Semiclassical analysis of vibroacoustic systems

Welch, Barry Alan (2005) Semiclassical analysis of vibroacoustic systems. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

In this thesis we present the development of semiclassical techniques and apply these techniques, with the aim of investigating elastic plate systems. For the circular plate the eigenvalues and numerical error in comparison to established results are calculated by an altered version of Gutzwiller’s Trace Formula. In addition this formula is applied to the square plate to find that the free edge boundary condition produces less accurate results than other cases.

The transfer matrix method of Bogomolny to calculate semiclassical phase correction terms is followed for the free edge boundary condition and a phase correction is found that improves in accuracy on the previously thought value and includes contributions from lower order wavenumber and boundary curvature terms.

A system with a diffractive centre is looked at by applying a quantum scattering technique and we find that in the case of the elastic plate that a diffraction coefficient cannot be determined without neglecting lower order terms and so the effects of these terms are still in question. By looking at the diffractive problems as a star graph model we found that the statistical properties follow those of the quantum billiard and that the model is applicable to plate systems.

Text

1027766.pdf - Version of Record

Available under License University of Southampton Thesis Licence.

Download (1MB)