bowed stringed instruments

What do you do to the instrument during the analysis?

As a basic rule, the eigenmodes of vibration of the structure can be analyzed in any of the production states. When using modal analysis, it does not matter whether the instrument is analyzed in its playing state (with the strings on) or in some state of construction (e.g. with the top plate off or with or without the bass bar). Of course, the eigenmodes of vibration of the free plates are entirely different than those of the completed instrument. Still, it can be useful during restoration work or when making new instruments to perform modal analysis of individual production states prior to completion of the instrument. When making new tonal copies, analysis of the eigenmodes of vibration of the white corpus (before the neck is glued in) has proven extremely helpful for estimating the expected resonance profile (and thus the sound) of the new instrument.

On the other hand, the instrument is always studied in its playing state when preparing an acoustic evaluation

What does the analysis involve?

Using a small pulse generator, the instrument is excited in the laboratory of the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING at 600 measurement points. The vibration response is recorded using a miniature sensor. This does not involve any intervention in or changes to the instrument. We only need to damp the strings with a thin strip of foam between the strings and the fingerboard. The instrument is softly arranged on secure foam padding and measured in its playable state.

view of the test setup for modal analysis of bowed stringed instruments. The coordinate test bench is equipped with linear ball bearings and displacement transducers to allow precise measurement of the test points.

A more detailed view of the modal analysis process. Elastic support with foam padding. Excitation using small impact hammers. Scanning at the bridge using an acceleration sensor. Violin: P.J. Hel (Lille)

Modal analysis of a cello (Domenico Montagnana, 1740). Using a small impact hammer and an acceleration sensor, approx. 600 different transfer functions are measured. The instrument is softly supported on foam padding. The coordinate test bench is equipped with linear ball bearings and displacement transducers to allow precise measurement of the test points.

As a basic rule, the eigenmodes of vibration of the instrument can be analyzed in any of the production states. During restoration work (e.g as shown here on a cello top plate by Antonio Stradivari), the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING commonly uses modal analysis also for individual non-playable states of the instrument.

Fig.: Modal analysis of a cello top plate. Comparison of the newly fitted bass bar with the vibration state of the old (not original) bass bar.

A "Fourier analyzer" is used for further processing of the signals produced by the pulse generator and the recording sensor. A "transfer function" is computed for each measurement point. The next figure shows an example of a transfer function.

Transfer function of a violin. Here, the ratio of the vibration response to the excitation force is plotted as a function of frequency. Above: Vibration level (Log. Mag.); Below: Phase.

To perform complete modal analysis of a violin, about 600 of these transfer functions are measured (each at a different coordinate point). Modal analysis software: "STAR Structure“.

The test points are measured using a coordinate test bench supported on linear ball bearings and transmitted to the computer.

If the instrument exhibits a strong "dynamic mobility" at a given frequency, a small excitation force will suffice to produce a strong vibration response. This means the computer will calculate a high value for the transfer function at this frequency. As part of this measurement, the resonances appear in the form of local maximum values or as "resonance peaks".

Then, the mode shapes of the instrument are computed based on all of the measured transfer functions. Below, you can see the user interface for our modal analysis software. The windows that are open are for single measurements, definition of coordinates and gridlines as well as frame model animation.

User interface of the modal analysis software for use in evaluating measurements, defining geometries and computing and displaying mode shapes.

Based on the results of the geometry definition and the vibration measurements, the mode shapes are finally displayed on the monitor in the form of a slow-motion skeleton animation

For details see: