Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The primary goal of this dissertation is to develop analytic representation formulas and power series to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lame' system inside phononic crystals. Then we obtain convergent power series for the Bloch wave spectrum using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the inclusion array and the Dirichlet spectra of the inclusions. Sufficient conditions for the separation of spectral branches of the dispersion relation for any fixed quasi-momentum are identified. Finally, we found a condition that is sufficient for the emergence of band gaps.

Committee Chair

Lipton, Robert P.

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