Modeshape

Mode shapes in physics are specific patterns of vibration that a structure or system can exhibit when it oscillates at its natural frequencies. These patterns describe the relative displacement of different parts of the system during vibration.

In applied mathematics, mode shapes are a manifestation of eigenvectors which describe the relative displacement of two or more elements in a mechanical system [1] or wave front.[2] A mode shape is a deflection pattern related to a particular natural frequency and represents the relative displacement of all parts of a structure for that particular mode.

Mathematical derivation

Mode shapes have a mathematical meaning as 'eigenvectors' or 'eigenfunctions' of the eigenvalue problem which arises, studying particular solutions of the partial differential equation of a system.

See also

References

  1. ^ College, Erik Cheever, Swarthmore. "Vibration Animations". lpsa.swarthmore.edu.{{cite web}}: CS1 maint: multiple names: authors list (link)
  2. ^ Bobkov, K. K.; Bubnov, M. M.; Aleshkina, S. S.; Likhachev, M. E. (22 May 2018). "Long-term mode shape degradation in large mode area Yb-doped pulsed fiber amplifiers". Laser Physics Letters. 14 (1) 015102. doi:10.1088/1612-202X/14/1/015102. S2CID 125527048 – via Institute of Physics.


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