Viscoelastic bending of beams of variable curvature radius and stiffness

Authors

  • Viachaslau A. Tamila Physical-Engineering Institute of the National Academy of Sciences of Belarus, Kuprevicha street, 10, 220141, Minsk
  • Yauheniya V. Kochyk Belarusian National Technical University, Nezavisimosti avenue, 65, 220013, Minsk
  • Ivan A. Tarasyuk Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk
  • Alexander S. Kravchuk Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

Keywords:

viscoelastic bending, large displacements, polymeric material

Abstract

E. P. Popov method of analysis of elastic beams flat bending with large displacements was generalized to the case of viscoelastic beams of variable curvature radius and stiffness using an example of bending of flat springs of variable thickness symmetrical profile. The problem is reduced to the solution of a number of boundary creep problems with link conditions on section joints by means of partitioning the original beam into sections with a constant curvature radius and stiffness. The solutions are based on exact non-linearized equation of curved sections motion (so-called nonlinear pendulum vibration equation) taking into account the changes in the magnitude of the bending moment under creep. Values of curvature radius and displacement of beams subjected to creep deformation were determined. Viscoelastic bending problem of flat polymeric spring of variable curvature radius and stiffness was solved analytically as an example.

Author Biographies

  • Viachaslau A. Tamila, Physical-Engineering Institute of the National Academy of Sciences of Belarus, Kuprevicha street, 10, 220141, Minsk

    doctor of science (technics), docent; head of the research center of deformation and casting technologies

  • Yauheniya V. Kochyk, Belarusian National Technical University, Nezavisimosti avenue, 65, 220013, Minsk

    lecturer at the department of mechanical engineering profile materials resistance, faculty of mechanical engineering

  • Ivan A. Tarasyuk, Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

    postgraduate student at the department of bioand nanomechanics, faculty of mechanics and mathematics

  • Alexander S. Kravchuk, Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

    doctor of science (physics and mathematics), docent; professor at the department of bio- and nanomechanics, faculty of mechanics and mathematics

References

  1. Popov E. P. Teoriya i raschet gibkikh uprugikh sterzhnei [Theory and Design of flexible elastic beams]. Moscow, 1986 (in Russ.).
  2. Kravchuk A. S., Tomilo E. V. Vyazkouprugii chistyi izgib sloistykh i kompozitsionnykh prizmaticheskikh brusʼev [Viscoelastic pure bending of laminated and composite prismatic beams]. Mekhanika mashin, mekhanizmov i materialov. 2014. No. 3 (28). P. 48–52 (in Russ.).
  3. Rabotnov Y. N. Elementy nasledstvennoi mekhaniki tverdykh tel [Elements of hereditary mechanics of solids]. Moscow, 1977 (in Russ.).
  4. Fernati P. V. Modelirovanie nelineinykh protsessov polzuchesti na osnove kubicheskoi teorii vyazkouprugosti [The modeling of nonlinear process of creep on the cube theory of viscoelasticity]. Vestnik Natsionalʼnogo Tekhnicheskogo Univ. «KhPI». Temat. vyp. : Informatika i modelirovanie. 2010. No. 21. P. 182–192 (in Russ.).

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Published

2017-12-03

Issue

No. 1 (2017): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Tamila, V.A. et al. 2017. Viscoelastic bending of beams of variable curvature radius and stiffness. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Dec. 2017), 39–46.