Hi,
You use modal analysis to find eigenfrequencies in the linear domain, regardless of vibration mode, be it longitudinal or other. If you have trouble finding the mode you are looking for, try to ballpark the expected frequency at which your desired vibration mode occurs, then limit the solver to look in an adequatly large span around it. For a rod you might be able to ballpark this using first principles and a spring-mass-analogy.
HTH
petb