PSI - Issue 33

ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000 Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceD rect Available online at www.sciencedirect.com ScienceDirect

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Procedia Structural Integrity 33 (2021) 365–370

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the IGF ExCo Abstract The problem on the dynamical stress concentrations near a cone-shaped crack weakening an elastic twice-truncated cone is solved in case of a steady state torsional oscillations. The problem is considered in a spherical coordinate system due to geometry of cone. The solution is found in a form of superposition of continuous solution and discontinuous one. Continuous solution is found via the use of G. Ya. Popov (2003) integral transform and reduction of the original continuous part of the problem to one-dimensional boundary value problem in vector form in the transform’s domain. The solution then was found in an explicit form. The discontinuous solution was derived with the help of Legendre and variation of Hankel integral transforms. And by solving singular integral equation with the method of orthogonal polynomials the solution of original problem is found. The wave field of an elastic twice truncated cone was investigated. The stress intensity factor near cracks edges was investigated. Also, first eigen frequencies were calculated for different crack’s geometrical characteristics. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo Keywords: Steady state oscillations; Twice truncated cone; Conical crack ; SIF Abstract The problem on the dynamical stress concentrations near a cone-shaped crack weakening an elastic twice-truncated cone is solved in case of a steady tate torsional o cill tions. The problem is considered i a spherical coordinate syst m due to geom try of cone. Th s lution is found in a form of superp sit on of continuous solution and di contin ous on . Continuous solution i found v a the use of G. Ya. P pov (2003) ntegral transform and reduction of the original continuous part f he problem to one-dimensional boundary value problem i vector fo m in the transform’s domai . The olution then was found in an explic t form. The discontinuous solution was derived with he help of Legendre and variation of Hankel integral transforms. And by solving s gular integral equation with the m t od orthogonal polynomials the solution of original problem is found. The wave fi ld of an elastic wic truncated c ne was investigated. The stress ntensity factor near cracks edges was in stigated. Also, first eigen f equencies w re calculated for iffer nt crack’s geometri al characteristics. © 2021 Th Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-review under responsibility of th scientifi committee of the IGF ExCo K ywords: Steady state oscillations; Twic truncated cone; Co ical rack ; SIF IGF26 - 26th International Conference on Fracture and Structural Integrity The dynamical stress concentration near a cone-shaped crack in a twice-truncated elastic cone K.Mysov a, *, N. Vaysfeld b a PhD student, Department of Mathematicas, Physics and IT, Odesa Mechnikov University, Dvoryanskaya str., 2, Odessa, 65082, Ukraine b Dr. of Sc., Prof., Department of Mathematics, Physics and IT, Odesa Mechnikov University , Dvoryanskaya str., 2, Odessa, 65082, Ukraine IGF26 - 26th International Conference on Fracture and Structural Integrity The dynamical stress concentration near a cone-shaped crack in a twice-truncated elastic cone K.Mysov a, *, N. Vaysfeld b a PhD student, Department of Mathematicas, Physics and IT, Odesa Mechnikov University, Dvoryanskaya str., 2, Odessa, 65082, Ukraine b Dr. of Sc., Prof., Department of Mathematics, Physics and IT, Odesa Mechnikov University , Dvoryanskaya str., 2, Ode sa, 65082, Ukraine

* Corresponding author. Tel.: +38 068 274 0227. E-mail address: kmysov2309@gmail.com * Corresponding author. Tel.: +38 068 274 0227. E-mail address: kmysov2309@gmail.com

2452-3216 © 202 1 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo 2452-3216 © 202 1 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-revi w under responsibility of the scientifi committee of the IGF ExCo

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the IGF ExCo 10.1016/j.prostr.2021.10.044