My research interests focus largely on numerical simulation of systems undergoing vibration. Here’s a few topics in which I am interested.

### Rattlebacks

I’ve recently developed an interest in rigid body dynamics, specifically modeling the dynamics of toys and other curiosities. This grew from an undergraduate research project I advised where the student aimed to simulate rattleback behavior. A rattleback, otherwise known as a celt or wobblestone, is a semi-ellipsoidal top that has a preferred direction of spin. If spun, say counter clockwise, the top spins happily, but if spun clockwise, the top will begin to rattle and reverse its direction of spin. The animation below, courtesy of Dr. Hugh Hunt, shows this reversal behavior.

We managed to come up with a nice simulation to mimic this behavior. The animation on the left shows the rattleback spinning happily, while the animation on the right shows the reversal.

Dr. Hunt and I also developed a simple explanation as to why this reversal occurs, which is supported by the equations of motion developed for the system. You can read all about it in this Journal of American Physics article found here, or you can download the article here. If you’d like to skip all of the math, you can jump right to Section IV.

As a side note, I highly recommend checking out the Journal of American Physics. They publish great articles about all sorts of interesting physics related projects, with the mission “to publish articles on the educational and cultural aspects of physics that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers.” I’m not associated with the journal, by the way, just a fan.

### Ground Vibrations

One aspect of my research the study of traffic induced ground vibration and how variation in soil properties can affect wave propagation. For example, here are a couple of interesting animations showing how wave interaction changes with the inclusion of a simple horizontal layer.

These animations have been computed with the latest version of the ElastoDynamics Toolbox for Matlab, developed by Mattias Schevenels, Stijn Francois and Geert Degrande at K.U. Leuven in Belgium. For further information visit the K.U. Leuven Structural Mechanics group page.

I’m interested in quantifying the effect soil variation has on the level of vibration which arrives at locations of interest. In the past I’ve considered inclined soil layers, cavities, and stochastic variation of soil stiffness. I’ve found these all produce significant particle velocity gains of more than 5dB.

My interest in this area began during my PhD where I began working on the Pipe-in-Pipe model. This model is used to quickly predict vibration levels due to underground railways. This is a joint project with the University of Cambridge and The University of Nottingham.

Recently, I’ve been working on a semi-analytic solution for thick-layered media with varying properties, finite element models of semi-infinite media using perfectly-matched layer absorbing boundaries, and vibration induced noise.

### Wavelet-Galerkin Methods

Another research interest I’m pursuing is the use of wavelet-Galerkin methods for solving nonlinear partial differential equations involving contact. This work is a collaborative effort with McGill University with the goal of improving computational modeling of rotor/stator interaction within turbine engines.

Wavelets tend to be highly localized functions which we hypothesize will allow us to capture rapid changes in the displacement response, and even nonsmoothness, known to be present in vibration problems involving contact. We can assume *apriori* that the solution will be periodic, since the turbine is exhibiting periodic motion, which allows us to impose periodic boundary conditions on the problem. We are currently working on formulating the unilateral contact problem as an optimization problem to find sparse solutions to the Galerkin problem.

Shown below are some of the popular wavelets taken from D. Lee Fugal’s book Conceptual Wavelets.