PSI - Issue 23

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

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ScienceDirect

Procedia Structural Integrity 23 (2019) 143–148

© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the ICMSMF organizers © 201 9 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. Abstract The paper presents a calculation of the stress fields that arise in cylindrical steel rods of circular cros -s cti , in the c s axisymmetric Pochh mmer – Chree wav s for the zero m de. The maximum tension and aximum shear on the surface of the rod and on i s xis are calculated. Frequency ranges are obtained for which the maximum stresses on the rod axis are several times higher than on the surface. © 201 9 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. 9th International Conference on Materials Structure and Micromechanics of Fracture Maximal stresses of the longitudinal Pochhammer – Chree waves Viacheslav Mokryakov* Ishlinsky Institute for Problems in Mechanics of RAS, pr. Vernadskogo, 101-1, Moscow, 119526, Russia Abstract The paper presents a calculation of the stress fields that arise in cylindrical steel rods of circular cross-section, in the case of the axisymmetric Pochhammer – Chree waves for the zero mode. The maximum tension and maximum shear on the surface of the rod and on its axis are calculated. Frequency ranges are obtained for which the maximum stresses on the rod axis are several times higher than on the surface. 9th International Conference on Materials Structure and Micromechanics of Fracture Maximal stresses of the longitudinal Pochhammer – Chree waves Viacheslav Mokryakov* Ishlinsky Institute for Problems in Mechanics of RAS, pr. Vernadskogo, 101-1, Moscow, 119526, Russia 1. Introduction Cylindrical rods with a circular cross section are a widespread structural element. The calculation of the strength of any structure requires finding its stress-strain state; in particular, the highest stress values (the maximum tension and the maximum shear). Stresses arise not only from static loads, but also from vibrations. Therefore, it is also necessary to study the stress-strain state caused by elastic waves. First, equations that describe the behavior of elastic waves in a round rod and give dispersion relations (frequency to wave number) were obtained by Pochhammer [1] and Chree [2, 3]. Numerical solutions of the equations were obtained later (in [4 – 11], etc.), where axisymmetric longitudinal, flexural, and torsional modes were considered. Now the development of this problem has several directions: changing the geometry, changing the material properties, changing the distribution of the structure properties (e.g., see [12-18]). 1. Introduction Cylindri al rods with a circular cross ectio are a widespread structural element. The calculation of the strength of any structure requires finding its stress-strai state; in particul r, the highest stress values (the maximum tension and the maximum shea ). Stresses arise not onl from static loads, but also from vibrations. Therefore, it is also neces ary to study t e str ss-strain state caused by elastic waves. First, equations that describ the behavior of lastic waves in a round rod and give dispersion relations (frequency to wave number) were obtained by Pochha mer [1] and Chree [2, 3]. Numerical soluti ns of the equations were obtained later (in [4 – 11], etc.), where axisymmetric longitudinal, flexur l, a d torsional modes were considered. Now the developm nt of this pr blem has several directions: changing the geometry, changing the material properties, changing the distribution of the structure properties (e.g., see [12-18]). Keywords: cylindrical rods; elasticity; Pochhammer – Chree waves; principal stresses; von Mises stress Keywords: cylindrical rods; elasticity; Pochhammer – Chree waves; principal stresses; von Mises stress

* Corresponding author. Tel.: +7-905-530-8233. E-mail address: mokr@ipmnet.ru * Corresponding author. Tel.: +7-905-530-8233. E-mail address: mokr@ipmnet.ru

2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. 2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the IC MSMF organizers.

2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the ICMSMF organizers 10.1016/j.prostr.2020.01.077