9. Modal Analysis of Mechanical Vibrations

Mechanical vibrations became an important design consideration during the early 1900s when machinery began to move at higher and higher speeds. Initially, mechanical vibrations were modeled as quasi-static events, i.e. structural responses were determined by treating dynamic forces as static even though they varied with time. The quasi-static approach is a practical and useful design tool provided the forcing frequency is much less than the fundamental frequency of the structure as discussed in Chapter 2. Fatigue analyses of many offshore structures are based on this assumption as ocean wave frequencies are much lower than natural frequencies of the structure. However, if the driving frequency is close to a natural frequency of a structure, the mass of the structure plays a significant role in dynamic response.