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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
The answer depends on how you want to model the damping.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
for a viscous damping on this book (pag815):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.