DOI QR코드

DOI QR Code

Modeling of supersonic nonlinear flutter of plates on a visco-elastic foundation

  • Received : 2018.08.02
  • Accepted : 2019.01.16
  • Published : 2019.05.25

Abstract

Numerical study of the flutter of a plate on a viscoelastic foundation is carried out in the paper. Critical velocity of the flutter of a plate on an elastic and viscoelastic foundation is determined. The mathematical model for the investigation of viscoelastic plates is based on the Marguerre's theory applied to the study of the problems of strength, rigidity and stability of thin-walled structures such as aircraft wings. Aerodynamic pressure is determined in accordance with the A.A. Ilyushin's piston theory. Using the Bubnov - Galerkin method, the basic resolving systems of nonlinear integro-differential equations (IDE) are obtained. At wide ranges of geometric and physical parameters of viscoelastic plates, their influence on the flutter velocity has been studied in detail.

Keywords

References

  1. Badalov, F.B. (1987), Methods for Solving Integral and Integro-differential Equations of the Hereditary Theory of Viscoelasticity, Mexnat, Tashkent.
  2. Badalov, F.B., Eshmatov, Kh. and Yusupov, M. (1987), "Some methods of solution the systems of integrodifferential equations in problems of viscoelasticity", Appl. Math. Mech., 51(5), 867-871.
  3. Badalov, F.B., Khudayarov, B.A. and Abdukarimov, A. (2007), "Effect of the hereditary kernel on the solution of linear and nonlinear dynamic problems of hereditary deformable systems", J. Machine. Manufact. Reliability, 36(4), 328-335. https://doi.org/10.3103/S1052618807040048.
  4. Badalov, F.B., Khudayarov, B.A. and Abdukarimov, A. (2007), "Investigation of the influence of heredity on the core solution of linear and nonlinear dynamic problems of genetically-deformed systems", Prob. Mech. Eng. Reliability, 4, 107-110.
  5. Bolotin, V.V. (1961), Non-Conservative Problems of the Theory of Elastic Stability, Fizmatgiz, Moscow, Russia.
  6. Chai, Y.Y., Song, Z.G. and Li, F.M. (2017), "Investigations on the influences of elastic foundations on the aerothermoelastic flutter and thermal buckling properties of lattice sandwich panels in supersonic airflow", Acta Astronautica, 140, 176-189. https://doi.org/10.1016/j.actaastro.2017.08.016.
  7. Chen, J. and Li, Q.S. (2017), "Nonlinear aeroelastic flutter and dynamic response of composite laminated cylindrical shell in supersonic air flow", Compos. Struct., 168(15), 474-484. https://doi.org/10.1016/j.compstruct.2017.02.019.
  8. Dixon, I.R. and Mei, C. (1993), "Finite element analysis of large-amplitude panel flutter of thin laminates", AIAA J., 31(4), 701-707. https://doi.org/10.2514/3.11606.
  9. Duc, N.D., Pobedrya, B.E., Bich, D.H. and Thang, P.T. (2014), "Nonlinear analysis on flutter of S-FGM thin circular cylindrical shells with metal-ceramic-metal layers surrounded on elastic foundations using Ilyushin supersonic aerodynamic theory", Proceedings of the 3rd International Conference on Engineering Mechanics and Automation (ICEMA 3), Hanoi, Vietnam, October.
  10. Eshmatov, B.K., Eshmatov, K. and Khodzhaev, D.A. (2013), "Nonlinear flutter of viscoelastic rectangular plates and cylindrical panels of a composite with a concentrated masses", J. Appl. Mech. Tech. Phys., 54(4), 578-587. https://doi.org/10.1134/S0021894413040081.
  11. Hasheminejad, S.M., Nezami, M. and Panah, M.A. (2013), "Flutter suppression of an elastically supported plate with electro-rheological fluid core under yawed supersonic flows", Int. J. Struct. Stability Dyn., 13(1), 1250073. https://doi.org/10.1142/S0219455412500733.
  12. Ilyushin, A.A. (1956), "The law of plane cross sections in supersonic aerodynamics", J. Appl. Math. Mech., 20(6), 733-755.
  13. Khudayarov, B.A. (2008), "Numerical study of the dependence of the critical flutter speed and time of a plate on rheological parameters", Int. Appl. Mech., 44(6), 676-682. https://doi.org/10.1007/s10778-008-0078-2.
  14. Khudayarov, B.A. (2010), "Mathematical modelling of nonlinear flutter of viscoelastic elements and units of the flying device", Math. Model. Comput. Simul., 22(6), 111-131.
  15. Khudayarov, B.A. and Bandurin, N.G. (2007), "Numerical investigation of nonlinear vibrations of viscoelastic plates and cylindrical panels in a gas flow", J. Appl. Mech. Tech. Phys., 48(2), 279-284. https://doi.org/10.1007/s10808-007-0036-5.
  16. Kiiko, I.A. and Pokazeev, V.V. (2005), "Vibrations and stability of a viscoelastic strip placed into gas flow", Report. Phys., 50(3), 158-160. https://doi.org/10.1134/1.1897993.
  17. Kiiko, I.A. and Pokazeev, V.V. (2013), "Flutter of viscoelastic strip", J. Eng. Math., 78(1), 213-222. doi.org/10.1007/s10665-012-9534-4.
  18. Liao, C.L. and Sun, Y.W. (1993), "Flutter analysis of stiffened laminated composite plates and shells in supersonic flow", AIAA J., 31(10), 1897-1905. https://doi.org/10.2514/3.11865.
