A variational approach to the problem of oscillations of an elastic half cylinder

Abstract

This paper is devoted to the spectral theory (more precisely, to<br />the variational theory of the spectrum) of guided waves in an<br />elastic half cylinder. We use variational methods to investigate<br />several aspects of propagating waves, including localization (see<br />Figure 1), existence criteria and the formulas to find them. We<br />approach the problem using two complementary methods: The<br />variational methods for non-overdamped operator pencils to<br />describe eigenvalues in definite spectral zones, and<br />Ljusternik-Schnirelman critical point theory to investigate<br />eigenvalues in the mixed spectral zone where the classical<br />variational theory of operator pencils is not applicable.