Composite wing vibration coupling control

Authors

  • Victor M. Ryabov St Petersburg State University, 7–9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Boris A. Yartsev St Petersburg State University, 7–9, Universitetskaya nab., St Petersburg, 199034, Russian Federation, Krylov State Research Center, 44, Moskovskoye shosse, St. Petersburg, 196158, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2023.214

Abstract

The paper discusses the possibility to control coupled bending-twisting vibrations of composite wing by means of the monoclinic structures in the reinforcement of the plating. Decomposing the potential straining energy and kinetic energy of natural vibration modes into interacting and non-interacting parts, it became possible to introduce the two coefficients that integrally consider the effect of geometry and reinforcement structure upon the dynamic response parameters of the wing. The first of these coefficients describes the elastic coupling of the natural vibration modes, the second coefficient describes the inertial one. The paper describes the numerical studies showing how the orientation of considerably anisotropic CRP layers in the plating affects natural frequencies, loss factors, coefficients of elastic and inertial coupling for several lower tones of natural bending-twisting vibrations of the wing. Besides, for each vibration mode, partial values of the above mentioned dynamic response parameters were determined by means of the relationships for orthotropic structures where instead of “free” shearing modulus in the reinforcement plant, “pure” shearing modulus is used. Joint analysis of the obtained results has shown that each pair of bendingtwisting vibration modes has its orientation angle ranges of the reinforcing layers where the inertial coupling caused by asymmetry of the cross-section profile with respect to the main axes of inertia decreases, down to the complete extinction, due to the generation of the elastic coupling in the plating material. These ranges are characterized by the two main features: 1) the difference in the natural frequencies of the investigated pair of bendingtwisting vibration modes is the minimum and 2) natural frequencies of bending-twisting vibrations belong to a stretch restricted by corresponding partial natural frequencies of the investigated pair of vibration modes. This result is of practical importance because it enables approximate analysis of real composite wings with complex geometry in the existing commercial software packages.

Keywords:

composite wing, coupled vibrations, elastic coupling, inertial connectivity, natural frequency, loss factors

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References

Литература

1. Daynes S., Weaver P. M. Review Stiffness tailoring using prestress in adaptive composite structures. Composite Structures 106, 282-287 (2013).

2. Munk M. M. Patent US 2484308 А. Propeller containing diagonally disposed fibrous material. Publ. October, 11. 1949.

3. Munk M. M. Patent US 2599718 А. Laminated propeller. Publ. June, 10. 1952.

4. Jones R. M. Mechanics of composite materials. Second edition. Taylor & Francies (1999).

5. Hayat K., de Lecea A. G. M., Moriones C. D., Ha S. K. Flutter performance of bend-twist coupled large-scale wind turbine blades. Journal of Sound and Vibration 370, 149-162 (2016).

6. Wang L., Kolios A., Nishino T., Delafin P.-L., Bird T. Structural optimisation of vertical-axis wind turbine composite blades based on finite element analysis and genetic algorithm. Composite Structures 153, 123-138 (2016).

7. Motley M. R., Barber R. B. Passive control of marine hydrokinetic turbine blades. Composite Structures 110, 133-139 (2014).

8. Li W., Zhou H., Liu H., Lin Y., Xu Q. Review on the blade design technologies of tidal current turbine. Renewable and Sustainable Energy Reviews 63, 414-422 (2016).

9. Azzam A., Li W. Theoretical and experimental methods on bend-twist coupling and damping properties with the relationship to lay-up of the composite propeller marine: A review. International Journal of Engineering Science and Technology 4 (6), 2907-2917 (2012).

10. Young Y. L. Dynamic hydroelastic scaling of self-adaptive composite marine rotors. Composite Structures 92, 97-106 (2010).

11. Bauchau O. A., Coffenberry B. S., Rehfield L.W. Composite box beam analysis; theory and experiments. Journal of Reinforced Plastics and Composites 6, 25-35 (1987).

