The spectral theory of the vibrating periodic beam

DOI10.1007/BF02108333zbMath0828.34078MaRDI QIDQ1894884

Vassilis G. Papanicolaou

Publication date: 10 January 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

inverse problemdeterminant formulafourth-order eigenvalue problemstructure of the spectrumpseudogapstransverse vibrations of a thin straight periodic beam

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

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Cites Work

• m-functions and Floquet exponents for linear differential systems
• The rotation number for almost periodic potentials
• The trace formula for Schrödinger operators on the line
• Sufficient conditions for the solution of the inverse problem for a vibrating beam
• Trace formulae and inverse spectral theory for Schrödinger operators
• The eigenvalue problem for a class of long, thin elastic structures with periodic geometry
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