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Stability analysis of inhomogeneous equilibrium for axially and transversely excited nonlinear beam
1. | Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042 |
2. | Department of Mathematical Sciences, George Mason University, Fairfax VA, 22030 |
References:
[1] |
A. A. Alqaisia and M. N. Hamdan, Bifurcation and chaos of an immersed cantilever beam in a fluid and carrying an intermediate mass, Journal of Sound and Vibration, 253 (2002), 859-888.
doi: 10.1006/jsvi.2001.4072. |
[2] |
A. Andrianov and A. Hermans, A VELFP on infinite, finite and shallow water, 17-th International workshop on water waves and floating bodies, Cambridge, UK, aPEIL (2002), 14-17. |
[3] |
E. Aulisa, A. Ibragimov, Y. Kaya and P. Seshaiyer, A stability estimate for fluid structure interaction problem with non-linear beam,, Accepted in the, ().
|
[4] |
E. Aulisa, A. Cervone, S. Manservisi and P. Seshaiyer, A multilevel domain decomposition approach for studying coupled flow application, Communications in Computational Physics, 6 (2009), 319-341.
doi: 10.4208/cicp.2009.v6.p319. |
[5] |
E. Aulisa, S. Manservisi, and P. Seshaiyer, A computational domain decomposition approach for solving coupled flow-structure-thermal interaction problems, Seventh Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 17 (2009), pp. 13-31. |
[6] |
E. Aulisa, S. Manservisi and P. Seshaiyer, A multilevel domain decomposition methodology for solving coupled problems in fluid-structure-thermal interaction, Proceedings of ECCM 2006, Lisbon, Portugal (2006). |
[7] |
R. W. Dickey, Dynamic stability of equilibrium states of the extendible beam, Proceedings of the American Mathematical Society, 41 (1973), 94-102.
doi: 10.1090/S0002-9939-1973-0328290-8. |
[8] | |
[9] |
D. A. Evensen, Nonlinear vibrations of beams with various boundary conditions, AIAA Journal, 6 (1968), 370-372.
doi: 10.2514/3.4506. |
[10] |
L. Ferguson, E. Aulisa, P. Seshaiyer, Computational modeling of highly flexible membrane wings in micro air vehicles, Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference Newport, RI (2006). |
[11] |
D. G. Gorman, I. Trendafilova, A. J. Mulholland and J. Horacek, Analytical modeling and extraction of the modal behavior of a cantilever beam in fluid interaction, Journal of Sound and Vibration, (2007), 231-245.
doi: 10.1016/j.jsv.2007.07.032. |
[12] |
A. E. Green and J. E. Adkins, "Large Elastic Deformations," Clarendon Press (Oxford), 1970. |
[13] |
H. W. Haslach, J. D. Humphrey, Dynamics of biological soft tissue or rubber: Internally pressurized spherical membranes surrounded by a fluid, Int J Nonlin Mech, 39 (2004), 399-420. |
[14] |
J. D. Humphrey, "Cardiovascular Solid Mechanics," Springer, 2002. |
[15] |
A. I. Ibragimov and P. Koola, The dynamics of wave carpet, P. 2288, OCEAN 2003 MTS/IEEE, proceedings. |
[16] |
R. A. Ibrahim, Nonlinear vibrations of suspended cables, Part III: Random excitation and interaction with fluid flow, Applied Mechanics Reviews, 57 (2004), 515-549.
doi: 10.1115/1.1804541. |
[17] |
J. E. Lagnese, Modelling and stabilization of nonlinear plates, International Series of Numerical Mathematics, 100 (1991), 247-264. |
[18] |
C. L. Lou and D. L. Sikarskie, Nonlinear Vibration of beams using a form-function approximation, ASME Journal of Applied Mechanics, 42 (1975), 209-214.
doi: 10.1115/1.3423520. |
[19] |
C. Mei, Finite element displacement method for large amplitude free flexural vibrations of beams and plates, Computers and Structures, 3 (1973), 163-174. |
[20] |
J. Padovan, Nonlinear vibrations of general structures, Journal of Sound and Vibration, 72 (1980), 427-441. |
[21] |
J. Peradze, A numerical alghorithm for Kirchhoff-Type nonlinear static beam, Journal of Applied Mathematics, in Press (2009).
