On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations
Authors:
F. E. Udwadia and D. K. Sharma
Journal:
Quart. Appl. Math. 42 (1985), 411-424
MSC:
Primary 35R30; Secondary 35L05, 73D50
DOI:
https://doi.org/10.1090/qam/766878
MathSciNet review:
766878
Full-text PDF Free Access
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Additional Information
- Mark J. Balas, Modal control of certain flexible dynamic systems, SIAM J. Control Optim. 16 (1978), no. 3, 450–462. MR 492165, DOI https://doi.org/10.1137/0316030
F. E. Udwadia and P. C. Shah, Identification of building structural systems from records obtained during strong ground motion, J. Engg. and Industry, ASME Transactions, 98, 1347–1362 (1976)
- F. E. Udwadia and D. K. Sharma, Some uniqueness results related to building structural identification, SIAM J. Appl. Math. 34 (1978), no. 1, 104–118. MR 465354, DOI https://doi.org/10.1137/0134009
- F. E. Udwadia, Controllability, observability and identification of classical linear dynamic systems, Solid Mech. Arch. 6 (1981), no. 2, 193–211. MR 620931
F. E. Udwadia, D. K. Sharma and P. C. Shah, Uniqueness of damping and stiffness distributions in the identification of soil and structural systems, J. Applied Mech., 45, 181–187 (1978)
D. Luenberger, Introduction to Linear and Nonlinear Programming, Addison Wesley, 1965
M. M. Sondhi and B. Gopinath, Determination of vocal-tract shape from impulse response at the lips, J. Acoustical Soc. Amer., 49, 1867–1873 (1971)
- B. Gopinath and M. M. Sondhi, Inversion of the telegraph equation and the synthesis of nonuniform lines, Proc. IEEE 59 (1971), 383–392. MR 0339916
- Robert Burridge, The Gel′fand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems, Wave Motion 2 (1980), no. 4, 305–323. MR 593133, DOI https://doi.org/10.1016/0165-2125%2880%2990011-6
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
Hilbert and Courant, Methods of Mat. Physics, Vol. I, Interscience Publishers, 1966
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
- Ivar Stakgold, Green’s functions and boundary value problems, John Wiley & Sons, New York-Chichester-Brisbane, 1979. A Wiley-Interscience Publication; Pure and Applied Mathematics. MR 537127
- E. C. Titchmarsh, The theory of functions, Oxford University Press, Oxford, 1958. Reprint of the second (1939) edition. MR 3155290
E. C. Titchmarsh, Theory of the Fourier Integral, Oxford Press, 1935
- Ivar Stakgold, Green’s functions and boundary value problems, John Wiley & Sons, New York-Chichester-Brisbane, 1979. A Wiley-Interscience Publication; Pure and Applied Mathematics. MR 537127
- I. M. Gel′fand and B. M. Levitan, On the determination of a differential equation from its spectral function, Izvestiya Akad. Nauk SSSR. Ser. Mat. 15 (1951), 309–360 (Russian). MR 0045281
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A. Bamberger, G. Chavent and P. Lailly, Etude mathematique et numerique d’un probleme inverse pour l’equation des ondes a’une dimension, Report LABORIA, No. 226, IRIA
- S. Kitamura and S. Nakagiri, Identifiability of spatially-varying and constant parameters in distributed systems of parabolic type, SIAM J. Control Optim. 15 (1977), no. 5, 785–802. MR 459856, DOI https://doi.org/10.1137/0315050
- Alan Pierce, Unique identification of eigenvalues and coefficients in a parabolic problem, SIAM J. Control Optim. 17 (1979), no. 4, 494–499. MR 534419, DOI https://doi.org/10.1137/0317035
- Toshihiro Kobayashi, Determination of unknown functions for a class of distributed parameter systems, SIAM J. Control Optim. 17 (1979), no. 4, 469–476. MR 534417, DOI https://doi.org/10.1137/0317033
M. Balas, Modal control of certain flexible dynamic systems, SIAM J. Control, 16, pp. 450–462 (1978)
F. E. Udwadia and P. C. Shah, Identification of building structural systems from records obtained during strong ground motion, J. Engg. and Industry, ASME Transactions, 98, 1347–1362 (1976)
F. E. Udwadia and D. K. Sharma, Some uniqueness results related to building structural identification, SIAM J. Applied Math., 34, 104–118 (1978)
F. E. Udwadia, Controllability, observability and identification of classical linear dynamic systems, Solid Mechanics Archives, 6, (1981)
F. E. Udwadia, D. K. Sharma and P. C. Shah, Uniqueness of damping and stiffness distributions in the identification of soil and structural systems, J. Applied Mech., 45, 181–187 (1978)
D. Luenberger, Introduction to Linear and Nonlinear Programming, Addison Wesley, 1965
M. M. Sondhi and B. Gopinath, Determination of vocal-tract shape from impulse response at the lips, J. Acoustical Soc. Amer., 49, 1867–1873 (1971)
B. Gopinath and M. M. Sondhi, Inversion of the telegraph equation and the synthesis of nonuniform lines, Proc. IEEE, 59, 383–392 (1971)
R. Burridge, The Gelfand-Levitan, the Marchensko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse-response problems, Wave Motion, 2, 305–323 (1980)
E. L. Ince, Ordinary Differential Equations, Dover, pp. 235–240
E. L. Ince, Ordinary Differential Equations, Dover
Hilbert and Courant, Methods of Mat. Physics, Vol. I, Interscience Publishers, 1966
E. L. Ince, Ordinary Differential Equations, Dover, pp. 275–278
I. Stakgold, Green’s Functions and Boundary Value Problems, Wiley, 1979
E. C. Titchmarsh, The Theory of Functions, Oxford Press, 1979
E. C. Titchmarsh, Theory of the Fourier Integral, Oxford Press, 1935
I. Stakgold, Green’s Functions and Boundary Value Problems, Wiley, 1979
I. M. Gelfand and B. M. Levitan, On the determination of a differential equation from its spectral function, Izvestiya Akad. Nauk SSR, 15, 309–360 (1951)
N. Levinson, The inverse Sturm-Liouville problem, Mat. Tidsskr, B, 25–30 (1949)
A. Bamberger, G. Chavent and P. Lailly, Etude mathematique et numerique d’un probleme inverse pour l’equation des ondes a’une dimension, Report LABORIA, No. 226, IRIA
S. Kitamura and S. Nakagiri, Identifiability of spatially-varying and constant parameters in distributed systems of parabolic type, SIAM J. Control and Optimization, 15, 785–802 (1977)
A. Pierce, Unique identification of eigenvalues and coefficients in a parabolic problem, SIAM J. Control and Optimization, 17 494–499 (1979)
T. Kobayashi, Determination of unknown functions for a class of distributed parameter systems, SIAM J. Control and Optimization, 17 469–476 (1979)
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Article copyright:
© Copyright 1985
American Mathematical Society