On the numerical reconstruction of a spring-mass system from its natural frequencies
DOI:
https://doi.org/10.22199/S0716-09172000000100003Keywords:
Inverse vibration problems, mass matrix, stiffness matrix, Jacobi matrix, problemas de vibración inversa, matriz de masa, matriz de rigidez, matriz Jacobiana.Abstract
References
[1] C. De Boor and E.B. Saff, Finite sequence of Orthogonal polynomials connected by a Jacobi matrix, Lin. Alg. Appl. 75, pp. 43-55, (1986).
[2] D. Boley and G.H. Golub, A survey of matrix inverse eigenvalue problem, Inverse Problems 3, pp. 595-622, (1987).
[3] S. Friedland and A.A. Melkman, On the eigenvalues of nonnegative Jacobi matrices, Lin. Alg. Appl. 25, pp. 239-253, (1979).
[4] G.M. Gladwell, Inverse Problems in Vibrations-2, Appl. Mech. Rev. 49, N 7, (1996)
[5] G.M.L. Gladwell, Inverse Problems in Vibration, Martinus Nijhoff Publishers, Dordrecht (1989).
[6] G.M.L. Gladwell and N.B. Willms, The reconstruction of a tridiagonal system from its frequency response at an interior point, Inverse Problems 4, pp. 1013-1024, (1988).
[7] W.B. Gragg and J.W. Harrow, The numerically stable reconstruction of Jacobi matrices from spectral data, Numer. Math. 44, pp. 317-335, (1984).
[8] F.P. Gantmakher and M.G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, State Publishing House for Technical-Theorical, Literature, MoscowLeningrad, USSR (Translation: US Atomic Energy Commission, Washington DC, 1961), (1950).
[9] H. Hochstadt, On Construction of a Jacobi matrix from spectral data, Lin. Alg. Appl. 8, pp. 435-446, (1974).
[10] Y.M. Ram, Inverse Eigenvalue Problems for a modified Vibrating System, SIAM J Appl 53, pp. 1762-1775, (1993).
[11] Y.M. Ram and J. Caldwell, Phiysical parameters reconstruction of a free-free mass-spring system from its spectra, SIAM J. Appl. Math. 52, pp. 140-152, (1992).
[12] Y.M. Ram and G.M.L. Gladwell, Constructing a finite element model of a vibratory rod form eigendata, J. Sound Vibration 169, pp. 229-237, (1994).
[13] R.L. Soto, A numerical reconstruction of a Jacobi matrix from spectral data, Tamkang Journal of Mathematics 20, No 1, pp.57-63, (1989).
[2] D. Boley and G.H. Golub, A survey of matrix inverse eigenvalue problem, Inverse Problems 3, pp. 595-622, (1987).
[3] S. Friedland and A.A. Melkman, On the eigenvalues of nonnegative Jacobi matrices, Lin. Alg. Appl. 25, pp. 239-253, (1979).
[4] G.M. Gladwell, Inverse Problems in Vibrations-2, Appl. Mech. Rev. 49, N 7, (1996)
[5] G.M.L. Gladwell, Inverse Problems in Vibration, Martinus Nijhoff Publishers, Dordrecht (1989).
[6] G.M.L. Gladwell and N.B. Willms, The reconstruction of a tridiagonal system from its frequency response at an interior point, Inverse Problems 4, pp. 1013-1024, (1988).
[7] W.B. Gragg and J.W. Harrow, The numerically stable reconstruction of Jacobi matrices from spectral data, Numer. Math. 44, pp. 317-335, (1984).
[8] F.P. Gantmakher and M.G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, State Publishing House for Technical-Theorical, Literature, MoscowLeningrad, USSR (Translation: US Atomic Energy Commission, Washington DC, 1961), (1950).
[9] H. Hochstadt, On Construction of a Jacobi matrix from spectral data, Lin. Alg. Appl. 8, pp. 435-446, (1974).
[10] Y.M. Ram, Inverse Eigenvalue Problems for a modified Vibrating System, SIAM J Appl 53, pp. 1762-1775, (1993).
[11] Y.M. Ram and J. Caldwell, Phiysical parameters reconstruction of a free-free mass-spring system from its spectra, SIAM J. Appl. Math. 52, pp. 140-152, (1992).
[12] Y.M. Ram and G.M.L. Gladwell, Constructing a finite element model of a vibratory rod form eigendata, J. Sound Vibration 169, pp. 229-237, (1994).
[13] R.L. Soto, A numerical reconstruction of a Jacobi matrix from spectral data, Tamkang Journal of Mathematics 20, No 1, pp.57-63, (1989).
Published
2017-06-14
How to Cite
[1]
J. Egaña Arancibia and R. L. Soto Montero, “On the numerical reconstruction of a spring-mass system from its natural frequencies”, Proyecciones (Antofagasta, On line), vol. 19, no. 1, pp. 27-41, Jun. 2017.
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