Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Fluid-structure interaction
Article Number 44
Number of page(s) 34
DOI https://doi.org/10.1051/mmnp/2020033
Published online 24 September 2020
  1. S.S. Antman, Nonlinear Problems of Elasticity. Springer (1995). [Google Scholar]
  2. M. Argentina and L. Mahadevan, Fluid-flow-induced flutter of a flag. Proc. National Acad. Sci. U.S.A. 102 (2005) 1829–1834. [CrossRef] [Google Scholar]
  3. H. Ashley and G. Zartarian, Piston theory: a new aerodynamic tool for the aeroelastician. J. Aeronaut. Sci. 23 (1956) 1109–1118. [CrossRef] [Google Scholar]
  4. A.V. Balakrishnan and A.M. Tuffaha, Aeroelastic flutter in axial flow-The continuum theory. AIP Conf. Proc. 1493 (2012) 58–66). [Google Scholar]
  5. J.M. Ball, Initial-boundary value problems for an extensible beam. J. Math. Anal. Applic. 42 (1973) 61–90. [CrossRef] [Google Scholar]
  6. V.V. Bolotin, Nonconservative Problems of the Theory of Elastic Stability. Macmillan (1963). [Google Scholar]
  7. S.P. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math. 136 (1989) 15–55. [CrossRef] [MathSciNet] [Google Scholar]
  8. I. Chueshov, E.H. Dowell, I. Lasiecka and J.T. Webster, Nonlinear elastic plate in a flow of gas: recent results and conjectures. Appl. Math. Optim. 73 (2016) 475–500. [Google Scholar]
  9. I. Chueshov and I. Lasiecka, Von Karman Evolution Equations: Well-posedness and Long Time Dynamics. Springer Science & Business Media (2010). [CrossRef] [Google Scholar]
  10. D. Culver, K. McHugh and E. Dowell, An assessment and extension of geometrically nonlinear beam theories. Mech. Syst. Signal Process. 134 (2019) 106340. [Google Scholar]
  11. M. Deliyianni and J.T. Webster, A theory of solutions for an inextensible cantilever. Preprint arXiv:2005.11836 (2020). [Google Scholar]
  12. R.W. Dickey, Free vibrations and dynamic buckling of the extensible beam. J. Math. Anal. Appl. 29 (1970) 443–454. [Google Scholar]
  13. O. Doaré and S. Michelin, Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency. J. Fluids Struct. 27 (2011) 1357–1375. [Google Scholar]
  14. E.H. Dowell, Aeroelasticity of Plates and Shells, Vol. 1. Springer Science & Business Media (1974). [Google Scholar]
  15. E.H. Dowell, R. Clark, D. Cox, et al. A Modern Course in Aeroelasticity, fifth ed. Springer (2015). [Google Scholar]
  16. E. Dowell and K. McHugh, Equations of motion for an inextensible beam undergoing large deflections. J. Appl. Mech. 83 (2016) 051007. [Google Scholar]
  17. S.S. Dragomir, Some Gronwall type inequalities and applications. Electron. J. Differ. Equ. 2003 (2003) 1–13. [Google Scholar]
  18. J.A. Dunnmon, S.C. Stanton, B.P. Mann and E.H. Dowell, Power extraction from aeroelastic limit cycle oscillations. J. Fluids Struct. 27 (2011) 1182–1198. [Google Scholar]
  19. C. Eloy, R. Lagrange, C, Souilliez and L. Schouveiler, Aeroelastic instability of cantilevered flexible plates in uniform flow. J. Fluid Mech. 611 (2008) 97–106. [Google Scholar]
  20. A. Erturk and D.J. Inman, Piezoelectric Energy Harvesting. John Wiley & Sons (2011). [CrossRef] [Google Scholar]
  21. R.H. Fabiano and S.W. Hansen, Modeling and Analysis of a Three-layer Damped Sandwich Beam. Conference Publications (2001). [Google Scholar]
  22. S.M. Han, H. Benaroya and T. Wei, Dynamics of transversely vibrating beams using four engineering theories. J. Sound Vibrat. 225 (1999) 935–988. [CrossRef] [Google Scholar]
  23. S. Hansen, Analysis of a plate with a localized piezoelectric patch, in Proceedings of the 37th IEEE Conference on Decision and Control, Cat. No. 98CH36171, Vol. 3 (1998) 2952–2957. [Google Scholar]
  24. P. Holmes and J. Marsden, Bifurcation to divergence and flutter in flow-induced oscillations: an infinite dimensional analysis. Automatica 14 (1978) 367–384. [CrossRef] [Google Scholar]
  25. J. Howell, K. Huneycutt, J.T. Webster and S. Wilder, A thorough look at the (in)stability of piston-theoretic beams. Math. Eng. 1 (2019) 614–647. [CrossRef] [Google Scholar]
  26. J.S. Howell, D. Toundykov and J.T. Webster, A cantilevered extensible beam in axial flow: semigroup well-posedness and postflutter regimes. SIAM J. Math. Anal. 50 (2018) 2048–2085. [CrossRef] [Google Scholar]
  27. L. Huang, Flutter of cantilevered plates in axial flow. J. Fluids Struct. 9 (1995) 127–147. [Google Scholar]
  28. L. Huang and C. Zhang, Modal analysis of cantilever plate flutter. J. Fluids Struct. 38 (2013) 273–289. [Google Scholar]
  29. D. Kim, J. Cossé, C.H. Cerdeira and M. Gharib, Flapping dynamics of an inverted flag. J. Fluid Mech. 736 (2013). [Google Scholar]
  30. H. Koch and I. Lasiecka, Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity-full von Karman systems, in Evolution Equations, Semigroups and Functional Analysis. Birkhauser, Basel (2002) 197–216. [Google Scholar]
  31. J.E. Lagnese, Boundary stabilization of thin plates. SIAM, Philadelphia (1989). [CrossRef] [Google Scholar]
