Miles’ equation

Abstract

The root mean square (r.m.s.) response of a single degree of freedom (SDOF) system when exposed to white noise random excitation can be approximated applying Miles’ equation. In this chapter, Miles’ equation is derived for a) a random enforced acceleration and b) a random applied force. A further approximation was introduced assuming a more or less flat PSD of acceleration and force in the vicinity of the natural frequency of the SDOF system. The accuracy of the approximation with Miles’ equation is investigated, and examples are worked out. Problems with solutions are provided to get more understanding of the limitations of Miles’ equation.