Skip to main content

Modal Damping

Modal damping is a global damping for each of the modes from modal analysis. Modal damping can be defined when doing modal superposition dynamic response analysis such as harmonic analysis and footfall analysis etc. When a model has materials with different damping characteristics, it is difficult to evaluate/estimate the modal damping. In this case, GSA gives an option in modal analysis to calculate the modal damping from the material damping defined for each of the elements used in the model. GSA calculates the modal damping for mode ii from the formula below:

ξi=k∑eξeφi.eTKeφi.eφiTKφi+m∑eξeφi.eTMeφi.eφiTMφi\xi_{i} = k\frac{\displaystyle\sum_{e}^{}{\xi_{e}\varphi_{i.e}^{T}Κ_{e}\varphi_{i.e}}}{\varphi_{i}^{T}Κ\varphi_{i}} + m\frac{\displaystyle\sum_{e}^{}{\xi_{e}\varphi_{i.e}^{T}Μ_{e}\varphi_{i.e}}}{\varphi_{i}^{T}Μ\varphi_{i}}

Where kk is the stiffness proportion damping factor in the range 00 to 11 and mm is the mass proportion of damping, where m=1−km = 1 - k, and the subscript ee refers to the element.