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Modal analysis using FEM
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<p>The goal of <a href="/facts/Modal_analysis/BLxYhRcE">modal analysis</a> in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free <a href="/facts/Vibration/sGgDqG71">vibration</a>. It is common to use the <a href="/facts/Finite_element_method/eUcfP1vn">finite element method</a> (FEM) to perform this analysis because, like other calculations using the FEM, the object being analyzed can have arbitrary shape and the results of the calculations are acceptable. The types of equations which arise from modal analysis are those seen in <a href="/facts/Eigensystem/8TjEoT8u">eigensystems</a>. The physical interpretation of the <a href="/facts/Eigenvalues/8TjEoT8u">eigenvalues</a> and <a href="/facts/Eigenvectors/8TjEoT8u">eigenvectors</a> which come from solving the system are that they represent the frequencies and corresponding mode shapes. Sometimes, the only desired modes are the lowest frequencies because they can be the most prominent modes at which the object will vibrate, dominating all the higher frequency modes. </p><p>It is also possible to test a physical object to determine its natural frequencies and mode shapes. This is called an <a href="/facts/Modal_analysis/BLxYhRcE">Experimental Modal Analysis</a>. The results of the physical test can be used to calibrate a finite element model to determine if the underlying assumptions made were correct (for example, correct material properties and boundary conditions were used). </p>