The Floquet Theory of the Periodic Euler-Bernoulli Equation

Journal of Differential Equations

Volumn 150, Issue 1, 1998, Pages 24-41

  Papanicolaou, Vassilis G ^a   Kravvaritis, Dimitrios ^b  

^a WICHITA STATE UNIVERSITY   (United States)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Algebraic geometric multiplicity; Euler Bernoulli equation for the vibrating beam; Floquet spectrum; Pseudospectrum

Indexed keywords

EID: 0040676470     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3474     Document Type: Article

References (21)

1. Barcilon V. Inverse Problem for a Vibrating Beam in the Free-Clamped Configuration. Philos. Trans. Ro. Soc. London Ser. A. 304:1982;211-251.
2. L. F. Caudill, P. A. Perry, A. W. Schueller, Isospectral sets for fourth-order ordinary differential operators, 1996.
3. Coddington E. A., Levinson N. Theory of Ordinary Differential Equations. 1987;Krieger, Melbourne.
4. Craig W. The Trace Formula for Schrödinger Operators on the Line. Commun. Math. Phys. 126:1989;379-407.
5. Dunford N., Schwartz J. T. Linear Operators. Part II: Spectral Theory; Self Adjoint Operators in Hilbert Space. 1988;Wiley, New York.
6. Gesztesy F., Holden H., Simon B., Zhao Z. Trace formulae and inverse spectral theory for Schrödinger operators. Bull. Amer. Math. Soc. 29:1993;250-255.
7. Gesztesy F., Weikard R. Floquet Theory Revisited. Differential Equations and Mathematical Physics. Proceedings of the International Conference. 1995;Univ. of Alabama at Birmingham, March 13-17, 1994, International Press.
8. G. M. L. Gladwell, Inverse Problems in Vibration, Nijhoff, Dordrecht, 1986.
9. Johnson R. m. Ann. Math. Pura Appl. (IV). CXLVII:1987;211-248.
10. Johnson R., Moser J. The Rotation Number for Almost Periodic Potentials. Comm. Math. Phys. 84:1982;403-438.
11. Magnus W., Winkler S. Hill's Equation. 1979;Dover, New York.
12. Malamud M. Necessary conditions for the existence of a transformation operator for higher order equations. Funktsional. Anal. i Philozhen. 16:1982;74-75.
13. McLaughlin J. R. On Constructing Solutions to an Inverse Euler-Bernoulli Problem. Inverse Problems of Acoustic and Elastic Waves. 1984;SIAM, Philadelphia. p. 341-347.
14. McLaughlin J. R. Analytical Methods for Recovering Coefficients in Differential Equations from Spectral Data. SIAM Rev. 28:1986;53-72.
15. Miller R. E. The Eigenvalue Problem for a Class of Long, Thin Elastic Structures with Periodic Geometry. Quarterly of Applied Mathematics. LII:1994;261-282.
16. Naimark M. A. Linear Differential Operators. Parts I, II. 1967, 1968;Ungar, New York.
17. Papanicolaou V. G. The Spectral Theory of the Vibrating Periodic Beam. Comm. Math. Phys. 170:1995;359-373.
18. Papanicolaou V. G., Kravvaritis D. An inverse spectral problem for the Euler- Bernoulli equation for the vibrating Beam. Inverse Problems. 13:1997;1083-1092.
19. Reed M., Simon B. Methods of Modern Mathematical Physics, VI: Analysis of Operators. 1978;Academic Press, New York.
20. Sachnovich L. A. Inverse Problems for Differential Equations of ordern. Matematicheskii Sbornik. 46:1958;61-76.
21. Timoshenko S, Young D. H. Elements of Strength of Materials. 1968;Van Nostrand, Princeton.