Forced vibrations

Abstract

The general solution for externally excited vibrating systems with an arbitrary excitation function was given by (4.42) in Chapter 4. However in technical vibrating systems one often deals with very special excitation functions, such as the impulse function, the step function, and periodic functions. Impulsive excitation forces are frequently encountered in vibrating vehicles, e.g., when a motor car travels along a road with a few potholes, or if an airplane encounters local air turbulence. Periodic excitation forces appear in vibrating systems incorporating unbalanced rotating subsystems, e.g., in unbalanced centrifuges and in cars with unbalanced wheels. Periodic forces are also responsible for nearly all disturbances in the dynamics of machines. Further, periodic excitation of a motor car can be caused by an undulating road surface and ships may be periodically excited by a swell. The multitude of applications justifies the investigation of vibrating systems with impulsive, step, and periodic excitation. Here one should also take into account the special properties of mechanical systems.