Abstract

The Fokker-Planck equation is a partial differential equation that governs the probability density function of the response of a system (linear or nonlinear) to wideband random excitation. The equation was first derived by researchers in the field of statistical mechanics in the 1910s and it has been applied to mechanical systems by engineers since the 1960s. The equation is not covered on engineering undergraduate courses and so it is not as well known as perhaps it ought to be. This talk will provide an overview of the equation and show how it can be used to find the statistics of nonlinear vibration for low order systems, and how weighted integrals of the equation can lead to very useful general results for complex high order systems. In the latter case, examples include results relating to entropy, energy flow, and energy harvesting. As a preamble the talk will include a discussion of the various types of engineering research and how work on the Fokker-Planck equation fits into the bigger picture.