SPATIAL PROBLEM OF INTERACTION P (LONGITUDINAL) - WAVES ON A CYLINDRICAL CAVITY IN AN ELASTIC MEDIUM

N.U. Kuldashov; M. Choriev; U.A.Urolov

doi:10.5281/zenodo.7965947

N.U. Kuldashov, M. Choriev, U.A.Urolov

Abstract. The spatial problem of diffraction of elastic waves, the angle of incidence relative to the longitudinal axis of the cavity, is considered. The aim of the study is the diffraction of elastic harmonic waves in a cavity depending on the angle of incidence. An analytical solution of the problem of diffraction of elastic waves in a cavity is obtained, which makes it possible to determine the force factors of the stress-strain state of the cavity from the angle of incidence. The environment is described by the Helmholtz equation and the solution of which is described by the Bessel and Neumann functions with complex arguments. The stress and permeability of the cavity point take on a maximum value in the region of long waves. A technique and algorithm for solving the spatial problem of diffraction of hormone waves in a cavity has been developed.

Keywords: cavity, wave, wave equation, wave incidence angle, Bessel and Neumann function.

References:

1. A. N. Guz, V. D. Kubenko, and M. A. Cherevko, Diffraction of elastic waves. Kyiv: Naukova Dumka, 1978. 308 p. 2. A. N. Guz, Elastic waves in bodies with initial stresses. T. 2. Patterns of distribution. Kyiv: Naukova Dumka, 1986. 536 p. 3. Baron M.L. Parnas R., Disspacements is and velocities produced by the diffraction of a pressure wave by a cylindrical cavity in an elastic medium. Trans ASME. J. Appl. Mech., 1962.29 No. 2 385-395 4. Safarov I.I., Kuldashov N.U., Boltaev Z.I. Oscillations and Waves in a Layered Homogeneous Viscoelastic Medium. International Journal of Emerging Engineering Research and Technology. Volume 6, Issue 3, 2018, PP 27-32. 5. Landau L.D., Lifshitz E.M. The Theory of Elasticity. - Moscow: Science. Ch. ed. Phys.-Math. literature, 1965. - 204 p. 6. Gray, E. Bessel functions and their applications to physics and mechanics. - M .: Publishing house of foreign. literature, 1953. - 372 p.125 7. K. Aki and P.G. Richards, 1980. Quantitative Seismology, Theory and Methods. Volume I: 557 pages 8. Grinchenko V.T., Meleshko V.V. Harmonic oscillations and waves in elastic bodies. - K .: Nauk. Dumka, 1981. - 284 p. 9. Safarov I.I., Teshaev M., Toshmatov E., Boltaev Z. and Homidov.F.F. Torsional vibrations of a cylindrical shell in a linear viscoelastic medium / IOP Conference Series: Materials Science and Engineering 883 (1) 012190 (2020). 10. Teshaev M.K, Safarov I.I, Kuldashov N.U, Ishmamatov M.R and Ruziev T.R, On the Distribution of Free Waves on the Surface of a Viscoelastic Cylindrical, Cavity / Journal of Vibrational Engineering and Technologies 8 (4) pp 579-585. (2020)