12. Libove C. Stresses and rate of twist in single-cell thin-walled beams with anisotropic walls. AIAA Journal 26 (9), 1107-1118 (1988).

13. Bauchau O. A., Hong C. H. Nonlinear composite beam theory. Transactions of the ASME. Journal of Applied Mechanics 55, 156-163 (1988).

14. Rehfield L. W., Atilgan A. R. Shear center and elastic axis and their usefulness for composite thin-walled beams. Proceedings of the American Society for Composites. Fourth Technical Conference, 179-188. Blacksburg, Virginia (1989).

15. Altenbach J., Altenbach H., Matzdorf V. A generalized Vlasov theory for thin-walled composite beam structures. Mechanics of Composite Materials 30 (1), 57-71 (1994).

16. Lentz W. K., Armanios E. A., Badir A. M. Constrained optimization of thin-walled composite beams with coupling. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 37th Structures. Structural Dynamics and Materials Conference. A Collection of Technical Papers. Part IV. April, 15-17, 2326-2334 (1996).

17. Mitra M., Gopalakrishnan S., Bhat M. S. A new convergent thin walled composite beam element for analysis of box beam structures. International Journal of Solids and Structures 41, 1491-1518 (2004).

18. Yu W., Liao L., Hodges D. H., Volovoi V. V. Theory of initially twisted, composite, thin-walled beams. Thin-Walled Structures 43, 1296-1311 (2005).

19. Shan L., Qiao P. Flexural-torsional buckling of fiber-reinforced plastic composite open channel beams. Composite Structures 68, 211-224 (2005).

20. Murray R. E., Doman D. A., Pegg M. J. Finite element modeling and effects of material uncertainties in a composite laminate with bend-twist coupling. Composite Structures 121, 362-376 (2015).

21. Librescu L., Song O. Thin-walled composite beams. Theory and application. Springer (2006).

22. Bank L. C., Kao C. H. The influence of geometric and material design variables on the free vibration of thin-walled composite material beams. Journal of Vibration, Acoustics, Stress and Reliability in Design 111, 290-297 (1989).

23. Koo K. N., Lee I. Aeroelastic behavior of a composite plate wing with structural damping. Computers and Structures 50 (2), 167-176 (1994).

24. Armanios E. A., Badir A. M. Free vibration analysis of anisotropic thin-walled closed-section beams. AIAA Journal 33 (10), 1905-1910 (1995).

25. Centolanza L. R., Smith E. C., Kumar B. Refined structural modeling and structural dynamics of elastically tailored composite rotor blades. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 37th Structures, Structural Dynamics and Materials Conference. A Collection of Technical Papers. Part IV. April 15-17, 2002-2012 (1996).

26. Qin Z., Librescu L. Aeroelastic instability of aircraft wings modelled as an isotropic composite thin-walled beams in incompressible flow. Journal of Fluids and Structures 18, 43-61 (2003).

27. Oh S.-Y., Song O., Librescu L. Effects of pretwist and presetting on coupled bending vibrations of rotating thin-walled composite beams. International Journal of Solids and Structures 40, 1203-1224 (2003).

28. Masaki Kameyama, Hisao Fukunaga. Optimum design of composite plate wings for aeroelastic characteristics using lamination parameters. Computers and Structures 85, 213-224 (2007).

29. Piovan M. T., Filipich C. P., Cortinez V. H. Exact solutions for coupled free vibrations of tapered shear-flexible thin-walled composite beams. Journal of Sound and Vibration 316, 298-316 (2008).

30. Santiuste C., Sanchez-Saez S., Barbero E. Dynamic analysis of bending-torsion coupled composite beams using the flexibility influence function method. International Journal of Mechanical Sciences 50, 1611-1618 (2008).

31. Vo T. P., Lee J., Ahn N. On sixfold coupled vibrations of thin-walled composite box beams. Composite Structures 89, 524-535 (2009).

