## Definition of modal analysis

Modal analysis is the process of finding the inherent natural vibration properties of a structure. If these are known, all complicated vibrations that the structure can undergo as a response to a certain excitation, can be expressed as a superposition of these natural vibration states. Therefore, if the natural vibration states are known, much of the vibration behavior of a structure can be predicted. A natural vibration state is defined by its mode shape, its natural frequency and the associated damping.

Vibration modes of a structure can be either purely simulated, e.g. from Finite Element (FE) Models or can be derived out of physical measurement results by fitting a mathematical model to these results. This latter process is called experimental modal analysis.

## Experimental modal analysis and modal testing

Modal analysis is a method to describe a vibrating structure in terms of its natural characteristics which are the frequency, damping and mode shapes – its dynamic properties. A standard setup for experimental modal testing requires sensor technology (force transducers, accelerometers, cameras or non-contact laser vibrometers), data acquisition and a computer for monitoring and analyzing the measurement data (DAQ). Without using a rigorous mathematical treatment, the linked whitepaper introduces some basic concepts about structural vibration and mathematical approaches for solving structural dynamics issues. Please sign up for reading the full whitepaper.

### Applications of experimental modal analysis

During an experimental modal test, first the vibration response of a structure is measured over frequency. The excitation should be spectrally broad to excite all relevant natural frequencies. Typically, the excitation spectrum is acquired as well, so that transfer function's (FRFs) response-input force can be recorded. The setup should be well defined to avoid any unwanted influences from the environment or the excitation process itself. A typical setup could be attachment of the structure to some soft rubber strings or putting it onto soft foam to decouple it from the environment and to excite it with e.g. a modal hammer.

Next, the measured FRFs are curve fitted to a mathematical model involving the inherent modes of the structure under test. The result of this process are the natural frequencies, the damping and the mode shapes of the structure. These modes reveal valuable insights for any engineer and developer, e.g. for simulation in an early stage when designing new products or optimizing the design e.g. with increased lightweight constructions in engineering and construction. Examples of modal analysis typically include entire car-bodies, a wide range of precision components in automotive, aerospace and mechanical engineering, but also cover small parts in microtechnology.

## Polytec Magazine

Experimental modal analysis of gear wheels

Brake discs on the test station
Experimental modal test with laser vibrometers

Laser vibrometry in the development of turbochargers for ship engines

## Experimental modal analysis of lightweight structures

### Excitation in experimental modal analysis

For vibration measurement and experimental modal testing, the underlying test structure needs to vibrate. Some test structures vibrate by themselves (motors or fans) and others need external excitation. For the first group operational modal analysis can be used to some extent, the second group is the typical subject of experimental modal testing. For such induced excitation in experimental modal analysis, there are different means. Typical excitation techniques in modal testing include excitation by shakers, broadband noise excitation by a loudspeaker or dedicated manual or automatic modal hammers. Some popular excitation signals for experimental modal analysis:

• Sine excitation is used to measure deflection shapes at one particular frequency
• Pseudo random signals are broadband excitation signals that show the same amplitude but random phase for each frequency
• Periodic chirp signals are a special type of pseudo random signals, differing by the phase of the individual sine signals, normally preferred when maximum excitation is required.
• White noise is a random signal with a flat spectrum adapted to the measured bandwidth
• and modal hammer excitation for repeatable force induction

### SIMO vs MIMO modal testing approach

The standard test is a single-input multiple output SIMO test. One excitation source and multiple response channels either with multiple acceleration sensors or in the case of a Scanning Laser Doppler vibrometer (SLDV) with a laser beam scanned over the surface is the most common test setup. The results can be directly analyzed and fed into a curve fitting software to extract the individual modes. MIMO – multiple-input multiple-output – setups are applied with highly damped larger structures or in cases where not all modes can be excited with one location of excitation like for symmetric structures, e.g. brake disks.

Modal testing of structures with closely coupled modes is a very frequent task. Structures often have modes that have almost the same resonant frequency. For example, a plate’s specific bending mode might occur at almost the same frequency as its torsion mode. This “accidental” frequency degeneracy is common among more complex geometries and structures. On the other hand, when a structure is planned to be highly symmetric, the coupled modes are expected “by design.” In finite element (FE) simulations, all of these modes appear separately. However, in real world testing, extracting the modes from measurement data can be challenging. This application note introduces a novel approach to separate closely spaced modes with MIMO testing (multiple input, multiple output) using a 3D scanning laser vibrometer and two automated modal hammers. Sign up for reading the full paper.

### Experimental modal analysis (EMA) software

As a result of the experimental modal test the operational deflection shapes as answers to this special modal test excitation are available. To compare these results with the calculated results from a numeric modal analysis based on a FE model a second step called curve fitting is required. In the pure measurement results, the modes are potentially still coupled. The dynamic behavior of a mechanical system can be described as the superposition of the Eigen-modes, one mode being considered as a single degree of freedom (SDOF). In curve fitting the SDOF results are extracted with various methods, typically based on single value decomposition (SVD).
Experimental modal analysis software packages like PolyWave allow for curve fitting and the comparison of the EMA test results with the FEA results in MAC analysis. The findings like damping values, Eigen-frequencies and Eigen-vectors are fed back into the model to update the FE model parameters.

## Measurement solutions for experimental modal analysis

For further information, find these additional sites and learn about Polytec solutions for importing, measuring, comparing, evaluating, post-processing and documenting any modal test data. How does the non-contact technology of laser Doppler vibrometry work? How to perform 1D, single-point measurements or when to scan entire sample surfaces, maybe even in 3D? For complex shaped and larger structures, automated testing with robotics can significantly reduce testing time and cost. Polytec operates several structural test centers around the globe – in Waldbronn Germany, Plymouth, MI USA and Yokohama Japan for measurements as a service. Contact Polytec for individual modal analysis and modal testing projects.