Determination of Response

Abstract

In addition to the outline in the introduction, methods of determining response have been given in Chapter 5. The purpose of this chapter is not to give further methods, but to consider in greater depth the normal mode method. It will be recalled that there are three main types of excitation, namely harmonic, transient and random. It has been shown that the normal mode method can be used to determine the response to harmonic and transient excitations; also this method yields the complex frequency response function, which is required in the determination of random response. For comparison the frequency response method yields directly steady-state solutions for harmonic problems and has similar applicability to the determination of random response as the normal mode method. The direct or numerical integration methods are applied in practice only to transient problems, but have added importance because of their applicability to non-linear problems. Thus the normal mode method is considered in greater depth here because of its versatility, but it is also the method which provides some physical understanding of the vibration of complex structures.