Modal analysis
Modal analysis is the study of the dynamic properties of systems in the frequency domain. It consists of mechanically exciting a studied component in such a way to target the modeshapes of the structure, and recording the vibration data with a network of sensors. 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.
Modern day experimental modal analysis systems are composed of 1) sensors such as
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.[1]
Typical excitation signals can be classed as
The analysis of the signals typically relies on
The animated display of the mode shape is very useful to NVH (noise, vibration, and harshness) engineers.
The results can also be used to correlate with
Structures
In
Although modal analysis is usually carried out by
Electrodynamics
The basic idea of a modal analysis in
Superposition of modes
Once a set of modes has been calculated for a system, the response at any frequency (within certain bounds) to many inputs at many points with different time histories can be calculated by superimposing the result from each mode. This assumes the system is linear.
Reciprocity
If the response is measured at point B in direction x (for example), for an excitation at point A in direction y, then the transfer function (crudely Bx/Ay in the frequency domain) is identical to that which is obtained when the response at Ay is measured when excited at Bx. That is Bx/Ay=Ay/Bx. Again this assumes (and is a good test for) linearity. (Furthermore, this assumes restricted types of damping and restricted types of active feedback.)
Identification methods
Identification methods are the mathematical backbone of modal analysis. They allow, through linear algebra, specifically through least square methods to fit large amounts of data to find the modal constants (modal mass, modal stiffness modal damping) of the system. The methods are divided on the basis of the kind of system they aim to study in SDOF( single degree of freedom) methods and MDOF (multiple degree of freedom systems) methods and on the basis of the domain in which the data fitting takes place in time domain methods and frequency domain methods.
See also
- Frequency analysis
- Modal analysis using FEM
- Modeshape
- Eigenanalysis
- Structural dynamics
- Vibration
- Modal testing
- Seismic performance analysis
References
- D. J. Ewins: Modal Testing: Theory, Practice and Application
- Jimin He, Zhi-Fang Fu (2001). Modal Analysis, Butterworth-Heinemann. ISBN 0-7506-5079-6.