Response of One-Degree-of-Freedom System to Harmonic Loading

Abstract

In this chapter, we will study the motion of structures idealized as single-degree-of-freedom systems excited harmonically, that is, structures subjected to forces or displacements whose magnitudes may be represented by a sine or cosine function of time. This type of excitation results in one of the most important motions in the study of mechanical vibrations as well as in applications to structural dynamics. Structures are very often subjected to the dynamic action of rotating machinery which produces harmonic excitations due to the unavoidable presence of mass eccentricities in the rotating parts of such machinery. Furthermore, even in those cases when the excitation is not a harmonic function, the response of the structure may be obtained using the Fourier Method, as the superposition of individual responses to the harmonic components of external excitation. This approach will be dealt with in Chap. 20as a special topic.