Transient Structural can simulate the time-history of vibration including all nonlinear effects, but it will take a long time and a lot of disk space to solve.

I recommend starting with a model that uses only linear materials and build a Modal analysis, then drag and drop a Harmonic Response analysis onto the Solution cell of Modal to setup a Mode Superposition (MSUP) Harmonic Response analysis. The benefit of this analysis is it solves very fast.

Once you have completed the analysis with linear materials, duplicate the model, convert it to a Transient Structural and add the material nonlinearity to perform the time-history analysis.