Mechanical joints may have nonlinear damping and stiffness, due to.frictional slipping between the connected members, etc. I am enclosing modeling advice from a colleague and related links.
– Tom Irvine
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If the nonlinearity stays fairly weak then there are a few options to do a worst case analysis:
1.) For broadband loads the linear model with low-level damping is usually a very conservative model for the system at high amplitude (in our cases we frequently see damping increase by a factor of 3-4). Of course if you have a sharp harmonic then you need to consider the downward shift in frequency, but that is usually small and you’re not likely to design something to have a strong excitation frequency just barely below resonance.
2.) To improve fidelity, these uncoupled 1DOF oscillator models with power-law dissipation (i.e. log(damping) vs log(displacement amplitude) = linear) can do a very good job of capturing how the damping changes with amplitude. It APPEARS (no guarantees with nonlinearity) that one can obtain a “worst case” analysis by using a linear model with damping near the maximum damping expected at that amplitude. However, a word of caution: the frequency shift smears the resonance peak, so one cannot necessarily assume that the damping measured by a half-power method will be accurate! We use a Hilbert transform or some other time domain technique to estimate damping at a time instant (and therefore at a certain amplitude). We have also used step-sine tests (in a paper for this year’s IMAC) with a phase condition to find the resonance frequency and damping with good success. In any event, an approach such as this will be less over-conservative than a linear model based on low-amplitude response and if one is careful it is probably possible to still make sure it is conservative.
3.) If there is nonlinearity then one should also think whether any nonlinear phenomena might come into play: super-harmonic resonance (exciting a mode at omega by applying a force at (1/2)*omega, (1/3)*omega, etc…; modal coupling (modes are excited that shouldn’t be based on linear theory), chaos, etc…
Dr. Matt Allen, University of Wisconsin-Madison
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