Better Understanding of Resonance through Modeling and VisualizationD.O. Ludwigsen, C. Jewett, and M. Jusczcyk
Students encounter cavity resonance and waveguide phenomena in acoustics courses and texts, where the study is usually limited to cases with simple geometries: parallelepipeds, cylinders, and spheres.
At Kettering University, we are beginning to employ finite element modeling in our acoustics classes to help undergraduates better understand the acoustic modes of actual structures. This approach to the time-independent wave equation (the Helmholtz equation) was first used in a research and measurements class to investigate two classic resonance problems.
For example, pressure mode shapes were measured by moving a small microphone. The measurements were then compared to results from a time-harmonic finite element model, and when possible, to predictions based on simplified models.
The dependence of the mode shape on varying cross-section enriched the understanding that the textbooks could deliver. In the noise control problem with a duct and resonator, the interaction of the resonator with standing waves of the duct was made clear through visualization. In particular, the model could simulate an infinite duct—not available in our lab!—to clarify the effect of the Helmholtz resonator.