# Applying Rayleigh Damping to a Model

Activating the command: "Analysis: Parameters...: Advanced: Damping" tab

The information on this page applies to the following analysis types except if indicated:

Mechanical Event Simulation (MES)

It is sometimes desirable to add some damping to a physical system. It is possible to adjust these parameters so as to mimic physical damping. For example, you may want to model the effects of friction or air resistance on a part. Damping is a function of velocity, so if there is no motion then there will be no damping. Alpha and beta are constants used to set the amount of damping. Rayleigh damping came out of linear theory (mass-spring-dashpot systems) where it is easy to view each mode independently.

Alpha and beta are calculated from the following system of equations:

(1)

where wi is obtained through modal analysis and xi are damping ratios specified by the user. From the above equation, it can be shown that if two damping ratios are assigned, xi and xj, corresponding to the natural circular frequencies wi and wj, alpha and beta can be determined from the following:

(2)

Equation 1 can also be re-arranged as follows:

(3)

From this equation, it is important to note that 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 (Alpha = 0.05 is the default) 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

In order to apply Rayleigh damping to a model, you must first activate the "Apply Rayleigh damping" checkbox in the "Damping" tab. Specify the value for alpha in the "Mass-related Rayleigh damping coefficient" field. Specify the value for beta in the "Stiffness-related Rayleigh damping coefficient" field.