A transient dynamic analysis is more involved than a static analysis because it generally requires more computer resources and more of your resources, in terms of the "engineering" time involved. You can save a significant amount of these resources by doing some preliminary work to understand the physics of the problem. For example, you can:
Analyze a simpler model first. A model of beams, masses, and springs can provide good insight into the problem at minimal cost. This simpler model may be all you need to determine the dynamic response of the structure.
If you are including nonlinearities, try to understand how they affect the structure's response by doing a static analysis first. In some cases, nonlinearities need not be included in the dynamic analysis.
Understand the dynamics of the problem. By doing a modal analysis, which calculates the natural frequencies and mode shapes, you can learn how the structure responds when those modes are excited. The natural frequencies are also useful for calculating the correct integration time step.
For a nonlinear problem, consider substructuring the linear portions of the model to reduce analysis costs. Substructuring is described in the Advanced Analysis Guide.