  19. Librescu, L. and Chandiramani, N.K. (1989), "Dynamic stability of transversely isotropic viscoelastic plates", J. Sound Vib., 130(3), 467-486. https://doi.org/10.1016/0022-460X(89)90070-9
  20. Mahmoudkhani, S., Sadeghmanesh, M. and Haddadpour, H. (2016), "Aero-thermo-elastic stability analysis of sandwich viscoelastic cylindrical shells in supersonic airflow", Compos. Struct., 147, 185-196. https://doi.org/10.1016/j.compstruct.2016.03.020.
  21. Merrett, C.G. (2016), "Time to flutter theory for viscoelastic composite aircraft wings", Compos. Struct., 154, 646-659. https://doi.org/10.1016/j.compstruct.2016.07.019.
  22. Movchan, A.A. (1956), "On oscillations of the plate, moving in a gas", J. Appl. Math. Mech., 20, 221-222.
  23. Movchan, A.A. (1957), "Stability of a blade moving through gas", J. Appl. Math. Mech., 21(5), 700-706.
  24. Pacheco, D., Marques, F.D., Natarajan, S. and Ferreira, A. (2017), "Nonlinear finite element post-flutter analysis of multibay composite panels in supersonic regime", Compos. Struct., 180(15), 883-891. https://doi.org/10.1016/j.compstruct.2017.08.058.
  25. Pagani, A., Petrolo, M. and Carrera, E. (2014), "Flutter analysis by refined 1D dynamic stiffness elements and doublet lattice method", Adv. Aircraft Spacecraft Sci., 1(3), 291-310. https://doi.org/10.12989/aas.2014.1.3.291.
  26. Pouresmaeeli, S. Ghavanloo, E. and Fazelzadeh, S.A. (2013), "Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium", Compos. Struct., 96, 405-410. https://doi.org/10.1016/j.compstruct.2012.08.051.
  27. Rao, G.V. and Rao, K.S. (1984), "Supersonic flutter of short panels on an elastic foundation", AIAA J., 22(6), 856-857. https://doi.org/10.2514/3.8698.
  28. Robinson, M.T.A. and Adali, S. (2016), "Nonconservative stability of viscoelastic rectangular plates with free edges under uniformly distributed follower force", Int. J. Mech. Sci., 107, 150-159. https://doi.org/10.1016/j.ijmecsci.2015.12.029.
  29. Shiau, L.C. (1992), "Supersonic flutter of composite sandwich panels", AIAA J., 30(12), 2987-2989. https://doi.org/10.2514/3.48987.
  30. Singha, M.K. and Mandal, M. (2008), "Supersonic flutter characteristics of composite cylindrical panels", Compos. Struct., 82(2), 295-301. https://doi.org/10.1016/j.compstruct.2007.01.007.
  31. Song, Z.G. and Li, F.M. (2012), "Active aeroelastic flutter analysis and vibration control of supersonic composite laminated plate", Compos. Struct., 94(2), 702-713. https://doi.org/10.1016/j.compstruct.2011.09.005.
  32. Song, Z.G., Li, F.M., Carrera, E. and Hagedorn, P. (2018), "A new method of smart and optimal flutter control for composite laminated panels in supersonic airflow under thermal effects", J. Sound Vib., 414(3), 218-232. https://doi.org/10.1016/j.jsv.2017.11.008.
  33. Verlan, A.F., Eshmatov, Kh., Khudayarov, B.A. and Bobonazarov, Sh.P. (2004), "Numerical solution of nonlinear problems of the dynamics of viscoelastic systems", Elect. Model., 26(3), 3-14.
  34. Volmir, A.S. (1972), Nonlinear Dynamics of Plates and Shells, Science Edition, Moscow, Russia.
  35. Wang, X., Yang, Z., Wang, W. and Tian, W. (2017), "Nonlinear viscoelastic heated panel flutter with aerodynamic loading exerted on both surfaces", J. Sound Vib., 409(24), 306-317. https://doi.org/10.1016/j.jsv.2017.07.033
  36. Yazdi, A.A. (2017), "Large amplitude flutter analysis of functionally graded carbon nanotube reinforced composite plates with piezoelectric layers on nonlinear elastic foundation", Proc. Inst. Mech. Eng. Part G J. Aerospace Eng., 233(2), 533-544. https://doi.org/10.1177/0954410017736546.
  37. Zenkour, A.M. (2017), "Vibration analysis of generalized thermoelastic microbeams resting on visco-Pasternak's foundations", Adv. Aircraft Spacecraft Sci., 4(3), 267-280. https://doi.org/10.12989/aas.2017.4.3.267.
  38. Zhao, H. and Cao, D. (2013), "A study on the aero-elastic flutter of stiffened laminated composite panel in the supersonic flow", J. Sound Vib., 332(19), 4668-4679. https://doi.org/10.1016/j.jsv.2013.04.006.

Cited by

  1. Numerical Simulation of Vibration of Composite Pipelines Conveying Pulsating Fluid vol.11, pp.9, 2019, https://doi.org/10.1142/s175882511950090x
  2. Numerical investigation of the effects angles of attack on the flutter of a viscoelastic plate vol.7, pp.3, 2019, https://doi.org/10.12989/aas.2020.7.3.215
  3. Dynamic stability and vibrations of thin-walled structures considering heredity properties of the material vol.869, 2019, https://doi.org/10.1088/1757-899x/869/5/052021
  4. Numerical study of nonlinear problems in the dynamics of thin-walled structural elements vol.264, 2021, https://doi.org/10.1051/e3sconf/202126405056
  5. Vibrations of dam-plate of a hydro-technical structure under seismic load vol.264, 2019, https://doi.org/10.1051/e3sconf/202126405057
  6. A generalized solution of a modified Cauchy problem of class R 2 for a hyperbolic equation of the second kind vol.1889, pp.2, 2019, https://doi.org/10.1088/1742-6596/1889/2/022121