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Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation

Year 2019, Volume: 68 Issue: 1, 514 - 527, 01.02.2019
https://doi.org/10.31801/cfsuasmas.431883

Abstract

In this study, we find the inverse coefficient in the Euler-Bernoulli beam equation with over determination conditions. We show the existence, stability of the solution by iteration method.

References

  • He X.Q., Kitipornchai S. and Liew K.M., Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction, Journal of the Mechanics and Physics of Solids, 53, (2005) 303-326.
  • Natsuki, T., Ni, Q.Q. and Endo, M.,Wave propagation in single-and double-walled carbon nano tubes filled with fluids, Journal of Applied Physics ,101, (2007) 034319.
  • Yana, Y., Heb, X.Q., Zhanga, L.X. and Wang C.M., Dynamic behavior of triple-walled carbon nano-tubes conveying fluid, Journal of Sound and Vibration ,319, (2010) 1003-1018.
  • Pourgholia, R, Rostamiana, M. and Emamjome, M., A numerical method for solving a nonlinear inverse parabolic problem, Inverse Problems in Science and Engineering, 18(8) (2010) 1151-1164.
  • Hill, G.W., On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica , 8 (1986) 1-36.
  • Ramm, G., Mathematical and Analytical Techniques with Application to Engineering, Springer , NewYork, 2005.
  • Mandell, M. J., On the properties of a periodic fluid, Journal of Statistical Physics, 15 (1976) 299-305.
  • Pratt L. R. and Haan, S.W., Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory, Journal of Chemical Physics 74 (1981) 1864.
  • Jang, T.S., A new solution procedure for a nonlinear infinite beam equation of motion, Commun. Nonlinear Sci. Numer. Simul., 39 (2016) 321--331.
  • Jang T.S., A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli--Euler--von Karman beam on a non-linear elastic foundation, Acta Mech, 225 , (2014) 1967-1984.
  • Baglan, I., Determination of a coefficient in a quasilinear parabolic equation with periodic boundary condition, Inverse Problems in Science and Engineering, (2015), 10.1080/17415977.2014.947479, 23:5.
  • Akbar, M. and Abbasi, M., A fourth-order compact difference scheme for the parabolic inverse problem with an overspecification at a point, Inverse Problems in Science and Engineering, 23:3, (2014) 457-478. DOI:10.1080/17415977.2014.922075.
Year 2019, Volume: 68 Issue: 1, 514 - 527, 01.02.2019
https://doi.org/10.31801/cfsuasmas.431883

Abstract

References

  • He X.Q., Kitipornchai S. and Liew K.M., Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction, Journal of the Mechanics and Physics of Solids, 53, (2005) 303-326.
  • Natsuki, T., Ni, Q.Q. and Endo, M.,Wave propagation in single-and double-walled carbon nano tubes filled with fluids, Journal of Applied Physics ,101, (2007) 034319.
  • Yana, Y., Heb, X.Q., Zhanga, L.X. and Wang C.M., Dynamic behavior of triple-walled carbon nano-tubes conveying fluid, Journal of Sound and Vibration ,319, (2010) 1003-1018.
  • Pourgholia, R, Rostamiana, M. and Emamjome, M., A numerical method for solving a nonlinear inverse parabolic problem, Inverse Problems in Science and Engineering, 18(8) (2010) 1151-1164.
  • Hill, G.W., On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica , 8 (1986) 1-36.
  • Ramm, G., Mathematical and Analytical Techniques with Application to Engineering, Springer , NewYork, 2005.
  • Mandell, M. J., On the properties of a periodic fluid, Journal of Statistical Physics, 15 (1976) 299-305.
  • Pratt L. R. and Haan, S.W., Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory, Journal of Chemical Physics 74 (1981) 1864.
  • Jang, T.S., A new solution procedure for a nonlinear infinite beam equation of motion, Commun. Nonlinear Sci. Numer. Simul., 39 (2016) 321--331.
  • Jang T.S., A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli--Euler--von Karman beam on a non-linear elastic foundation, Acta Mech, 225 , (2014) 1967-1984.
  • Baglan, I., Determination of a coefficient in a quasilinear parabolic equation with periodic boundary condition, Inverse Problems in Science and Engineering, (2015), 10.1080/17415977.2014.947479, 23:5.
  • Akbar, M. and Abbasi, M., A fourth-order compact difference scheme for the parabolic inverse problem with an overspecification at a point, Inverse Problems in Science and Engineering, 23:3, (2014) 457-478. DOI:10.1080/17415977.2014.922075.
There are 12 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

İrem Baglan 0000-0002-1877-9791

Publication Date February 1, 2019
Submission Date October 26, 2017
Acceptance Date February 2, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Baglan, İ. (2019). Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 514-527. https://doi.org/10.31801/cfsuasmas.431883
AMA Baglan İ. Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):514-527. doi:10.31801/cfsuasmas.431883
Chicago Baglan, İrem. “Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 514-27. https://doi.org/10.31801/cfsuasmas.431883.
EndNote Baglan İ (February 1, 2019) Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 514–527.
IEEE İ. Baglan, “Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 514–527, 2019, doi: 10.31801/cfsuasmas.431883.
ISNAD Baglan, İrem. “Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 514-527. https://doi.org/10.31801/cfsuasmas.431883.
JAMA Baglan İ. Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:514–527.
MLA Baglan, İrem. “Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 514-27, doi:10.31801/cfsuasmas.431883.
Vancouver Baglan İ. Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):514-27.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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