1 Reply Latest reply on Mar 18, 2017 3:04 PM by Alessandro Tornincasa

    Values of Rayleigh Damping Coefficients in Non-Linear Dynamic Simulation (Aluminium)

    David Barbado

      I'm working with a model of a rigid catenary. The majority of the pieces are made of aluminium.


      I know that I need the frequences in order to calculate propperly the coefficients but I only want an aproximation.


      Could someone give me a typical range of this values?


      I have tried 2 options:


      - Both coefficientes = 0  -------> Very high vibration of the beam


      - Both coefficientes = 1 -------> Very low vibration of the beam


      Thank you.

        • Re: Values of Rayleigh Damping Coefficients in Non-Linear Dynamic Simulation (Aluminium)
          Alessandro Tornincasa

          Here are some suggestions.


          - If [C] = Alpha * [M] (with Beta = 0), the higher modes of the structure will be assigned very little damping. - - While if [C] = Beta * [K] (with Alpha = 0), the higher modes will be heavily damped.

          Thus, by assigning appropriate values to alpha and beta, the user can filter or retain the effect of the higher modes.


          Based on the above discussion, it is easy to also think of each mode damping independently. For example, one can think of the first harmonic damping to half its magnitude in 10 seconds, whereas the second mode might damp to half its magnitude in 2 seconds. Rayleigh damping is an empirical means by which to damp all frequencies. Of course, because there are only two parameters (alpha and beta), the user can only specify how two given frequencies should damp. All other frequencies damp as well, but following the Rayleigh model.


          For the simple mass-spring-dashpot systems, the user picks two frequencies and sets by how fast each should damp. This gives two equations and two unknowns which is a solvable system! For FEA, generally "rule of thumb" arguments are used to choose alpha and beta. It is suggested to try different values for each and observe how the solution changes. It should be noted that damping is used to mimic physical damping, so caution is warranted. But, when one is interested in the static solution, it is appropriate to apply as much damping as possible. This will result in one obtaining equilibrium faster.


          Testing has shown that alpha is the easier parameter to manipulate. Some general values and their effect are listed below:

          - Alpha=0.05 very little damping

          - Alpha=2.5 noticeable damping

          - Alpha=5-10 very noticeable damping

          - Alpha>10 pronounced damping and some difference between final deformed shapes obtained using different alpha values