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<title>Modal analysis</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Modal analysis</span></span>

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<p><b>Modal analysis</b> is the study of the dynamic properties of systems in the <a href="Frequency_domain" title="Frequency domain">frequency domain</a>. It consists of mechanically exciting a studied component in such a way to target the <a href="Normal_mode" title="Normal mode">modeshapes</a> 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 <a href="Shaker_(testing_device)" title="Shaker (testing device)">shaker</a>, or the <a href="White_noise" title="White noise">noise pattern</a> in a room when excited by a loudspeaker.

</p><p>Modern day experimental modal analysis systems are composed of 1) sensors such as <a href="Transducer" title="Transducer">transducers</a> (typically <a href="Accelerometer" title="Accelerometer">accelerometers</a>, <a href="Load_cell" title="Load cell">load cells</a>), or non contact via a <a href="Laser_vibrometer" class="mw-redirect" title="Laser vibrometer">Laser vibrometer</a>, or <a href="Photogrammetry" title="Photogrammetry">stereophotogrammetric cameras</a> 2) data acquisition system and an analog-to-digital converter front end (to <a href="Digitize" class="mw-redirect" title="Digitize">digitize</a> <a href="Analog_signal" title="Analog signal">analog</a> instrumentation signals) and 3) host PC (<a href="Personal_computer" title="Personal computer">personal computer</a>) to view the data and analyze it.

</p><p>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 <a href="Reciprocity_(engineering)" title="Reciprocity (engineering)">reciprocity</a>. In recent years MIMO (multi-input, multiple-output) have become more practical, where <a href="Coherence_theory_(optics)" title="Coherence theory (optics)">partial coherence analysis</a> 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.<sup id="cite_ref-MIMO-SIMO-IMPACT_1-1" class="reference"><a href="#cite_note-MIMO-SIMO-IMPACT-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Typical excitation signals can be classed as <a href="Impulse_function" class="mw-redirect" title="Impulse function">impulse</a>, <a href="Broadband" title="Broadband">broadband</a>, swept <a href="Sine" class="mw-redirect" title="Sine">sine</a>, chirp, and possibly others. Each has its own advantages and disadvantages.

</p><p>The analysis of the signals typically relies on <a href="Fourier_analysis" title="Fourier analysis">Fourier analysis</a>. The resulting <a href="Transfer_function" title="Transfer function">transfer function</a> will show one or more <a href="Resonances" class="mw-redirect" title="Resonances">resonances</a>, whose characteristic <a href="Mass" title="Mass">mass</a>, <a href="Frequency" title="Frequency">frequency</a> and <a href="Damping_ratio" class="mw-redirect" title="Damping ratio">damping ratio</a> can be estimated from the measurements.

</p><p>The animated display of the mode shape is very useful to <a href="Noise%2C_vibration%2C_and_harshness" title="Noise, vibration, and harshness">NVH (noise, vibration, and harshness)</a> engineers.

</p><p>The results can also be used to correlate with <a href="Finite_element_analysis" class="mw-redirect" title="Finite element analysis">finite element analysis</a> normal mode solutions.

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<div class="mw-heading mw-heading2"><h2 id="Structures">Structures</h2></div>

<p>In <a href="Structural_engineering" title="Structural engineering">structural engineering</a>, 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 <a href="Earthquake_engineering" title="Earthquake engineering">earthquake engineering</a>, as it is imperative that a building's natural frequency does not match the <a href="Frequency" title="Frequency">frequency</a> 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 <a href="Resonate" class="mw-redirect" title="Resonate">resonate</a> 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.

</p><p>Although modal analysis is usually carried out by <a href="Computers" class="mw-redirect" title="Computers">computers</a>, it is possible to hand-calculate the period of <a href="Vibration" title="Vibration">vibration</a> of any high-rise building through idealization as a fixed-ended cantilever with lumped masses.

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<div class="mw-heading mw-heading2"><h2 id="Electrodynamics">Electrodynamics</h2></div>

<p>The basic idea of a modal analysis in <a href="Electrodynamics" class="mw-redirect" title="Electrodynamics">electrodynamics</a> is the same as in mechanics. The application is to determine which electromagnetic wave modes can stand or propagate within conducting enclosures such as <a href="Waveguide" title="Waveguide">waveguides</a> or <a href="Resonator" title="Resonator">resonators</a>.

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<div class="mw-heading mw-heading2"><h2 id="Superposition_of_modes">Superposition of modes</h2></div>

<p>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.

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<div class="mw-heading mw-heading2"><h2 id="Reciprocity">Reciprocity</h2></div>

<p>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.)

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<div class="mw-heading mw-heading2"><h2 id="Identification_methods">Identification methods</h2></div>

<p>Identification methods are the mathematical backbone of modal analysis. They allow, through <a href="Linear_algebra" title="Linear algebra">linear algebra</a>, specifically through <a href="Least_squares" title="Least squares">least square methods</a> 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 <a href="Mass-spring-damper_model" title="Mass-spring-damper model">SDOF</a> (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 <a href="Time_domain" title="Time domain">time domain</a> methods and <a href="Frequency_domain" title="Frequency domain">frequency domain</a> methods.

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<ul><li><a href="Frequency_spectrum" class="mw-redirect" title="Frequency spectrum">Frequency analysis</a></li>

<li><a href="Modal_analysis_using_FEM" title="Modal analysis using FEM">Modal analysis using FEM</a></li>

<li><a href="Modeshape" title="Modeshape">Modeshape</a></li>

<li><a href="Eigenanalysis" class="mw-redirect" title="Eigenanalysis">Eigenanalysis</a></li>

<li><a href="Structural_dynamics" title="Structural dynamics">Structural dynamics</a></li>

<li><a href="Vibration" title="Vibration">Vibration</a></li>

<li><a href="Modal_testing" title="Modal testing">Modal testing</a></li>

<li><a href="Seismic_performance_analysis" class="mw-redirect" title="Seismic performance analysis">Seismic performance analysis</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-MIMO-SIMO-IMPACT-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-MIMO-SIMO-IMPACT_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-MIMO-SIMO-IMPACT_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">"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 <a rel="nofollow" class="external autonumber" href="https://link.springer.com/chapter/10.1007/978-3-319-04774-4_19">[1]</a></span>

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<ul><li>D. J. Ewins: <i>Modal Testing: Theory, Practice and Application</i></li>

<li>Jimin He, Zhi-Fang Fu (2001). <i>Modal Analysis</i>, Butterworth-Heinemann. <style data-mw-deduplicate="TemplateStyles:r1238218222">

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</style><a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7506-5079-6</bdi>.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://www.slideshare.net/AlexandreCarlos1/133501854-djewinsmodaltestingtheoryandpractice">Ewins - Modal Testing theory and practice</a></li>

<li><a rel="nofollow" class="external text" href="http://www.noisestructure.com/products/MPE_SDOF.php">Free Excel sheets to estimate modal parameters</a></li>

<li><a rel="nofollow" class="external text" href="https://www.uml.edu/research/sdasl/education/modal-space.aspx">Modal Space - a long series of articles on mmodal analysis - a tutorial by Peter Avitabile</a></li>

<li><a rel="nofollow" class="external text" href="https://trackonomic.com/what-is-modal-analysis/">What is Modal Analysis? - Trackonomic</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-04-01" href="https://en.wikipedia.org/wiki/?title=Modal_analysis&oldid=1283353637">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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