Physical Sciences and Mathematics Commons^™

The Vibrational Modes Of Spheroidal Cavities In Elastic Solids, David Stewart

Doctoral Dissertations

"A general analysis of all possible cavity shapes is given with a discussion of the mathematical difficulties involved for the various cases. Special emphasis is given to cavity shapes describable in terms of the coordinate surfaces of coordinate systems separating the scalar wave equation. 112 such shapes are identified and discussed. Free boundary condition equations for spheres and spheroids are derived in complete generality in terms of potentials. The difference in the vibrations of a solid and those of a cavity of the same shape is discussed and made clear. The impossibility of deriving a frequency equation for uniform radial …