PSI - Issue 33

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K. Mysov et al. / Procedia Structural Integrity 33 (2021) 365–370 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

370

1.5  = .

/ 2   = ,

Fig. 2. SIF for

4. Conclusions In the work the new approach for stress state estimation of the cone weakened by a crack in the case of steady state oscillations is demonstrated. The problem solving was reduced to solving of singular integral equation which was solved approximately with the help of orthogonal polynomial method. Thus, allowing to construct a solution with regard of singularity order at the end of integration interval. The formula for calculation of SIF at cracks edges was derived. It can be used to calculate and analyze SIF for different values of linear size, angular size and location of crack inside the cone. The first eigen frequencies of the cone were calculated. References 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 Popov G. Ya., 1982. Concentration of elastic stresses near stamps, cuts, thin inclusions, and reinforcements, Nauka, Moscow, pp. 131 Popov, G. Ya., 2003. New transforms for the resolving equations in elastic theory and new integral transforms, with applications to boundary-value problems of mechanics. International Applied Mechanics 39(12), 1400–1424. Grinchenko V. T., Meleshko V. V., 1981. Harmonic vibrations and waves in elastic bodies [in Russian], Naukova Dumka, Kiev, 1981, pp. 171-181.