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Spectrum of the Free Rod Under Tension and Compression by Chasman, L. Mercredi; Chung, Jooyeon is a scholarly article available to read on EtoBox.

What is Spectrum of the Free Rod Under Tension and Compression about?

In this paper, we study the spectrum of the one-dimensional vibrating free rod equation $u^{(4)}-\tau u"=\mu u$ under tension $(\tau>0)$ or compression $(\tau<0)$. The eigenvalues $\mu$ as functions of the tension/compression parameter $\tau$ exhibit three distinct types of behavior. In particular, eigenvalue branches in the lower half-plane exhibit a cascading pattern of barely-avoided crossings. We provide a complete description of the eigenfunctions and eigenvalues by implicitly parameterizing the eigenvalue curves. We also establish properties of the eigenvalue curves such as monotonicity, crossings, asymptotic growth, cascading and phantom spectral lines.

Author

Chasman, L. Mercredi; Chung, Jooyeon

Published

2017

Language

EN