32. Mirtalaie S. H., Hajabasi M. A. Study of coupled lateral-torsion free vibrations of laminated composite beam: analytical approach. World Academy of Science, Engineering and Technology 54, 699-704 (2011).

33. Mirtalaie S. H., Mohammadi M., Hajabasi M. A., Hejripour F. Coupled lateral-torsion free vibrations analysis of laminated composite beam using differential quadrature method. World Academy of Science, Engineering and Technology 67, 117-122 (2012).

34. Рябов В. М., Ярцев Б. А. Собственные затухающие колебания композитных конструкций. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 4, 32-38 (2012).

35. Motley M. R., Kramer M. R., Young Y. L. Free surface and solid boundary effects on the free vibration of cantilevered composite plates. Composite Structures 96, 365-375 (2013).

36. Sina S. A., Haddadpour H. Axial-torsional vibrations of rotating pretwisted thin walled composite beams. International Journal of Mechanical Sciences 80, 93-101 (2014).

37. Kim N. I., Lee J. Divergence and flutter behavior of Beck’s type of laminated box beams. International Journal of Mechanical Sciences 84, 91-101 (2014).

38. Szekr´enyes A. Coupled flexural-longitudinal vibration of delaminated composite beams with local stability analysis. Journal of Sound and Vibration 333, 5141-5164 (2014).

39. Sayyad A. S., Ghugal Y. M. On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results. Composite Structures 129, 177-201 (2015).

40. Рябов В. М., Ярцев Б. А. Собственные затухающие колебания анизотропных коробчатых стержнейиз полимерных композиционных материалов. 1. Постановка задачи. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 3 (61), вып. 2, 221-229 (2016). https://doi.org/10.21638/11701/spbu01.2016.206

41. Рябов В. М., Ярцев Б. А. Собственные затухающие колебания анизотропных коробчатых стержнейиз полимерных композиционных материалов. 2. Численныйэксперимент. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 3 (61), вып. 3, 429-439 (2016). https://doi.org/10.21638/11701/spbu01.2016.311

42. Рябов В. М., Ярцев Б. А. Неклассические колебания моноклиннойкомпозитнойполосы. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 8 (66), вып. 4, 695-708 (2021). https://doi.org/10.21638/spbu01.2021.415

43. Фын Я. Ц. Введение в теорию аэроупругости, пер. с англ. Москва, Физматлит (1959).

44. Васидзу К. Вариационные методы в теории упругости и пластичности, пер. с англ. Москва, Мир (1987).

45. Voigt W. Lehrbuch der Kristallphysik. Leipzig, Berlin, Teubner (1928).

References

1. Daynes S., Weaver P. M. Review Stiffness tailoring using prestress in adaptive composite structures. Composite Structures 106, 282-287 (2013).

2. Munk M. M. Patent US 2484308 А. Propeller containing diagonally disposed fibrous material. Publ. October, 11. 1949.

3. Munk M. M. Patent US 2599718 А. Laminated propeller. Publ. June, 10. 1952.

4. Jones R. M. Mechanics of composite materials. Second edition. Taylor & Francies (1999).

5. Hayat K., de Lecea A. G. M., Moriones C. D., Ha S. K. Flutter performance of bend-twist coupled large-scale wind turbine blades. Journal of Sound and Vibration 370, 149-162 (2016).

6. Wang L., Kolios A., Nishino T., Delafin P.-L., Bird T. Structural optimisation of vertical-axis wind turbine composite blades based on finite element analysis and genetic algorithm. Composite Structures 153, 123-138 (2016).

7. Motley M. R., Barber R. B. Passive control of marine hydrokinetic turbine blades. Composite Structures 110, 133-139 (2014).

8. Li W., Zhou H., Liu H., Lin Y., Xu Q. Review on the blade design technologies of tidal current turbine. Renewable and Sustainable Energy Reviews 63, 414-422 (2016).

9. Azzam A., Li W. Theoretical and experimental methods on bend-twist coupling and damping properties with the relationship to lay-up of the composite propeller marine: A review. International Journal of Engineering Science and Technology 4 (6), 2907-2917 (2012).

