Finite element method | Numerical differential equations | Numerical linear algebra

Modal analysis using FEM

The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. It is common to use the finite element method (FEM) to perform this analysis because, like other calculations using the FEM, the object being analyzed can have arbitrary shape and the results of thecalculations are acceptable. The types of equations which arise from modal analysis are those seen in eigensystems. The physical interpretation of the eigenvalues and eigenvectors which come from solving the system are thatthey 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 frequencymodes. It is also possible to test a physical object to determine its natural frequencies and mode shapes. This is called an Experimental Modal Analysis. 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). (Wikipedia).

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From playlist Y12 Chem Mod 8 Applying Chemical Ideas

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From playlist Understanding Wavelets

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From playlist FEM@LLNL Seminar Series

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From playlist Fourier

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From playlist Big Data in Biomedicine Conference 2015

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From playlist FEM@LLNL Seminar Series

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Quadratic eigenvalue problem | Seismic analysis | Vibration | Finite element method | Linear algebra | Finite element method in structural mechanics | Matrix (mathematics) | Inverse iteration