Have a personal or library account? Click to login
A Numerical Solution of Hereditary Equations with a Weakly Singular Kernel for Vibration Analysis of Viscoelastic Systems / Vienâdojumu Ar Vâjo Singulâro Kodolu Skaitliskais Risinâjums Iedzimto Viskoelastîgo Sistçmu Vibrâciju Analîzei Cover

A Numerical Solution of Hereditary Equations with a Weakly Singular Kernel for Vibration Analysis of Viscoelastic Systems / Vienâdojumu Ar Vâjo Singulâro Kodolu Skaitliskais Risinâjums Iedzimto Viskoelastîgo Sistçmu Vibrâciju Analîzei

By: Botir Usmonov  
Open Access
|Feb 2016

References

  1. Anderssen, R. S., Davies, A. R., de Hoog, F. R. (2008). On the sensitivity of interconversion between relaxation and creep. Rheol. Acta, 47, 159-167.10.1007/s00397-007-0223-6
  2. Badalov, F. B. (1980). Method of Series in Nonlinear Hereditary Theory of Viscoelasticity. Tashkent, Fan (in Russian).
  3. Badalov, F. B., Ganikhanov, Sh. F. (2002). Vibration of hereditary-deformable elements of structure of flying vehicles [Ô.Á. Áàäàëîâ, Ø. Ô. Ãàíèõàíîâ Âèáðàöèÿ íàñëåäñòâåííî-äåôîðìèðóåìûõ ýëåìåíòîâ êîíñòðóêöèè ëåòàòåëüíûõ àïïàðàòîâ]. TSAI, Uzbekistan (in Russian). 230 pp. (in Russian).
  4. Badalov, F. B., Usmonov, B. Sh. (2004). New solution setting for bending- aileron flutter of vehicle. Rep. Acad. Sci. Uzbekistan, 6, 30-33 (in Russian).
  5. Chandiramani, N. K., Librescu, L, Aboudi, J. (1989). The theory of orthotropic viscoelastic shear deformable composite flat panels and their dynamic stability. Int. J. Solids Struct., 25 (5), 465-482.10.1016/0020-7683(89)90060-7
  6. Chandiramani, N. K., Librescu, L. (1989). Dynamic stability of unidirectional fiber-reinforced viscoelastic composite plates. Appl. Mech. Rev., 42 (11), 39-47.10.1115/1.3152405
  7. Christensen, R. M. (1982). Theory of Viscoelasticity. Academic Press, New York. 365 pp.
  8. Cupial, P., Niziol, J. (1995). Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer. J. Sound Vibr., 183 (1), 99-114.10.1006/jsvi.1995.0241
  9. DiTaranto, R. A. (1965). Theory of vibratory bending for elastic and viscoelastic layered finite-length beams. Trans. Amer. Soc. Mech. Eng. E., 87, 881-886.10.1115/1.3627330
  10. Flugge, W. (1975). Viscoelasticity. 2nd revised edition, Springer-Verlag, Berlin. 194 pp.10.1007/978-3-662-02276-4
  11. Flory, A., McKenna, G. B. (2004). Finite step rate correction in stress relaxation experiments: A comparison of two methods. Mech. Time-Dependent Mater., 8, 17-37.10.1023/B:MTDM.0000027681.86865.4a
  12. Knauss, W. G., Zhao, J. (2007). Improved relaxation time coverage in ramp-strain histories. Mech. Time-Dependent Mater., 11, 199-216.10.1007/s11043-007-9035-4
  13. Menon, S., Tang, J. (2004). A state-space approach for the dynamic analysis of viscoelastic systems. Comput. Struct., 82, 1123-1130.10.1016/j.compstruc.2004.03.023
  14. Muravyov, A. (1997). Analytical solutions in the time domain for vibration problems of discrete viscoelastic systems. J. Sound Vibr., 199 (2), 337-348.10.1006/jsvi.1996.0603
  15. Muravyov, A. (1998). Forced vibration responses of a viscoelastic structure. J. Sound Vibr., 218 (5), 892-907.10.1006/jsvi.1998.1819
  16. Potapov, V. D. (1985). Stability of Viscoelastic Elements of Designs [Ïîòàïîâ Â.Ä. Óñòîé÷èâîñòü âÿçêîóïðóãèõ ýëåìåíòîâ êîíñòðóêöèé]. Stroyizdat, Moscow (in Russian).
  17. Sorvari, J., Malinen, M. (2007). Numerical interconversion between linear viscoelastic material functions with regularization. Int. J. Solids Struct., 44, 1291-1303.10.1016/j.ijsolstr.2006.06.029
  18. Usmonov, B., Ko, J. H., Badalov, F. B. (2007). Vibration Analysis of One-Dimensional Viscoelastic Structures. International Forum on Rotorcraft Multidisciplinary Technology, Korea, Seoul, October 15-17. Seoul.
  19. Usmonov, B. (2009). Study of two degree flutter for a small aircraft. In: Proceedings of Modern Problems of Applied Mathematics and Information Technologies, Al Khorezmiy, Tashkent, 18-21 September 2009. Tashkent.
  20. Usmonov, B. (2008). An investigation of a viscoelastic material damping effect. In: Proceedings of the International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, June 25-27. University of Genoa, Genoa.
  21. Usmonov, B. (2009). An analytical investigation of steady-state flutter of the hereditary deformable plates in supersonic flow field. In: 4th International Conference on Physics and Control (PhysCon 2009), September 1-4, Catania, Italy.
  22. Usmonov, B. (2008). Stability one-dimensional nonlinear hereditary system. EUROMECH - European Mechanics Society. Sixth EUROMECH Nonlinear Dynamics Conference. June 30 - July 4, Saint Petersburg, Russia.
  23. Zenkour, A. M. (2004). Buckling of fiber-reinforced viscoelastic composite plates using various plate theories. J. Eng. Math., 50, 75-93.10.1023/B:ENGI.0000042123.94111.35
DOI: https://doi.org/10.1515/prolas-2015-0048 | Journal eISSN: 2255-890X | Journal ISSN: 1407-009X
Language: English
Page range: 326 - 330
Submitted on: Apr 22, 2015
Published on: Feb 19, 2016
Published by: Latvian Academy of Sciences
In partnership with: Paradigm Publishing Services
Publication frequency: 6 issues per year

© 2016 Botir Usmonov, published by Latvian Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.