Exact Shared Modal Functions and Frequencies for Fixed and Free Isospectral Membrane Shapes Formed from Triangles
For two different but isospectral polygonal membrane shapes (sharing the same complete vibration spectrum) formed from seven congruent elemental isosceles triangles, some exact shared frequencies and analytical modal function expressions which display the nodal curves are given explicitly. Both Dirichlet (fixed) and Neumann (free) boundary conditions are considered. Figures of the first few nodal patterns are drawn: they are quite distinctive and not all merely restricted to regular rectilinear sub-divisions. Computed modal function contour plots enable the overall sequential mode numbers to be assigned. The exact frequencies and sequential mode numbers for these analytical modes could be used as benchmarks in experimental investigations. The relevance for simply-supported polygonal plates is also discussed.
Journal of Sound and Vibration
Engineering not elsewhere classified