Transverse Vibrations of Multi Degree Freedom Systems:

The beams or shafts have distributed mass and like such they contain infinite degrees of freedom if their distributed mass is let. In additionally, to their own mass, they might be supporting some loads that may be more than one. In Section 15.3.4 mass of the shaft/beam was neglected and the supported single load was considered only. It was a single degree freedom system. For letting general case, we need to proceed step-by-step and utilizes empirical methods to find out the fundamental natural frequency of the transverse vibration system as it has the largest displacement and so maximum stress.