Waveguide Propagation in Extended Plates of Variable Thickness

ABSTRACT

In this paper we construct conjugate spectral problem and the conditions of biorthogonality for distribution in extended plates of variable thickness of the problem considered. It describes the procedure of solving problems and a numerical result is on wave propagation in an infinitely large plate of variable thickness. Viscous properties of the material are taken into account by means of an integral operator Voltaire. Research is conducted in the framework of the spatial theory of visco elastic. The technique is based on the separation of spatial variables and formulates the boundary eigenvalue problem that can be solved by the method of orthogonal pivotal condensation Godunov. Numerical values obtained the real and imaginary parts of the phase velocity depending on the wave numbers. The numerical result coincides with the known data.

In this paper we construct conjugate spectral problem and the conditions of biorthogonality for distribution in extended plates of variable thickness of the problem considered. It describes the procedure of solving problems and a numerical result is on wave propagation in an infinitely large plate of variable thickness. Viscous properties of the material are taken into account by means of an integral operator Voltaire. Research is conducted in the framework of the spatial theory of visco elastic. The technique is based on the separation of spatial variables and formulates the boundary eigenvalue problem that can be solved by the method of orthogonal pivotal condensation Godunov. Numerical values obtained the real and imaginary parts of the phase velocity depending on the wave numbers. The numerical result coincides with the known data.

Cite this paper

Ibragimovich, S. , Sharipovich, A. and Ihterovich, B. (2014) Waveguide Propagation in Extended Plates of Variable Thickness.*Open Access Library Journal*, **1**, 1-9. doi: 10.4236/oalib.1101166.

Ibragimovich, S. , Sharipovich, A. and Ihterovich, B. (2014) Waveguide Propagation in Extended Plates of Variable Thickness.

References

[1] Safarov, I.I., Jumayev, Z.F. and Boltayev, Z.I. (2011) Harmonic Wave in an Infinite Cylinder with Radial Cracks with the Damping Material. Journal of Problems in Mechanics, No. 1, 20-25.

[2] Safarov, I.I. and Boltaev, Z.I. (2011) The Propagation of Harmonic of Waves in a Plate of Variable Thickness. Math. Institutions of higher Education, The Povolzhye Region, Series: Phys.-mat. Sciences, No. 4, 31-39.

[3] Safarov, I.I., Teshaev, M.K.H. and Boltaev, Z.I. (2012) Wave Processes in a Mechanical Waveguide. LAP LAMBERT Academic Publishing, Saarbrücken, 217 p.

[4] Grinchenko, V.T. and Myaleshka, V.V. (1981) Harmonic Oscillations and Waves in Elastic Bodies. K.: Science Dumka, 283 p.

[5] Bozorov, M.B., Safarov, I.I. and Shokin, Y.I. (1996) Numerical Simulation of the of Oscillations Homogeneous and Inhomogeneous Dissipative Mechanical Systems. SB RAS, Novosibirsk, 188 p.

[6] Koltunov, M.A. (1976) Creep and the Relaxation. Higher School, Moscow, 276 p.

[7] Sunchaliev, R.M. (1972) Filatov, On Some Methods for Investigation of Nonlinear Tasks of the Theory of Viscoelastic. DAN SSSR, 1972.206, No. 1, 201-203.

[8] Gakhov, F.D. (1963) Boundary Value Problems. Fizmatgiz, Moscow, 639 p.

[9] Neimark, M.A. (1969) Linear Differential Operators. Science, Moscow, 526 p.

[10] Godunov, S.K. (1961) On the Numerical Solution of Boundary Value Problems for Systems of Linear Ordinary Differential Equations. The Success of Mathematical Sciences, 16, 171-174.

[1] Safarov, I.I., Jumayev, Z.F. and Boltayev, Z.I. (2011) Harmonic Wave in an Infinite Cylinder with Radial Cracks with the Damping Material. Journal of Problems in Mechanics, No. 1, 20-25.

[2] Safarov, I.I. and Boltaev, Z.I. (2011) The Propagation of Harmonic of Waves in a Plate of Variable Thickness. Math. Institutions of higher Education, The Povolzhye Region, Series: Phys.-mat. Sciences, No. 4, 31-39.

[3] Safarov, I.I., Teshaev, M.K.H. and Boltaev, Z.I. (2012) Wave Processes in a Mechanical Waveguide. LAP LAMBERT Academic Publishing, Saarbrücken, 217 p.

[4] Grinchenko, V.T. and Myaleshka, V.V. (1981) Harmonic Oscillations and Waves in Elastic Bodies. K.: Science Dumka, 283 p.

[5] Bozorov, M.B., Safarov, I.I. and Shokin, Y.I. (1996) Numerical Simulation of the of Oscillations Homogeneous and Inhomogeneous Dissipative Mechanical Systems. SB RAS, Novosibirsk, 188 p.

[6] Koltunov, M.A. (1976) Creep and the Relaxation. Higher School, Moscow, 276 p.

[7] Sunchaliev, R.M. (1972) Filatov, On Some Methods for Investigation of Nonlinear Tasks of the Theory of Viscoelastic. DAN SSSR, 1972.206, No. 1, 201-203.

[8] Gakhov, F.D. (1963) Boundary Value Problems. Fizmatgiz, Moscow, 639 p.

[9] Neimark, M.A. (1969) Linear Differential Operators. Science, Moscow, 526 p.

[10] Godunov, S.K. (1961) On the Numerical Solution of Boundary Value Problems for Systems of Linear Ordinary Differential Equations. The Success of Mathematical Sciences, 16, 171-174.