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Yıl 2022, Cilt: 7 Sayı: 3, 146 - 156, 30.12.2022

İrem Bağlan Timur Canel

Öz

Kaynakça

  • 1 H. P. W. Gottlieb, “Isospectral Euler-Bernoulli beams with continuous density and rigidity functions,” Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, vol. 413, no. 1844, pp. 235–250, 1987.
  • [2] C.W. Soh, “Euler-Bernoulli beams from a symmetry standpoint—characterization of equivalent equations,” JournalofMathematicalAnalysisandApplications, vol. 345, no. 1, pp. 387–395, 2008.
  • [3] O. I. Morozov and C. W. Soh, “The equivalence problem for the Euler-Bernoulli beam equation via Cartan’s method,” Journal of Physics A: Mathematical and Theoretical, vol. 41, no. 13, 135206, pp. 135–206, 2008.
  • [4] J. C. Ndogmo, “Equivalence transformations of the Euler-Bernoulli equation,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2172–2177, 2012.
  • [5] E. Ozkaya and M. Pakdemirli, “Group-theoretic approach to ¨ axially accelerating beam problem,” Acta Mechanica, vol. 155, no. 1-2, pp. 111–123, 2002.
  • [6] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, NY, USA, 4th edition,1944.
  • [7] A. H. Bokhari, F. M. Mahomed, and F. D. Zaman, “Invariantboundary value problems for a fourth-order dynamic EulerBernoulli beam equation,” Journal of Mathematical Physics, vol.53, no. 4, 2012.
  • [8] He X.Q., Kitipornchai S., 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, 303-326, 2005.
  • [9] Natsuki T., Ni Q.Q., Endo M.,”Wave propagation in single-and double-walled carbon nano tubes filled with fluids”, Journal of Applied Physics, 101, 034319, 2007.
  • [10] Yana Y., Heb X.Q., Zhanga L.X., Wang C.M., ”Dynamic behavior of triple-walled carbon nano-tubes conveying fluid”, Journal of Sound and Vibration ,319, 1003-1018, 2010.
  • [11] T.S. Jang, ”A new solution procedure for a nonlinear infinite beam equation of motion”, Commun. Nonlinear Sci. Numer. Simul., 39 , 321–331,2016.
  • [12] T.S.Jang, ” 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 , pp. 1967-1984,2014.
  • [13] Mohebbi A.&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, 457-478, DOI:10.1080/17415977.2014.922075,2014.
  • [14] 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 ,1151-1164,2010.
  • [15] I. Baglan and F.Kanca, ”An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition”,Math. Meth. Appl. Sci. , DOI: 10.1002/mma.3112,2015.
  • [16] 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, 1-36,1986.

Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions

Yıl 2022, Cilt: 7 Sayı: 3, 146 - 156, 30.12.2022

İrem Bağlan Timur Canel

Öz

In this study, which aims to solve the inverse problem of a linear Euler-Bernoulli equation,
the boundary condition has been periodically defined and integral overdetermination conditions. The
conditions of the data used in the generalized Fourier method used to solve the problem have regularity
and consistency.

Anahtar Kelimeler

inverse problem euler bernoulli equation periodic boundary condition

Kaynakça

  • 1 H. P. W. Gottlieb, “Isospectral Euler-Bernoulli beams with continuous density and rigidity functions,” Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, vol. 413, no. 1844, pp. 235–250, 1987.
  • [2] C.W. Soh, “Euler-Bernoulli beams from a symmetry standpoint—characterization of equivalent equations,” JournalofMathematicalAnalysisandApplications, vol. 345, no. 1, pp. 387–395, 2008.
  • [3] O. I. Morozov and C. W. Soh, “The equivalence problem for the Euler-Bernoulli beam equation via Cartan’s method,” Journal of Physics A: Mathematical and Theoretical, vol. 41, no. 13, 135206, pp. 135–206, 2008.
  • [4] J. C. Ndogmo, “Equivalence transformations of the Euler-Bernoulli equation,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2172–2177, 2012.
  • [5] E. Ozkaya and M. Pakdemirli, “Group-theoretic approach to ¨ axially accelerating beam problem,” Acta Mechanica, vol. 155, no. 1-2, pp. 111–123, 2002.
  • [6] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, NY, USA, 4th edition,1944.
  • [7] A. H. Bokhari, F. M. Mahomed, and F. D. Zaman, “Invariantboundary value problems for a fourth-order dynamic EulerBernoulli beam equation,” Journal of Mathematical Physics, vol.53, no. 4, 2012.
  • [8] He X.Q., Kitipornchai S., 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, 303-326, 2005.
  • [9] Natsuki T., Ni Q.Q., Endo M.,”Wave propagation in single-and double-walled carbon nano tubes filled with fluids”, Journal of Applied Physics, 101, 034319, 2007.
  • [10] Yana Y., Heb X.Q., Zhanga L.X., Wang C.M., ”Dynamic behavior of triple-walled carbon nano-tubes conveying fluid”, Journal of Sound and Vibration ,319, 1003-1018, 2010.
  • [11] T.S. Jang, ”A new solution procedure for a nonlinear infinite beam equation of motion”, Commun. Nonlinear Sci. Numer. Simul., 39 , 321–331,2016.
  • [12] T.S.Jang, ” 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 , pp. 1967-1984,2014.
  • [13] Mohebbi A.&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, 457-478, DOI:10.1080/17415977.2014.922075,2014.
  • [14] 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 ,1151-1164,2010.
  • [15] I. Baglan and F.Kanca, ”An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition”,Math. Meth. Appl. Sci. , DOI: 10.1002/mma.3112,2015.
  • [16] 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, 1-36,1986.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume VII Issue III
Yazarlar

İrem Bağlan 0000-0002-1877-9791

Timur Canel 0000-0002-4282-1806

Yayımlanma Tarihi 30 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 7 Sayı: 3

Kaynak Göster

APA Bağlan, İ., & Canel, T. (2022). Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions. Turkish Journal of Science, 7(3), 146-156.
AMA Bağlan İ, Canel T. Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions. TJOS. Aralık 2022;7(3):146-156.
Chicago Bağlan, İrem, ve Timur Canel. “Analysis of Inverse Euler-Bernoulli Equation With Periodic Boundary Conditions”. Turkish Journal of Science 7, sy. 3 (Aralık 2022): 146-56.
EndNote Bağlan İ, Canel T (01 Aralık 2022) Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions. Turkish Journal of Science 7 3 146–156.
IEEE İ. Bağlan ve T. Canel, “Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions”, TJOS, c. 7, sy. 3, ss. 146–156, 2022.
ISNAD Bağlan, İrem - Canel, Timur. “Analysis of Inverse Euler-Bernoulli Equation With Periodic Boundary Conditions”. Turkish Journal of Science 7/3 (Aralık 2022), 146-156.
JAMA Bağlan İ, Canel T. Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions. TJOS. 2022;7:146–156.
MLA Bağlan, İrem ve Timur Canel. “Analysis of Inverse Euler-Bernoulli Equation With Periodic Boundary Conditions”. Turkish Journal of Science, c. 7, sy. 3, 2022, ss. 146-5.
Vancouver Bağlan İ, Canel T. Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions. TJOS. 2022;7(3):146-5.
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