Title: Recent Advances in Parametric Excitation
By Professor Richard Rand,
Dept. Theoretical and Applied Mechanics,
Abstract: Parametric Excitation refers to dynamics problems in which the forcing function enters into the governing differential equation as a variable coefficient. The paradigm example is given by Mathieu's equation:
x'' + (d + e cos t) x = 0.
This has application to many engineering systems, the simplest example of which is the vertical forcing of a pendulum.
In this lecture, the basics of parametric excitation will be reviewed and some new results will be presented.
Current research work involves using perturbation methods and bifurcation theory to obtain approximate solutions to differential equations arising from nonlinear dynamics problems in engineering and biology.