Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation

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.

Keywords

• Euler Bernoulli beam equation,Fourier method,quasi-linear mixed problem,periodic boundary condition

References

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. Ramm, G., Mathematical and Analytical Techniques with Application to Engineering, Springer , NewYork, 2005.
7. Mandell, M. J., On the properties of a periodic fluid, Journal of Statistical Physics, 15 (1976) 299-305.
8. 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.

9. Jang, T.S., A new solution procedure for a nonlinear infinite beam equation of motion, Commun. Nonlinear Sci. Numer. Simul., 39 (2016) 321--331.
10. 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.
11. 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.
12. 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.