PSI - Issue 28

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ScienceDirect

Procedia Structural Integrity 28 (2020) 770–775 Structural Integrity Procedia 00 (2020) 000–000 Structural Integrity Procedia 00 (2020) 000–000

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© 2020 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 European Structural Integrity Society (ESIS) ExCo To solve this problem, it is proposed to reduce the equations of dynamic incoherent thermoelasticity relatively to the displace ments to two jointly and one separately solved equations. The solution of the two separately solved problems is carried out by the method of integral transformations, which allows us to construct the exact solutions for the separately solved problems in the explicit forms. In the case of the problem formulated using a system of two partial di ff erential equations, it is proposed to use the apparatus of a matrix di ff erential calculus. The matrix Greens function is constructed and the solution of the problem is derived in explicit form. c 2020 The Authors. Published by Elsevier B.V. his is an open access article under the CC BY-NC-ND license (http: // creativec mmons.org / licenses / by-nc-nd / 4.0 / ) r-review under responsibility of the European Structural Integrity Society (ESIS) ExCo. Keywords: Steady state oscillations ; dynamic incoherent thermoelasticity ; vector boundary problem ; integral transformation Abstract We consider the steady state problem of incoherent thermoelasticity for a finite hollow elastic cylinder on the inner and outer cylindrical surfaces of which ideal contact conditions are given. Without limiting the generality of reasoning, we consider a dynamic normal load applying at the upper face of the cylinder, and there are no tangential stress there. The bottom face of the cylinder is fixed. It is required to determine the thermos-wave field of the cylinder under steady state oscillations. To solve this problem, it is proposed to reduce the equations of dynamic incoherent thermoelasticity relatively to the displace ments to two jointly and one separately solved equations. The solution of the two separately solved problems is carried out by the method of integral transformations, which allows us to construct the exact solutions for the separately solved problems in the explicit forms. In the case of the problem formulated using a system of two partial di ff erential equations, it is proposed to use the apparatus of a matrix di ff erential calculus. The matrix Greens function is constructed and the solution of the problem is derived in explicit form. c 2020 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 European Structural Integrity Society (ESIS) ExCo. Keywords: Steady state oscillations ; dynamic incoherent thermoelasticity ; vector boundary problem ; integral transformation 1st Virtual European Conference on Fracture Dynamic thermoelasticity problem for a finite hollow cylinder with a cut along the generatrix H. Lutsenko a , N. Vaysfeld b a PhD student, Department of Mathematics, 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 Abstract We consider the steady state problem of incoherent thermoelasticity for a finite hollow elastic cylinder on the inner and outer cylindrical surfaces of which ideal contact conditions are given. Without limiting the generality of reasoning, we consider a dynamic normal load applying at the upper face of the cylinder, and there are no tangential stress there. The bottom face of the cylinder is fixed. It is required to determine the thermos-wave field of the cylinder under steady state oscillations. 1st Virtual European Conference on Fracture Dynamic thermoelasticity problem for a finite hollow cylinder with a cut along the generatrix H. Lutsenko a , N. Vaysfeld b a PhD student, Department of Mathematics, 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

1. Main Text 1. Main Text

Round shafts with a cut along the generatrix are part of many mechanisms, as a result, it makes sense to study their properties under di ff erent loads. The statement of this problem is most similar to a press with a cylindrical tip. The di ff erent approachs of solving of the thermoelasticity problems were described by A. D. Kovalenko (1965). The method of how we separate the original Lame equations to two jointly and one separately solved equations was first introduced by Popov, G. Ya (2002). The applying of integral transforms to the thermoelasticity problems was Round shafts with a cut along the generatrix are part of many mechanisms, as a result, it makes sense to study their properties under di ff erent loads. The statement of this problem is most similar to a press with a cylindrical tip. The di ff erent approachs of solving of the thermoelasticity problems were described by A. D. Kovalenko (1965). The method of how we separate the original Lame equations to two jointly and one separately solved equations was first introduced by Popov, G. Ya (2002). The applying of integral transforms to the thermoelasticity problems was

∗ Corresponding author. Tel.: + 380-937-069-915 E-mail address: georglutsenko@gmail.com ∗ Corresponding author. Tel.: + 380-937-069-915 E-mail address: georglutsenko@gmail.com

2452-3216 © 2020 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 European Structural Integrity Society (ESIS) ExCo 10.1016/j.prostr.2020.10.089 2210-7843 c 2020 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 European Structural Integrity Society (ESIS) ExCo. 2210-7843 c 2020 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 European Structural Integrity Society (ESIS) ExCo.