Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions

Analysis of Inverse Euler-Bernoulli Equation with Periodic Boundary Conditions

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.

___

  • 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.