ABSTRACT
Many engineering systems, such as turbomachines, bridges, and aircraft, are modeled with hundreds if not thousands of degrees-of-freedom. Each degree-of-freedom has a frequency of vibration, much in the same way as a single degree-of-freedom oscillator has a natural frequency. However, systems with multiple degrees-of-freedom are more complicated due to the physical coupling that exists between pairs of degrees-of-freedom. In this chapter we introduce a new concept – called the mode of vi-
bration –which exists in systems of two or more degrees-of-freedom. A vibrating linear system, while moving in very complicated patterns, can be modeled as n uncoupled vibrating oscillators if special coordinates – called principal coordinates –are used. We will demonstrate that the single degree-of-freedom oscillator is the basis for solving many linear multi degree-of-freedom (MDOF) vibrating systems.
