PSI - Issue 82

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2026) 000–000 Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2026) 000–000

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ScienceDirect

Procedia Structural Integrity 82 (2026) 246–252

© 2026 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 ICSID organizers Abstract The use of functionally graded engineering materials for various applications continuously grows in our time. This fact leads to need of detailed studying of wide spectra of problems associated with the behaviour of these modern materials and structural components under loading. Dissipation of energy is one of these problems. The aim of the present paper is to study the energy dissipation problem on theoretical level. The study is focused on functionally graded multilayered beam structures under torsion that is a function of the time (the angle of twist varies with time). The beam layers are functionally graded and exhibit viscoelastic behaviour. The viscoelastic model of Maxwell is applied in the analysis of energy dissipation. Analytical expression for the dissipated energy per unit volume is derived assuming that the coefficient of viscosity depends on the time. This expression is integrated to obtain the dissipated energy for the whole beam structure. The solution obtained is used for exploring how the dissipated energy is influenced by the change of a variety of parameters of the model. Various diagrams illustrating variation of the dissipated energy are presented. © 2026 The Authors. Copy from the contract: 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 ICSID organizers Keywords: Dissipation of energy; Viscoelastic behaviour; Multilayered beam; Functionally graded material; Structural component 1. Introduction In many load-bearing engineering applications there are beam structural members of circular cross-section loaded in torsion. Therefore, the study of various aspects of the mechanical behavior of this type of structural members represents important task of the modern engineering. Deepening of the knowledge for beam structures under torsion Abstract The use of functionally graded engineering materials for various applications continuously grows in our time. This fact leads to need of detailed studying of wide spectra of problems associated with the behaviour of these modern materials and structural components under loading. Dissipation of energy is one of these problems. The aim of the present paper is to study the energy dissipation problem on theoretical level. The study is focused on functionally graded multilayered beam structures under torsion that is a function of the time (the angle of twist varies with time). The beam layers are functionally graded and exhibit viscoelastic behaviour. The viscoelastic model of Maxwell is applied in the analysis of energy dissipation. Analytical expression for the dissipated energy per unit volume is derived assuming that the coefficient of viscosity depends on the time. This expression is integrated to obtain the dissipated energy for the whole beam structure. The solution obtained is used for exploring how the dissipated energy is influenced by the change of a variety of parameters of the model. Various diagrams illustrating variation of the dissipated energy are presented. © 2026 The Authors. Copy from the contract: 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 ICSID organizers Keywords: Dissipation of energy; Viscoelastic behaviour; Multilayered beam; Functionally graded material; Structural component 1. In many load-bearing engineering applications there are beam structural members of circular cross-section loaded in torsion. Therefore, the study of various aspects of the mechanical behavior of this type of structural members represents important task of the modern engineering. Deepening of the knowledge for beam structures under torsion 8th International Conference on Structural Integrity and Durability (ICSID2025) Dissipation of energy in beams with functionally graded layers Victor Rizov* Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria

* Corresponding author. Tel.: + (359-2) 963 52 45 / 664; fax: + (359-2) 86 56 863. E-mail address: v_rizov_fhe@uacg.bg * Corresponding author. Tel.: + (359-2) 963 52 45 / 664; fax: + (359-2) 86 56 863. E-mail address: v_rizov_fhe@uacg.bg

2452-3216 © 2026 The Authors. Copy from the contract: 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 ICSID organizers 2452-3216 © 2026 The Authors. Copy from the contract: 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 ICSID organizers

2452-3216 © 2026 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 ICSID organizers 10.1016/j.prostr.2026.04.038