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Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation

Year 2019, , 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, , 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

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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