Hi, sorry for my ignorance.. but is it possible to find the natural frequencies of a structure using "nonlinear time history analysis" instead of "modal analysis"? I'm asking this because the structure that I'm analyzing contains non linear elements (cables) and sap2000 in the modal analysis considers only linear elements.
Sure, but not quite. The term 'natural frequency' usually has special meaning that derives from the math that underlines linear systems. A nonlinear system may or may not exhibit 'modal' behavior.
One thing you can do is to linearize the model, replacing the nonlinear cables with linear ones, then doing modal analysis on that. Judge the output based on how far you think the linearization took you from reality.
The other thing you can do is to run the nonlinear time history using a step velocity input, then look at the output traces. If the output is dominated by one sinusoid, then maybe you're done. If you can't read it by eye though, you may have to resort to frequency analysis of the output. Depends a lot on what you intend to do with it.
What happens if you define a forcing function that closely approximates a step function and then run your nonlinear time-history analysis? Do you see any oscillation in the system response? (I bet you do.) Maybe you could look at the spectrum of that response and get an idea of your "eigenvalues" (such as they are).
I suppose it would be wise to keep decreasing the step size and also increasing the slope of the "step" until you stop seeing a difference in the response, but I'm winging it here. Try it and let us know what happens.
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Thanks, it is a truss bridge where the "floor'' is appended to the truss using cables. My concern is that, since one of its modal frequncies is about 2Hz, it may experience resonance when lots of pedestrian walk/run on it (see the millenium bridge).