Modal analysis using FEM: Difference between revisions

Revision as of 00:13, 7 August 2018

Revision as of 16:29, 19 October 2022

Line 32:

This is the general form of the eigensystem encountered in structural

engineering using the [[Finite element method|FEM]]. To represent the free-vibration solutions of the structure, harmonic motion is assumed,.<ref>Bathe, Klaus Jürgen, '' Finite Element Procedures'', 2nd Ed., Prentice-Hall Inc., New Jersey, 1996, page 786</ref> soThis assumption means that <math>[\ddot U]</math>

is taken to equal <math>\lambda [U]</math>,

where <math>\lambda</math> is an eigenvalue (with units of reciprocal time squared, e.g., <math>\mathrm{s}^{-2}</math>),.

andUsing this, the equation reduces to:<ref>Clough, Ray W. and Joseph Penzien, ''Dynamics of Structures'', 2nd Ed.,

McGraw-Hill Publishing Company, New York, 1993, page 201</ref>