Can we say that a rotordynamic study of a machine is part of vibration analysis?Or is rotordynamic study is different from vibration analysis?

A rotordynamic study is typically a computer model simulation of the rotor system with the intention of designing a rotor system that will have low vibrations. A rotordynamic study can be used to predict the level of vibrations to be expected in the field.

In the case of a existing machine with vibration problems, a rotordynamic study might be done in conjunction with a vibration analysis to correlate the rotor model with the actual vibration measured in the field, and then be used to change the machine design to solve the vibration issues.

But in general a rotordynamic study and a vibration analysis are two different but complementary things.