Comparative analysis of initial state in inhomogeneous rods
DOI:
https://doi.org/10.21638/11701/spbu01.2016.112Abstract
The development and improvement of models of inhomogeneous bodies in the presence of residual stress and deformation fields plays an important role in the mechanics of deformable solid body. From the viewpoint of practical applications, one of the most prospective inhomogeneity type is the class of functionally graded composites (FGC), which material properties vary depending on coordinates. The gradient of properties in such materials is due to the inhomogeneous chemical composition, or the microstructure, or the atomic order. Research on beam-like FGC is the very first global step of exploration of FGC properties. A key question in the problem of monitoring of technical conditions of an object is often a question of proper selection of material’s damage characteristics detectiontechnique, and conducting a set of corresponding experimental investigations. A failure under loading belowthe allowable one is often due to unaccounted preliminary state (PS). It is important to provide the analysis of different types of inhomogeneity of material properties and PS factors (including residual stress and deformations) on dynamic characteristics. In the present paper the effect of various types of PS on acoustical characteristics spectrum (eigenfrequencies, frequency-response functions) is analyzed in FGC-beams. In the framework of the Timoshenko model, such PS factors are considered as residual stress, residual deflection, and residual angle of rotation of the principal axe of the beam due to bending. The computational experiments are conducted and analyzed. Refs 19. Figs 4.Downloads
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References
Литература
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References
1. Birman V., Byrd L.W., “Modeling and Analysis of Functionally Graded Materials and Structures”, Applied Mechanics Reviews 60, Issue 5, 195–216 (2007).
2. Candan S., Elishakoff I., “Apparently first closed-form solution for vibrating inhomogeneous beams”, Int. J. Solids Struct. 38, Issue 19, 3411–3441 (2001).
3. Wu L., WangQ., Elishakoff I., “Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode”, J. Sound Vib. 284, Issue 3–5, 1190–1202 (2005).
4. Tovstik P. E., “The vibrations and stability of a prestressed plate on an elastic foundation”, J. Appl. Math. Mech. 73(1), 77–87 (2009).
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6. Vatulyan A. O., Dudarev V.V., Nedin R.D., Residual stress: modelling and identification (SFedU Publ., Rostov-on-Don, 2014, 206 p.) [in Russian].
7. Kieback B. et al., “Processing techniques for functionally graded materials”, Materials Science and Engineering A. 362, Issue 1–2, 81–105 (2003).
8. Uglov A. L., Erofeev V. I., Smirnov A. N., Acoustical testing of an equipment while its production and exploitation (Nauka, Moscow, 2009, 279 p.) [in Russian].
9. Nedin R.D., Vatulyan A. O., “Concerning one approach to the reconstruction of heterogeneous residual stress in plate”, ZAMM: Z. Angew. Math. Mech. 94(1–2), 142–149 (2014).
10. Nedin R., Nesterov S., Vatulyan A., “On an inverse problem for inhomogeneous thermoelastic rod”, Int. J. Solids Struct. 51, Issue 3–4, 767–773 (2014).
11. Trefftz E., “Zur theorie der stabilitat des elastischen gleichgewichts”, ZAMM: Z. Angew. Math. Mech. 12(2), 160–165 (1933) [in German].
12. Nedin R.D., Vatulyan A.O., “Inverse Problem of Non-homogeneous Residual Stress Identification in Thin Plates”, Int. J. Solids Struct. 50, Issue 13, 2107–2114 (2013).
13. Nedin R.D., Vatulyan A.O., Advanced Structured Materials. Shell-like Structures. Non-classical Theories and Applications. Ch. 13: On the Reconstruction of Inhomogeneous Initial Stresses in Plates (Eds H.Altenbach, V. Eremeyev, Berlin; Heidelberg, Springer-Verlag, 2011).
14. Bogachev I.V., Dudarev V.V., Nedin R.D., Vatulyan A.O., “Identification of inhomogeneous residual stress state in elastic cylinder within the framework of plane strain”, Advanced Materials Research 996, 404–408 (2014).
15. Vatulyan A.O., Nedin R.D., “Models of residually stressed state and principles of its identification”, Mathematical Forum. Results of science. The South of Russia 8, Part 2, 32–52 (2014) [in Russian].
16. Dudarev V.V., Nedin R.D., Vatulyan A. O., “Nondestructive identification of inhomogeneous residual stress state in deformable bodies on the basis of the acoustic sounding method”, Advanced Materials Research 996, 409–414 (2014).
17. Handbook of Advanced Materials. Ch. 10: Functionally graded materials (Ed. by J. K.Wessel. John Wiley & Sons, Inc., 2004).
18. Suresh S., Mortensen A., Fundamentals of functionally graded materials (IOM Communications, London, 1998).
19. Malinin N. N., Applied theory of plasticity and creep (Mashinostroyeniye, Moscow, 1968) [in Russian].
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Published
2020-10-19
How to Cite
Vatulyan, A. O., & Nedin, R. D. (2020). Comparative analysis of initial state in inhomogeneous rods. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 3(1), 1. https://doi.org/10.21638/11701/spbu01.2016.112
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
