Eigenvalue analysis
An eigenvalue analysis providing eigenmodes and eigenfrequencies comes as a part of the earthquake analysis in GEO5. The motivation for the eigenvalue analysis is the need for low eigenfrequencies that are required when setting the Rayleigh damping.
The modal analysis is based on the discretized undamped equation of motion for free oscillations which come in form:
where: | M | - | mass matrix |
K | - | stiffness matrix | |
ω | - | i-th eigenfrequency | |
ϕ | - | i-th eigenmode |
When choosing a particular eigenfrequency for Rayleigh damping it is useful to assess whether the frequency corresponds more to horizontal or vertical oscillations. The modal participation factors in x and z directions.
Further details are available in the theoretical manual on our website.
Literature:
Z. Bittnar, P. Řeřicha, Metoda konečných prvků v dynamice konstrukcí, SNTL, 1981.
T. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice Hall, INC., Engelwood Clifts, New Jersey 07632, 1987
Z. Bittnar, J. Šejnoha, Numerical methods in structural engineering, ASCE Press, 1996