Fourier-type integral transforms in modeling of transversal oscillation

Yıl 2015, , 18 - 22, 17.01.2015

Oleg Yaremko , Nataliia Yaremko Nikita Tyapin

https://doi.org/10.18100/ijamec.36094

Cited By: 1

Öz

The model of transversal oscillation for an elastic piecewise-homogeneous rod is constructed. In order to find a solution of this model   a   Fourier-type integral transforms method for the fourth-order differential equations is developed. The decomposition theorem is proved by Cauchy contour integration method. The conditions of existence for fundamental solutions of the initial - boundary value problem are established and explicit expressions of these fundamental solutions are found. 

Anahtar Kelimeler

eigenfunction, fourth-order differential equation, fundamental solution, Green's function.

Original Research Paper

Öz

Kaynakça

• Ahtjamov A.M., Sadovnichy V. A, Sultanaev J.T.(2009) Inverse Sturm--Liouville theory with non disintegration boundary conditions. -Moscow: Publishing house of the Moscow university.
• Bavrin I.I., Matrosov V.L., Jaremko O. E.(2006) Operators of transformation in the analysis, mathematical physics and Pattern recognition. Moscow, Prometheus, p 292.
• Bejtmen G., Erdeji A., (1966) High transcendental function, Bessel function, Parabolic cylinder function, Orthogonal polynomials. Reference mathematical library, Moscow, p 296.
• Brejsuell R., (1990) Hartley transform, Moscow, World, p 584.
• Vladimirov V. S., Zharinov V.V., (2004) The equations of mathematical physics, Moscow, Phys mat lit, p 400.
• Gantmaxer F.R., (2010) Theory matrix. Moscow, Phys mat lit, p 560.
• Grinchenko V. T., Ulitko A.F., Shulga N.A., (1989) Dynamics related fields in elements of designs. Electro elasticity. Kiev. Naukova Dumka,p 279.
• Lenyuk M.P., (1991) Hybrid Integral transform (Bessel, Lagrange, Bessel), the Ukrainian mathematical magazine. p. 770-779.
• Lenyuk M.P., (1989) Hybrid Integral transform (Bessel, Fourier, Bessel), Mathematical physics and non-linear mechanics, p. 68-74
• Lenyuk M.P.(1989) Integral Fourier transform on piece-wise homogeneous semi-axis, Mathematica, p. 14-18.
• Najda L. S., (1984) Hybrid integral transform type Hankel- Legendary, Mathematical methods of the analysis of dynamic systems. Kharkov, р 132-135.
• Protsenko V. S., Solovev A.I.. (1982) Some hybrid integral transform and their applications in the theory of elasticity of heterogeneous medium. Applied mechanics, p 62-67.
• Rvachyov V. L., , Protsenko V. S., (1977) Contact problems of the theory of elasticity for anon classical areas, Kiev. Naukova Dumka.
• Sneddon I.. (1955) Fourier Transform, Moscow.
• Sneddon I., Beri D. S., (2008) The classical theory of elasticity. University book, p. 215.
• Uflyand I. S. (1967) Integral transforms in the problem of the theory of elasticity. Leningrad. Science, p. 402
• Uflyand I. S..(1967) On some new integral transformations and their applications to problems of mathematical physics. Problems of mathematical physics. Leningrad, p. 93-106
• Arfken, G. B.; Weber, H. J. (2000), Mathematical Methods for Physicists (5th ed.), Boston, assachusetts: Academic Press.
• Jaremko O. E., (2007) Matrix integral Fourier transform for problems with discontinuous coefficients and conversion operators. Proceedings of the USSR Academy of Sciences. p. 323-325.
• 