## Modal Analysis of Geometrically Discontinuous Energy Harvester

This task was first performed when I was first getting involved with the structural health monitoring group at UCSD. A Ph.D. student was working on research regarding a non-linear energy harvesting oscillator (Figure 2). The nascent stages of research required as eigenanalysis of a theoretical model of the oscillator to validate research from a previous study.

I needed to generate mode shapes and natural frequencies for the first ten modes so they could be validated against previous research. The difficulty in the problem was that the steel cantilevered beam had PZT laminates on both sides at the base of the beam, and the tip of the cantilever was outfitted with a permanent magnet. These posed interesting boundary and continuity conditions that needed to be met to solve the problem.

The mode shapes are pictured in Figure 1. The natural frequencies matched the testing that was previously conducted so the research was able to continue. I used a Mathematica script to solve the partial differential equation that governed the beam dynamics and to impose all boundary and continuity conditions.