PSI - Issue 28

K. Mysov et al. / Procedia Structural Integrity 28 (2020) 352–357 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 2. ( a ) First eigen frequencies for different cone linear size for cone without a crack; ( b ) First eigen frequencies for different cone linear size for cone with a crack.

It is also obvious that eigen frequencies of cone with the crack (Table 1, Fig. 2. a ) are different and smaller than those for cone without the crack (Table 2, Fig. 2. b ). This proves the fact that appearance of the crack in body changes it’s eigen frequencies specter. 4. Conclusions The solution of the initial problem was derived analytically. The investigation of the cone’s eigen frequencies depending on different parameters on the crack’s and cone’s geometrical sizes was done. There was observed the boundary resonance phenomena on the spherical surface of the cone. This fact can be used as significant mark during the nondestructive testing. The problem can be complicated by adding a cone-shaped crack inside the cone instead of the spherical crack. References Popov G. Ya., 1982. Concentration of elastic stresses near stamps, cuts, thin inclusions, and reinforcements, Nauka, Moscow, pp. 131 Mysov K., Vaysfeld N., 2019. The wave field of a twice-truncated elastic cone under torsion moment impact, Proceedings of the Second International Conference on Theoretical, Applied and Experimental Mechanics, Structural integrity 8, 242-247. https://doi.org/10.1007/978-3 030-21894-2. Popov G. Ya., 1992. The non-axisymmetric problem of the stress concentration in an unbounded elastic medium near a spherical slit, Applied Mathematics and Mechanics 56, 770–779. https://doi.org/10.1016/0021-8928(92)90052-A Grinchenko V. T., Meleshko V. V., 1981. Harmonic vibrations and waves in elastic bodies [in Russian], Naukova Dumka, Kiev, 1981, pp. 171-181.