This chapter begins with the solution of equation (9.1) when the applied forces are random. The next section presents methods of improving the convergence and accuracy of the modal method of forced response. This is followed by an analysis of the response of structures to imposed displacements. Finally, the techniques of reducing the number of degrees of freedom presented in Section 8.8 are extended to forced response analysis.

Response to random excitation

Harmonic, periodic and transient forces, which are treated in Chapter 9, are termed determinisitic, since their magnitude can be described by explicit mathematical relationships. In the case of random forces, which are caused by gales, confused seas, rough roads, turbulent boundary layers and earthquakes, there is no way of predicting an exact value at a future instant of time. Such forces can only be described by means of statistical techniques.

This section begins by describing how to represent the applied forces statistically. This is followed by an analysis of the response which is also described statistically.

Representation of the excitation

A typical plot of a randomly varying force, f(t), against t (which represents time) is shown in Figure 10.1. Although it is possible to plot f(t) for a given time interval, if it has been measured during this interval, it is not possible to predict from this the precise value of f(t) at any value of t outside the interval. However, the essential features of the process f(t) can be described by means of statistical concepts.