Modal Analysis

Modal Analysis testing is the form of vibration testing of an object whereby the natural (modal) frequencies, modal masses, modal damping ratios and mode shapes of the object under test are determined.

A modal test consists of an acquisition phase and an analysis phase. The complete process is often referred to as a Modal Analysis or Experimental Modal Analysis. Examples would include measuring the vibration of a car’s body when it is attached to a shaker, or the noise pattern in a room when excited by a loudspeaker.

Modal analysis is an important technique in Rotor Dynamics and Structural dynamics, where the natural frequency or shaft critical frequencies (Translational Mode, Pivot Modes, and 1^st Bending Modes) are measured and calculated. It is important during the design stage or during any modification to the structure to ascertain the natural frequencies and to ensure that they are designed to provide sufficient frequency separation from the operating speed range of the rotor, or other frequency of interest.

There are several ways to do modal testing but impact hammer testing (Modal Impact Bump Test) and shaker (vibration tester) testing are commonplace. In both cases energy is supplied to the system with a known frequency content. Where structural resonances occur, there will be an amplification of the response, clearly seen in the response spectra. Using the response spectra and force spectra, a Transfer Function can be obtained. The transfer function (or Frequency Response Function (FRF)) is often curve fitted to estimate the modal parameters; however, there are many methods of modal parameter estimation and it is the topic of much research.

Modal analysis is the study of the dynamic properties of systems in the frequency domain. Examples would include measuring the vibration of a car’s body when it is attached to a shaker, or the noise pattern in a room when excited by a loudspeaker. Modal analysis is an important technique in rotor and structural dynamics, where the engineer should attempt to keep the natural frequency or shaft critical frequencies (Transitional Mode, Pivot Modes, and 1^st Bending Modes) away from the operating speed range of the rotor, or any other frequency of interest. This may not always be possible to avoid, for example during a transient run up period, and for this reason vibration engineering is used to calculate the amount of damping required at the frequencies, and can be used to provide minimum shaft ramp up rates for specific frequency ranges where modes are present, as well as other useful dynamics information.

Modern day experimental modal analysis systems are composed of:

• sensors such as transducers (typically accelerometers, load cells), or non-contact via a Laser vibrometer or stereophotogrammetric camera
• data acquisition system and an analogue-to-digital converter front end (to digitize analogue instrumentation signals) and
• host PC (personal computer) to view the data and analyse it.

Classically this was done with a SIMO (single-input, multiple-output) approach, that is, one excitation point, and then the response is measured at many other points. In the past a hammer survey, using a fixed accelerometer and a roving hammer as excitation, gave a MISO (multiple-input, single-output) analysis, which is mathematically identical to SIMO, due to the principle of reciprocity. In recent years MIMO (multi-input, multiple-output) have become more practical, where partial coherence analysis identifies which part of the response comes from which excitation source. Using multiple shakers leads to a uniform distribution of the energy over the entire structure and a better coherence in the measurement. A single shaker may not effectively excite all the modes of a structure.

Typical excitation signals can be classed as impulse, broadband, swept sine, chirp, and possibly others. Each has its own advantages and disadvantages.

The analysis of the signals typically relies on Fourier analysis. The resulting transfer function will show one or more resonances, whose characteristic mass, frequency and damping can be estimated from the measurements.