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Linear Modal Damping vs. Rayleigh Damping

[ Edited ]
Hello Experts!,
I always have the same question: how to prescribe correctly the Damping effects in a FE model to be solved with the Advanced Nonlinear Dynamics Transient analysis (SOL601, 129) module using implict direct integration?.

In Nonlinear Static/Transient Analysis we have the following types of dampings:
• Damping from numerical integration: achieved by modifying the Newmark time integration parameters (alpha=0.25 and delta=0.5 by default) via NXSTRAT card for Iteration & Convergence parameters.
• Rayleigh Damping: this is mine!!. In Rayleigh damping C=alpha*M + beta*K, where alpha & beta are the Rayleigh Damping constants. If I do a SEARCH for RAYLEIGH in ALL the NX NASTRAN 8.1 manuals I only find ONE reference that says the following: "Rayleigh damping is supported and specified with PARAM ALPHA1 and ALPHA2. Only ALPHA1 is supported for SOL 701". Here the question is
• Also wen selecting "Low Speed Dynamic Analysis" the solver will include mass & damping effects in the analysis. The damping is evaluated as C=beta*K, where K is the initial stiffness matrix and beta is the Rayleigh damping parameter.
• And finally I understand we have the DAMPER ELEMENTS like PBUSH elements to mesh damping explicitely on elements.

But what I am looking for is a correlation between the modal damping we use for instance in LINEAR modal time history analysis of say 2% and the equivalent damping to prescribe DIRECTLY in a nonlinear transient implicit dynamic analysis using Rayleigh parameters alfa & beta constants, any HELP is welcome -- thanks!. I need an approach for selection of Rayleigh damping coefficients to be used in seismic analyses to produce response that is consistent with Modal damping response to account for nonlinearities of both material & geometry.

Por instance, solving the CANTILEVER BEAM example posed yesterday as NonLinear Transient Dynamic (SOL601,129) I get the following answer for displacements of T2 Translation and T2 Accelerations vs. time for tip node #21 and also the T2 Constraint Force at node#1:








Comparing results we can see that the nonlinear transient dynamic response (SOL601,129) WITHOUT PRESCRIBING ANY RAYLEIGH DAMPING values are the most demanding values, then the need to prescribe correctly the damping constant for nonlinear transient dynamic analysis. Please note this is a simply beam model where not any nonlinearity of large displacements neither material exist, but in real problems this could be critical.



Best regards,
Blas.