Modal analysis using FEM: Difference between revisions

Revision as of 01:35, 1 August 2009

Revision as of 01:40, 1 August 2009

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where <math> [M] </math> is the mass matrix,

<math> [\ddot U] </math> is the 2nd time derivative of the displacement

<math> [U] </math> (i.e., the acceleration), <math> [\dot U] </math>

is the velocity, <math> [C] </math> is a damping matrix,

<math> [K] </math> is the stiffness matrix, and <math> [F] </math>

is the force vector. The onlygeneral termsproblem, keptwith arenonzero damping, is a [[quadratic eigenvalue problem]]. However, for vibrational modal analysis, the damping is generally ignored, leaving only the 1st and 3rd terms on the left hand side:

which give the following system:

:<math>

[M] [\ddot U] + [K] [U] = [0]

[K] [U] =

[0]

</math>