3. Modal Analysis of Multi-Degree-of-Freedom Systems

The preceding chapter dealt with the basics of rotor vibrations concerning a single-degree-of-freedom (single-dof, 1-dof) system. An actual machine should, however, be analyzed as a multi-degree-of-freedom (multi-dof) system where multiple masses are arranged according to the shape of the rotor shafting. The equation of motion for such a system is represented using matrices. Eigenvalue analysis of the multi-dof system gives the natural frequencies and eigenmodes. These are important factors in rotor design because they represent the resonance frequencies and the vibration mode shapes at critical speeds. This chapter also discusses modal analysis, in which a multi-dof system is reduced to an assemblage of single-dof systems utilizing the orthogonal condition of the eigenmodes. In other words, a complicated actual system is simplified to a set of simple 1-dof systems corresponding to each mode. In addition, a simple estimation method of the natural frequency and the damping ratio is presented based on the orthogonality condition.