Fundamentals of Modal Testing

Understanding modes

• Single degree of freedom models
• Two degree of freedom modes
• Mode shapes - complicating the coordinate system to make life easy
• Eigenvalues and Eigenvectors - know what the analyst is doing, but let him worry about the details
• Forcing the modes - one at a time or both at the same time.
• Three-to-infinity degrees of freedom; similar to 2DoF but more complex record keeping
• Finite element model - myriad springs and masses - more analysts' details

Why do a modal test?

• Troubleshooting
• Understanding test and service failures when there is no modal model to point to the failure mechanism
• Verifying a finite element model

The analyst-tester team - the analyst's role
The model has thousands of degrees of freedom, but the test has at most hundreds of transducers. The analyst must reduce model size down to test size. He must reduce the mass matrix down to test size for orthogonality calculations. What's a mass matrix? What's orthogonality?

The Test Setup

• Rigid boundaries
• Flexible boundaries
• Rigid boundaries with freed directions
• Free-free boundaries
• Accounting for constrained boundary points

The frequency response function. What is it? Why do we use it?

Acceleration measurements

• Types of accelerometer
• Compatibility with computer front end
• Keeping track of large accelerometer systems; bar code applications; smart accelerometers
• Accelerometer system checkout

Force measurements

• Modal hammers; advantages and disadvantages; hammer and tip selection
• Modal shakers: selection, stingers, location, orientation

Base forced measurements; acceleration-to-acceleration frequency response measurement

Measurement variables: excitation types;

• Excitation filters; response filters; frequency band and resolution
• Averaging strategy
• Sample rejection
• Force levels and data ranges

Evaluating data quality; expected results, coherence, reciprocity, preliminary modal extraction

When things go wrong: poor reciprocity, noisy data, can't get good fits, poor orthogonality

Modal data extraction

• Modal indicator functions
• Complex exponential parameter extraction
• Circle fit shape extraction - good for interpreting questionable data or finding local modes
• Polyreference method
• The correlation matrix
• The stability diagram and parameter extraction; modal confidence factor; mode shape extraction

Verification methods: function synthesis; modal assurance criteria; orthogonality matrix

Displaying modes: portraying the geometry; animation; static display

Course summary