An inverse spectral problem for the Euler-Bernoulli equation for the vibrating beam

Inverse Problems

Volumn 13, Issue 4, 1997, Pages 1083-1092

  Papanicolaou, Vassilis G ^a   Kravvaritis, Dimitrios ^b  

^a WICHITA STATE UNIVERSITY   (United States)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039255739     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/13/4/013     Document Type: Article

References (15)

1. Barcilon V 1982 Inverse problem for a vibrating beam in the free-clamped configuration Phil. Trans. R. Soc. A 304 211-51
2. Barcilon V 1987 Sufficient conditions for the solution of the inverse problem for a vibrating beam Inverse Problems 3 181-93
3. Bishop R E D and Johnson D C 1960 The Mechanics of Vibration (Cambridge: Cambridge University Press)
4. Borg G 1946 Eine umkehrung der Sturm-Liouvilleschen eigenwertaufgabe Acta Math. 78 1-96
5. Coddington E A and Levinson N 1987 Theory of Ordinary Differential Equations (Malabar, FL: Krieger)
6. Dunford N and Schwartz J T 1988 Linear Operators. Part II: Spectral Theory; Self Adjoint Operators in Hubert Space (New York: Wiley)
7. Gelfand I M and Levitan B M 1951 On the determination of a differential equation from its spectral function Izv. Akad. Nauk Ser. Mat. 15 309-60 Gelfand I M and Levitan B M 1951 On the determination of a differential equation from its spectral function Am. Math. Soc. Trans. Ser. 2 1 253-304
8. Gelfand I M and Levitan B M 1951 On the determination of a differential equation from its spectral function Izv. Akad. Nauk Ser. Mat. 15 309-60 Gelfand I M and Levitan B M 1951 On the determination of a differential equation from its spectral function Am. Math. Soc. Trans. Ser. 2 1 253-304
9. Gladwell G M L 1986 Inverse Problems in Vibration (Boston, MA: Martinus Nijhoff)
10. Levinson N 1949 The inverse Sturm-Liouville problem Matematisk Tidsskrift. B 25-30
11. McLaughlin J R 1984 On Constructing Solutions to an Inverse Euler-Bernoulli Problem Inverse Problems of Acoustic and Elastic Waves ed F Santosa et al (Philadelphia, PA: SIAM) pp 341-7
12. Papanicolaou V G 1995 The spectral theory of the vibrating periodic beam Commun. Math. Phys. 170 359-73
13. Timoshenko S and Young D H 1968 Elements of Strength of Materials 5th edn (Princeton, NJ: Van Nostrand)
14. Yurko V A 1990 A problem in elasticity theory Prikl. Matem. Mekhan. 54 998-1002 (Engl. transl. PMM USSR 54 820-4)
15. Yurko V A 1990 A problem in elasticity theory Prikl. Matem. Mekhan. 54 998-1002 (Engl. transl. PMM USSR 54 820-4)