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Nonlinear vibrations of a fluid-filled, soft circular shell: experiments and system identification

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Abstract

Vibration experiments are carried out on a slightly corrugated circular cylindrical shell made of polyethylene terephthalate fabric. The shell is liquid-filled, it is pressurized by a liquid column that applies a pressure of 100 mmHg, and the two edges are clamped to fix supports. Forced vibrations of the shell are experimentally studied in the linear (small amplitude) and in the geometrically nonlinear (large amplitude) regime. The large-amplitude vibrations of the liquid-filled shell are characterized by a strong softening behavior that cannot be captured by any quadratic nonlinear stiffness. Since compressed fibers do not carry load, a piecewise linear stiffness with viscous damping is thus introduced in a reduced-order model, resulting in a very good agreement between experimental and simulated responses. The stiffness parameters and the damping ratios are identified from the experimental results. The damping ratio grows linearly with the excitation amplitude, indicating a predominant hydrodynamic damping. In particular, the damping ratio increases 2.75 times from the small-amplitude vibrations to a maximum amplitude of 1.26 mm. This is a very significant increase that highlights the necessity to introduce nonlinear damping to model shell structures.

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References

  1. Amabili, M., Païdoussis, M.P.: Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl. Mech. Rev. 56(4), 349–356 (2003)

    Article  Google Scholar 

  2. Alijani, F., Amabili, M.: Non-linear vibrations of shells: a literature review from 2003 to 2013. Int. J. Non-linear Mech. 58, 233–257 (2014)

    Article  Google Scholar 

  3. Chen, J.C., Babcock, C.D.: Nonlinear vibration of cylindrical shells. AIAA J. 13, 868–876 (1975)

    Article  Google Scholar 

  4. Gonçalves, P.B., Batista, R.C.: Nonlinear vibration analysis of fluid-filled cylindrical shells. J. Sound Vib. 127, 133–143 (1988)

    Article  Google Scholar 

  5. Amabili, M., Pellicano, F., Païdoussis, M.P.: Nonlinear dynamics and stability of circular cylindrical shells containing flowing fluid. Part III: Truncation effect without flow and experiments. J. Sound Vib. 237, 617–640 (2000)

    Article  Google Scholar 

  6. Amabili, M.: Comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: lagrangian approach. J. Sound Vib. 264, 1091–1125 (2003)

    Article  Google Scholar 

  7. Amabili, M.: Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  8. Amabili, M.: Nonlinear vibrations of angle-ply laminated circular cylindrical shells: skewed modes. Compos. Struct. 94, 3697–3709 (2012)

    Article  Google Scholar 

  9. Pellicano, F.: Vibrations of circular cylindrical shells: theory and experiments. J. Sound Vib. 303, 154–170 (2007)

    Article  Google Scholar 

  10. Jansen, E.L.: The effect of static loading and imperfections on the nonlinear vibrations of laminated cylindrical shells. J. Sound Vib. 315, 1035–1046 (2008)

    Article  Google Scholar 

  11. Ribeiro, P.: On the influence of membrane inertia and shear deformation on the geometrically non-linear vibrations of open, cylindrical, laminated clamped shells. Compos. Sci. Technol. 69, 176–185 (2009)

    Article  Google Scholar 

  12. Amabili, M., Balasubramanian, P., Ferrari, G.: Travelling wave and non-stationary response in nonlinear vibrations of water-filled circular cylindrical shells: experiments and simulations. J. Sound Vib. 381, 220–245 (2016)

    Article  Google Scholar 

  13. Breslavsky, I.D., Amabili, M., Legrand, M.: Static and dynamic behavior of circular cylindrical shell made of hyperelastic arterial material. J. Appl. Mech. 83, 051002 (2016)

    Article  Google Scholar 

  14. Amabili, M.: Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials. Cambridge University Press, Cambridge (2018)

    Book  Google Scholar 

  15. Amabili, M., Breslavsky, I.D., Reddy, J.N.: Nonlinear higher-order shell theory for incompressible biological hyperelastic materials. Comput. Methods Appl. Mech. Eng. 346, 841–861 (2019)

