# Multi-Degree-of-Freedom Rotor-Bearing Systems

• Chong-Won Lee
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 21)

## Abstract

Many investigations in linear rotor dynamics deal with the problems of natural, unbalance and transient vibrations. Powerful approximation methods, e.g., the finite element method, are available for solving these problems. In most cases, a fine partitioning of the rotor model is necessary and this leads to large linear differential equation systems for the unknown displacements; this is called the displacement method. With such large systems the calculation is very time consuming, especially for transient vibrations due to a short circuit, blade break and so on. Therefore methods are needed which allow a reduction and possibly a decoupling of the equations. A classical technique for calculating the response of non-rotating elastic systems with symmetric and proportional damping is known as modal analysis. The idea is to reduce a system of simultaneous ordinary differential equations to a set of independent ordinary differential equations. The successful application of the method requires the solution of an eigenvalue problem associated with the given system. The eigenvectors or natural modes possess the orthogonality property, which permits the formulation of an expansion theorem for the response. The expansion in terms of the system natural modes leads to a set of independent ordinary differential equations of the same form as that describing the behavior of a single degree of freedom system.

## Keywords

Vibration Analysis Nyquist Plot Modal Vector State Space Form Complex Notation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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