10. Young Y. L. Dynamic hydroelastic scaling of self-adaptive composite marine rotors. Composite Structures 92, 97-106 (2010).

11. Bauchau O. A., Coffenberry B. S., Rehfield L.W. Composite box beam analysis; theory and experiments. Journal of Reinforced Plastics and Composites 6, 25-35 (1987).

12. Libove C. Stresses and rate of twist in single-cell thin-walled beams with anisotropic walls. AIAA Journal 26 (9), 1107-1118 (1988).

13. Bauchau O. A., Hong C. H. Nonlinear composite beam theory. Transactions of the ASME. Journal of Applied Mechanics 55, 156-163 (1988).

14. Rehfield L. W., Atilgan A. R. Shear center and elastic axis and their usefulness for composite thin-walled beams. Proceedings of the American Society for Composites. Fourth Technical Conference, 179-188. Blacksburg, Virginia (1989).

15. Altenbach J., Altenbach H., Matzdorf V. A generalized Vlasov theory for thin-walled composite beam structures. Mechanics of Composite Materials 30 (1), 57-71 (1994).

16. Lentz W. K., Armanios E. A., Badir A. M. Constrained optimization of thin-walled composite beams with coupling. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 37th Structures. Structural Dynamics and Materials Conference. A Collection of Technical Papers. Part IV. April, 15-17, 2326-2334 (1996).

17. Mitra M., Gopalakrishnan S., Bhat M. S. A new convergent thin walled composite beam element for analysis of box beam structures. International Journal of Solids and Structures 41, 1491-1518 (2004).

18. Yu W., Liao L., Hodges D. H., Volovoi V. V. Theory of initially twisted, composite, thin-walled beams. Thin-Walled Structures 43, 1296-1311 (2005).

19. Shan L., Qiao P. Flexural-torsional buckling of fiber-reinforced plastic composite open channel beams. Composite Structures 68, 211-224 (2005).

20. Murray R. E., Doman D. A., Pegg M. J. Finite element modeling and effects of material uncertainties in a composite laminate with bend-twist coupling. Composite Structures 121, 362-376 (2015).

21. Librescu L., Song O. Thin-walled composite beams. Theory and application. Springer (2006).

22. Bank L. C., Kao C. H. The influence of geometric and material design variables on the free vibration of thin-walled composite material beams. Journal of Vibration, Acoustics, Stress and Reliability in Design 111, 290-297 (1989).

23. Koo K. N., Lee I. Aeroelastic behavior of a composite plate wing with structural damping. Computers and Structures 50 (2), 167-176 (1994).

24. Armanios E. A., Badir A. M. Free vibration analysis of anisotropic thin-walled closed-section beams. AIAA Journal 33 (10), 1905-1910 (1995).

25. Centolanza L. R., Smith E. C., Kumar B. Refined structural modeling and structural dynamics of elastically tailored composite rotor blades. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 37th Structures, Structural Dynamics and Materials Conference. A Collection of Technical Papers. Part IV. April 15-17, 2002-2012 (1996).

26. Qin Z., Librescu L. Aeroelastic instability of aircraft wings modelled as an isotropic composite thin-walled beams in incompressible flow. Journal of Fluids and Structures 18, 43-61 (2003).

27. Oh S.-Y., Song O., Librescu L. Effects of pretwist and presetting on coupled bending vibrations of rotating thin-walled composite beams. International Journal of Solids and Structures 40, 1203-1224 (2003).

28. Masaki Kameyama, Hisao Fukunaga. Optimum design of composite plate wings for aeroelastic characteristics using lamination parameters. Computers and Structures 85, 213-224 (2007).

29. Piovan M. T., Filipich C. P., Cortinez V. H. Exact solutions for coupled free vibrations of tapered shear-flexible thin-walled composite beams. Journal of Sound and Vibration 316, 298-316 (2008).

