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Dr. Wieland Beckert (wbeckert)
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Username: wbeckert

Post Number: 1
Registered: 07-2003
Posted on Monday, September 20, 2004 - 12:07 pm:   

A sample descriptor ("harmonic.pde") for using FlexPDE for the harmonic analysis of transient stress problems is provided in the Flexpde\samples\time_dependend\stress folder. Additional to the mass inertia term rho*Dtt(u) it contains a damping term proportional to the velocity Dt(u).
I want to do a similar harmonic analysis including damping, but with a different damping model. A widely common approach for considering damping in FE model analyses is Rayleigh-damping, using a linear combination of the system mass-matrix [M] and the system-stiffness matrix [K] for the construction of a system damping matrix:
[C]=alpha*[M]+beta*[K] .
The approach is founded on the matrix equation for the vector of nodal DOF {U}:
[K]*{U}+[C]*{Dt[U]}+[M]*{Dtt[U]}={F},
to which the system of PDE's is internally transformed by the symbolic equation interpreter of FlexPDE.
Since the user has no direct access to the system matrices, the damping matrix [C] may not be directly constructed.
Is there any chance to provide a formulation for the velocity term (~*Dt(u)) in the PDE-form, that reproduces an appropriate Rayleigh-Damping-matrix contribution for the internal matrix-equation?

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