The discussion centers on calculating the transfer function of multi-degree-of-freedom (MDOF) damped systems, specifically focusing on a 4 DOFs system and the natural frequencies involved. Participants seek methods for modeling damping in these systems, contrasting approaches for both known and unknown sources of damping.
Participants do not reach a consensus on a single method for calculating the transfer function of damped systems, as different modeling approaches and assumptions about damping are discussed.
Participants mention the complexity of the eigenproblem and the implications of different damping models, but do not resolve the mathematical steps or assumptions involved in these calculations.
serbring said:I need to calculate the transfer function of a 4 DOFs system, in particular I need to calculate the system natural frequencies. Do you know to figure out these? On books I have found how to get it in the undamped case. Thanks
AlephZero said:The answer depends on how you want to model the damping.
In the general case where you have known physical sources of damping (e.g. dashpots) in the model, you have a 4x4 quadratic eigenproblem and both the eigenvalues and vectors (mode shapes) will be complex. In other words, the motion of the different DOFs in a mode are not in phase with each other.
In practice, for small levels of damping where the physical cause of the damping is not known explicitly, you would use a modal damping model based on the undamped modes and frequencies.