Stochastic or random vibrations occur in a variety of applications of mechanicalengineering. Examples are: the dynamics of a vehicle on an irregular roadsurface; the variation in time of thermodynamic variables in municipal wasteincinerators due to fluctuations in heating value of the waste; the vibrationsof an airplane flying through turbulence; the fluctuating wind loads acting oncivil structures; the response of off-shore structures to random wave loading.Attention will be focussed on problems of external noise. That is, we shall consider models of mechanical engineering structures where the source of random behavior comes from outside: e.g. a prescribed random force or a prescribed random displacement. The structures inhibit inertia, damping and restoring, linear and non-linear. The main questions we intend to answer are: how do these structures respond to random excitation, and how can we quantify the random behavior of response variables in a manner that an engineer is able to make rational design decisions
