Modal analysis studies the dynamic properties of systems in the frequency domain by exciting a structure to identify its modeshapes, often using a shaker or analyzing the noise pattern. Modern systems employ transducers like accelerometers or laser vibrometers, paired with data acquisition and a personal computer for analysis. Techniques range from SIMO and MISO to advanced partial coherence analysis in MIMO setups. Excitation signals include impulse, broadband, and swept sine waves. Analysis relies on Fourier analysis to derive transfer functions revealing resonances with characteristic mass, frequency, and damping ratio. These insights assist NVH engineers and support correlation with finite element analysis.
Structures
In structural engineering, modal analysis uses the overall mass and stiffness of a structure to find the various periods at which it will naturally resonate. These periods of vibration are very important to note in earthquake engineering, as it is imperative that a building's natural frequency does not match the frequency of expected earthquakes in the region in which the building is to be constructed. If a structure's natural frequency matches an earthquake's frequency, the structure may continue to resonate and experience structural damage. Modal analysis is also important in structures such as bridges where the engineer should attempt to keep the natural frequencies away from the frequencies of people walking on the bridge. This may not be possible and for this reasons when groups of people are to walk along a bridge, for example a group of soldiers, the recommendation is that they break their step to avoid possibly significant excitation frequencies. Other natural excitation frequencies may exist and may excite a bridge's natural modes. Engineers tend to learn from such examples (at least in the short term) and more modern suspension bridges take account of the potential influence of wind through the shape of the deck, which might be designed in aerodynamic terms to pull the deck down against the support of the structure rather than allow it to lift. Other aerodynamic loading issues are dealt with by minimizing the area of the structure projected to the oncoming wind and to reduce wind generated oscillations of, for example, the hangers in suspension bridges.
Although modal analysis is usually carried out by computers, it is possible to hand-calculate the period of vibration of any high-rise building through idealization as a fixed-ended cantilever with lumped masses.
Electrodynamics
The basic idea of a modal analysis in electrodynamics is the same as in mechanics. The application is to determine which electromagnetic wave modes can stand or propagate within conducting enclosures such as waveguides or resonators.
Superposition of modes
Once a set of modes has been calculated for a system, the response to any kind of excitation can be calculated as a superposition of modes. This means that the response is the sum of the different mode shapes each one vibrating at its frequency. The weighting coefficients of this sum depend on the initial conditions and on the input signal.
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
- D. J. Ewins: Modal Testing: Theory, Practice and Application
- Jimin He, Zhi-Fang Fu (2001). Modal Analysis, Butterworth-Heinemann. ISBN 0-7506-5079-6.
External links
- Ewins - Modal Testing theory and practice
- Free Excel sheets to estimate modal parameters
- Modal Space - a long series of articles on mmodal analysis - a tutorial by Peter Avitabile
- What is Modal Analysis? - Trackonomic
References
"Comparison of Modal Parameters Extracted Using MIMO, SIMO, and Impact Hammer Tests on a Three-Bladed Wind Turbine, Experimental Mechanics Series 2014, pp 185-197 [1] https://link.springer.com/chapter/10.1007/978-3-319-04774-4_19 ↩