# The spectral theory of the vibrating periodic beam

@article{Papanicolaou1995TheST,
title={The spectral theory of the vibrating periodic beam},
author={Vassilis G. Papanicolaou},
journal={Communications in Mathematical Physics},
year={1995},
volume={170},
pages={359-373}
}
• V. Papanicolaou
• Published 1 June 1995
• Mathematics
• Communications in Mathematical Physics
AbstractWe study the spectral theory of the fourth-order eigenvalue problem $$\left[ {a(x)u''(x)} \right]^{\prime \prime } = \lambda \rho (x)u(x), - \infty< x< \infty ,$$ , where the functionsa and ϱ are periodic and strictly positive. This equation models the transverse vibrations of a thin straight (periodic) beam whose physical characteristics are described bya and ϱ.We examine the structure of the spectrum establishing the fact that the periodic and antiperiodic eigenvalues are the…
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