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  2. Modal analysis - Wikipedia

    en.wikipedia.org/wiki/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 ...

  3. Modal analysis using FEM - Wikipedia

    en.wikipedia.org/wiki/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 the calculations are acceptable.

  4. Sturm–Liouville theory - Wikipedia

    en.wikipedia.org/wiki/Sturm–Liouville_theory

    The boundary conditions ("held in a rectangular frame") are W = 0 when x = 0, L 1 or y = 0, L 2 and define the simplest possible Sturm–Liouville eigenvalue problems as in the example, yielding the "normal mode solutions" for W with harmonic time dependence, (,,) = ⁡ ⁡ ⁡ where m and n are non-zero integers, A mn are arbitrary constants ...

  5. Problem solving - Wikipedia

    en.wikipedia.org/wiki/Problem_solving

    Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue ...

  6. Finite element method - Wikipedia

    en.wikipedia.org/wiki/Finite_element_method

    The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.

  7. Eigenmode expansion - Wikipedia

    en.wikipedia.org/wiki/Eigenmode_expansion

    Eigenmode expansion (EME) is a computational electrodynamics modelling technique. It is also referred to as the mode matching technique[1] or the bidirectional eigenmode propagation method (BEP method). [2] Eigenmode expansion is a linear frequency-domain method. It offers very strong benefits compared with FDTD, FEM and the beam propagation ...

  8. Galerkin method - Wikipedia

    en.wikipedia.org/wiki/Galerkin_method

    t. e. In mathematics, in the area of numerical analysis, Galerkin methods are a family of methods for converting a continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying linear constraints determined by finite sets of basis functions.

  9. Dynamic mode decomposition - Wikipedia

    en.wikipedia.org/wiki/Dynamic_mode_decomposition

    Dynamic mode decomposition (DMD) is a dimensionality reduction algorithm developed by Peter J. Schmid and Joern Sesterhenn in 2008. [1][2] Given a time series of data, DMD computes a set of modes each of which is associated with a fixed oscillation frequency and decay/growth rate. For linear systems in particular, these modes and frequencies ...