    Article  MathSciNet  Google Scholar 

  16. Bustos, C.A., García-Herrera, C.M., Celentano, D.J.: Modelling and simulation of the mechanical response of a Dacron graft in the pressurization test and an end-to-end anastomosis. J. Mech. Behav. Biomed. Mater. 61, 36–44 (2016)

    Article  Google Scholar 

  17. Amabili, M., Balasubramanian, P., Breslavsky, I., Ferrari, G., Tubaldi, E.: Viscoelastic characterization of woven Dacron for aortic grafts by using direction-dependent quasi-linear viscoelasticity. J. Mech. Behav. Biomed. Mater. 82, 282–290 (2018)

    Article  Google Scholar 

  18. Ferrari, G., Balasubramanian, P., Tubaldi, E., Giovanniello, F., Amabili, M.: Experiments on dynamic behaviour of a Dacron aortic graft in a mock circulatory loop. J. Biomech. 86, 132–140 (2019)

    Article  Google Scholar 

  19. Amabili, M., Balasubramanian, P., Ferrari, G., Franchini, G., Giovanniello, F., Tubaldi, E.: Identification of viscoelastic properties of Dacron aortic grafts subjected to physiological pulsatile flow. J. Mech. Behav. Biomed. Mater. 110, 103804 (2020)

    Article  Google Scholar 

  20. Amabili, M., Garziera, R.: Vibrations of circular cylindrical shells with nonuniform constraints, elastic bed and added mass, part I: empty and fluid-filled shells. J. Fluids Struct. 14, 669–690 (2000)

    Article  Google Scholar 

  21. Doedel, E.J., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Y.A., Sandstede, B., Wang, X.: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont). AUTO97. Concordia University, Montreal (1997)

    Google Scholar 

  22. Amabili, M.: Nonlinear damping in nonlinear vibrations of rectangular plates: derivation from viscoelasticity and experimental validation. J. Mech. Phys. Solids 118, 275–292 (2018)

    Article  MathSciNet  Google Scholar 

  23. Amabili, M.: Nonlinear damping in large-amplitude vibrations: modelling and experiments. Nonlinear Dyn. 93, 5–18 (2018)

    Article  Google Scholar 

  24. Balasubramanian, P., Ferrari, G., Amabili, M.: Identification of the viscoelastic response and nonlinear damping of a rubber plate in nonlinear vibration regime. Mech. Syst. Signal Process. 111, 376–398 (2018)

    Article  Google Scholar 

  25. Amabili, M.: Derivation of nonlinear damping from viscoelasticity in case of nonlinear vibrations. Nonlinear Dyn. 97, 1785–1797 (2019)

    Article  Google Scholar 

  26. Colin, M., Thomas, O., Grondel, S., Cattan, E.: Very large amplitude vibrations of flexible structures: experimental identification and validation of a quadratic drag damping model. J. Fluids Struct. 97, 103056 (2020)

    Article  Google Scholar 

  27. Elliot, S.J., Ghandchi Tehrani, M., Langley, R.S.: Nonlinear damping and quasi-linear modelling. Philos. Trans. R. Soc. A 373, 20140402 (2015)

    Article  MathSciNet  Google Scholar 

  28. Amabili, M., Balasubramanian, P., Bozzo, I., Breslavsky, I.D., Ferrari, G., Franchini, G., Giovanniello, F., Pogue, C.: Nonlinear dynamics of human aortas for material characterization. Phys. Rev. X 10, 011015 (2020)

    Google Scholar 

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Acknowledgments

The last author acknowledges the financial support of the NSERC Discovery Grant, the Canada Foundation for Innovation John R. Evans Leaders Fund Award and the Canada Research Chair program.

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Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, Macdonald Engineering Building, 817 Sherbrooke Street West, Montreal, QC, H3A 0C3, Canada

    Prabakaran Balasubramanian, Giovanni Ferrari & Marco Amabili

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  1. Prabakaran Balasubramanian
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  2. Giovanni Ferrari
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  3. Marco Amabili
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Correspondence to Marco Amabili.

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Balasubramanian, P., Ferrari, G. & Amabili, M. Nonlinear vibrations of a fluid-filled, soft circular shell: experiments and system identification. Nonlinear Dyn 102, 1409–1418 (2020). https://doi.org/10.1007/s11071-020-06007-5

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