30. Santiuste C., Sanchez-Saez S., Barbero E. Dynamic analysis of bending-torsion coupled composite beams using the flexibility influence function method. International Journal of Mechanical Sciences 50, 1611-1618 (2008).

31. Vo T. P., Lee J., Ahn N. On sixfold coupled vibrations of thin-walled composite box beams. Composite Structures 89, 524-535 (2009).

32. Mirtalaie S. H., Hajabasi M. A. Study of coupled lateral-torsion free vibrations of laminated composite beam: analytical approach. World Academy of Science, Engineering and Technology 54, 699-704 (2011).

33. Mirtalaie S. H., Mohammadi M., Hajabasi M. A., Hejripour F. Coupled lateral-torsion free vibrations analysis of laminated composite beam using differential quadrature method. World Academy of Science, Engineering and Technology 67, 117-122 (2012).

34. Ryabov V. M., Yartsev B. A. Coupled damping vibrations of composite structures. Vestnik St Petersburg University. Mathematics 45 (4), 168-173 (2012)

35. Motley M. R., Kramer M. R., Young Y. L. Free surface and solid boundary effects on the free vibration of cantilevered composite plates. Composite Structures 96, 365-375 (2013).

36. Sina S. A., Haddadpour H. Axial-torsional vibrations of rotating pretwisted thin walled composite beams. International Journal of Mechanical Sciences 80, 93-101 (2014).

37. Kim N. I., Lee J. Divergence and flutter behavior of Beck’s type of laminated box beams. International Journal of Mechanical Sciences 84, 91-101 (2014).

38. Szekr´enyes A. Coupled flexural-longitudinal vibration of delaminated composite beams with local stability analysis. Journal of Sound and Vibration 333, 5141-5164 (2014).

39. Sayyad A. S., Ghugal Y. M. On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results. Composite Structures 129, 177-201 (2015).

40. Ryabov V. M., Yartsev B. A. Natural damped vibrations of anisotropic box beams of polymer composite materials: 1. Statement of the problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 3 (61), iss. 2, 221-229 (2016). https://doi.org/10.21638/11701/spbu01.2016.206 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 49, iss. 2, 130-137 (2016). https://doi.org/10.3103/S1063454116020126].

41. Ryabov V. M., Yartsev B. A. Natural damped vibrations of anisotropic box beams of polymer composite materials: II. Numerical experiments. Vestnik of Saint Petersburg University. Mathematics Mechanics. Astronomy 3 (61), iss. 3, 429-439 (2016). https://doi.org/10.21638/11701/spbu01.2016.311 (In Russian) [Eng. transl.: Vestnik St Petersburg University, Mathematics 49, iss. 3, 260-268 (2016). https://doi.org/10.3103/S1063454116030110].

42. Ryabov V. M., Yartsev B. A. Nonclassical vibrations of a monoclinic composite strip. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8 (66), iss. 4, 695-708 (2021). https://doi.org/10.21638/spbu01.2021.415 (In Russian) [Eng. transl.: Vestnik St Petersburg University, Mathematics 54, iss. 4, 437-446 (2021). https://doi.org/10.1134/S1063454121040166].

43. Fung Y. C. An introduction to the theory of aeroelasticity. New York, John Wiley and Sons (1955). [Rus. ed.: Fung Y. C. Vvedenie v teoriiu aerouprugosti. Moscow, Fizmatlit Publ. (1959)].

44. Washizu K. Variational methods in elasticity and plasticity. Pergamon Press (1982). [Rus. ed.: Washizu K. Variatsionnye metody v teorii uprugosti i plastichnosti. Moscow, Mir Publ. (1987)].

45. Voigt W. Lehrbuch der Kristallphysik. Leipzig, Berlin, Teubner (1928).

Published

2023-05-10

How to Cite

Ryabov, V. M., & Yartsev, B. A. (2023). Composite wing vibration coupling control. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 344–356. https://doi.org/10.21638/spbu01.2023.214

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Section

Mechanics

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