1) For the modal analysis that using linear analysis, what is the value of the isolator effective stiffness that STKO uses? Since the initial stiffness that we define in the element properties is not the effective stiffness.
The eigen analysis in OpenSees uses the current stiffness of the material that you are using. There is no way to tell OpenSees to use a different (equivalent) stiffness.
What we did in that webinar, is to perform an initial analysis with the nonlinear bearing element, and from that we computed the equivalent stiffness. Then there was a custom script (just before the last eigen analysis) where we compute the equivalent stiffness, remove the bearing element, and replace them with elastic springs with the equivalent stiffness.
3）For some values of singleFPBearing element initial stiffness will occur the instability results of acceleration, does STKO has the recommendation range of the initial stiffness of singleFPBearing element?
We don't have a general recommendation for it. Try to play with the stiffness values to understand when it becomes unstable and try to understand why