Research

My primary area of interest is applied evolutionary partial differential equations (PDE) studying problems at the intersection of functional analysis, mathematical modeling, and physical applications in mechanical engineering.  More specifically, my work has been motivated by fluid-structure interactions, where the principal phenomenon of interest is instability. 


Instability occurs in many applications like aircraft paneling, suspension bridges, pipes conveying fluid, and energy harvesting devices. Naturally, in the majority of these applications, one seeks to suppress or minimize instability. Nevertheless, in energy harvesting, dynamic instability is encouraged. It has been shown experimentally that extraction of energy is feasible via large, flow-induced deflections of cantilevered beams and cantilevered plates. From these displacements, mechanical energy can be harvested from the flow via piezoelectric laminates or patches (for which oscillating strains induce currents). 


To effectively and efficiently harvest energy in this manner, one must be able to capture and predict the post-onset behaviors of the unstable cantilever, and thus, one must have a viable PDE model for the large deflections.  I am interested in modeling, analyzing, and simulating such PDEs. More details about my work can be found in my publications listed below.