  32. J.E. Lagnese and G. Leugering, Uniform stabilization of a nonlinear beam by nonlinear boundary feedback. J. Differ. Eq. 91 (1991) 355–388. [CrossRef] [MathSciNet] [Google Scholar]
  33. E. De Langre and O. Doaré, Edge flutter of long beams under follower loads. In Memoriam: Huy Duong Bui (2015) 283. [Google Scholar]
  34. I. Lasiecka and J. Ong, Global solvability and uniform decays of solutions to quasilinear equation with nonlinear boundary dissipation. Commun. Partial Differ. Eq. 24 (1999) 2069–2107. [CrossRef] [Google Scholar]
  35. I. Lasiecka, M. Pokojovy and X. Wan, Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound. Nonlinear Anal. 186 (2019) 219–258. [CrossRef] [Google Scholar]
  36. I. Lasiecka and R. Triggiani, Control theory for partial differential equations, in Abstract Parabolic Systems: Continuous and Approximation theories, Vol. 1. Cambridge University Press (2000). [Google Scholar]
  37. D. Levin and E. Dowell, Improving piezoelectric energy harvesting from an aeroelastic system , International Forum on Aeroelasticity and Structural Dynamics IFASD 2019 9-13 June 2019, Savannah, Georgia, USA (2019). [Google Scholar]
  38. T.F. Ma, V. Narciso and M.L. Pelicer, Long-time behavior of a model of extensible beams with nonlinear boundary dissipations. J. Math. Anal. Applic. 396 (2012) 694–703. [CrossRef] [Google Scholar]
  39. K.A. McHugh, Personal correspondence (2019). [Google Scholar]
  40. K.A. McHughand E.H. Dowell, Nonlinear response of an inextensible, cantilevered beam subjected to a nonconservative follower force. J. Comput. Nonlinear Dyn. 14 (2019) 031004. [Google Scholar]
  41. K.A. McHugh, P. Beran, M. Freydin and E.H. Dowell, Flutter and limit cycle oscillations of a cantilevered plate in supersonic/hypersonic flow, in Proceedings of IFASD 2019, Savannah GA (2019). [Google Scholar]
  42. D.J. Mead and S. Markus, The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions. J. Sound Vibrat. 10 (1969) 163–175. [CrossRef] [Google Scholar]
  43. A.O. Ozer, Dynamic and electrostatic modeling for a piezoelectric smart composite and related stabilization results. Preprint arXiv:1707.04744 (2017). [Google Scholar]
  44. M.P. Païdoussis, Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 1. Academic Press (1998). [Google Scholar]
  45. D.L. Russell, A comparison of certain elastic dissipation mechanisms via decoupling and projection techniques. Quart. Appl. Math. 49 (1991) 373–396. [CrossRef] [Google Scholar]
  46. D.L. Russell, A general framework for the study of indirect damping mechanisms in elastic systems. J. Math. Anal. Applic. 173 (1993) 339–358. [CrossRef] [Google Scholar]
  47. L. Scardia, The nonlinear bending-torsion theory for curved rods as Γ-limit of three-dimensional elasticity. Asymptotic Anal. 47 (2006) 317–343. [Google Scholar]
  48. C. Semler, G.X. Li and M.P. Païdoussis, The non-linear equations of motion of pipes conveying fluid. J. Sound Vibrat. 169 (1994) 577–599. [CrossRef] [Google Scholar]
  49. M. Serry and A. Tuffaha, Static stability analysis of a thin plate with a fixed trailing edge in axial subsonic flow: Possion integral equation approach. Preprint arXiv:1708.06956 (2017). [Google Scholar]
  50. M.A. Shubov and V.I. Shubov, Asymptotic and spectral analysis and control problems for mathematical model of piezoelectric energy harvester. Math. Eng. Sci. Aerospace (MESA) 7 (2016). [Google Scholar]
  51. S.C. Stanton, A. Erturk, B.P. Mann, E.H. Dowell and D.J. Inman, Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects. J. Intell. Mater. Syst. Struct. 23 (2012) 183–199. [Google Scholar]
  52. D. Tang, S.C. Gibbs and E.H. Dowell, Nonlinear aeroelastic analysis with inextensible plate theory including correlation with experiment. AIAA J. 53 (2015) 1299–1308. [Google Scholar]
  53. D.M. Tang and E.H. Dowell, Aeroelastic response and energy harvesting from a cantilevered piezoelectric laminated plate. J. Fluids Struct. 76 (2018) 14–36. [Google Scholar]
  54. D. Tang, M. Zhao and E.H. Dowell, Inextensible beam and plate theory: computational analysis and comparison with experiment. J. Appl. Mech. 81 (2014) 061009. [Google Scholar]
  55. L. Tang and M.P. Pa, On the instability and the post-critical behaviour of two-dimensional cantilevered flexible plates in axial flow. J. Sound Vibrat. 305 (2007) 97–115. [CrossRef] [Google Scholar]
  56. V.V. Vedeneev, Panel flutter at low supersonic speeds. J. Fluids Struct. 29 (2012) 79–96. [Google Scholar]
  57. S. Woinowsky-Krieger, The effect of an axial force on the vibration of hinged bars. J. Appl. Mech. 17 (1950) 35–36. [Google Scholar]
  58. W. Zhao, M.P. Païdoussis, L. Tang, M. Liu and J. Jiang, Theoretical and experimental investigations of the dynamics of cantilevered flexible plates subjected to axial flow. J. Sound Vibrat. 331 (2012) 575–587. [CrossRef] [Google Scholar]

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