doi: 10.1155/2009/818269. |
[22] |
J. N. Reddy, Finite element modeling of structural vibrations: A review of recent advances,, The Shock Vibration Digest, 11 (): 25.
|
[23] |
J. N. Reddy, An introduction to Nonlinear Finite Element Analysis, Oxford University, 2004.
doi: 10.1093/acprof:oso/9780198525295.001.0001. |
[24] |
D. L. Russel, A comparison of certain dissipation mechanisms via decoupling and projection techniques, Quart. Appl. Math., XLIX (1991), 373-396. |
[25] |
P. Seshaiyer and J. D. Humphrey, A sub-domain inverse finite element characterization of hyperelastic membranes, including soft tissues, ASME J Biomech Engr., 125 (2003), 363-371.
doi: 10.1115/1.1574333. |
[26] |
W. Shyy, Y. Lian, J. Tang, D. Viieru and H. Liu, Aerodynamics of Low Reynolds Number Flyers, Cambridge University Press, 2007.
doi: 10.1017/CBO9780511551154. |
[27] |
G. Singh, G. V. Rao and N. G. R. Iyengar, Reinvestigation of large amplitude free vibrations of beams using finite elements, Journal of Sound and Vibration, 143 (1990), 351-355. |
[28] |
H. Wagner and V. Ramamurti, Beam vibrations-A review, The Shock and Vibration Digest, 9 (1977), 17-24. |
[29] |
O. C. Zienkiewicz and R. L. Taylor, "The Finite Element Method," McGraw-Hill, 1993, |
show all references
References:
[1] |
A. A. Alqaisia and M. N. Hamdan, Bifurcation and chaos of an immersed cantilever beam in a fluid and carrying an intermediate mass, Journal of Sound and Vibration, 253 (2002), 859-888.
doi: 10.1006/jsvi.2001.4072. |
[2] |
A. Andrianov and A. Hermans, A VELFP on infinite, finite and shallow water, 17-th International workshop on water waves and floating bodies, Cambridge, UK, aPEIL (2002), 14-17. |
[3] |
E. Aulisa, A. Ibragimov, Y. Kaya and P. Seshaiyer, A stability estimate for fluid structure interaction problem with non-linear beam,, Accepted in the, ().
|
[4] |
E. Aulisa, A. Cervone, S. Manservisi and P. Seshaiyer, A multilevel domain decomposition approach for studying coupled flow application, Communications in Computational Physics, 6 (2009), 319-341.
doi: 10.4208/cicp.2009.v6.p319. |
[5] |
E. Aulisa, S. Manservisi, and P. Seshaiyer, A computational domain decomposition approach for solving coupled flow-structure-thermal interaction problems, Seventh Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 17 (2009), pp. 13-31. |
[6] |
E. Aulisa, S. Manservisi and P. Seshaiyer, A multilevel domain decomposition methodology for solving coupled problems in fluid-structure-thermal interaction, Proceedings of ECCM 2006, Lisbon, Portugal (2006). |
[7] |
R. W. Dickey, Dynamic stability of equilibrium states of the extendible beam, Proceedings of the American Mathematical Society, 41 (1973), 94-102.
doi: 10.1090/S0002-9939-1973-0328290-8. |
[8] | |
[9] |
D. A. Evensen, Nonlinear vibrations of beams with various boundary conditions, AIAA Journal, 6 (1968), 370-372.
doi: 10.2514/3.4506. |
[10] |
L. Ferguson, E. Aulisa, P. Seshaiyer, Computational modeling of highly flexible membrane wings in micro air vehicles, Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference Newport, RI (2006). |
[11] |
D. G. Gorman, I. Trendafilova, A. J. Mulholland and J. Horacek, Analytical modeling and extraction of the modal behavior of a cantilever beam in fluid interaction, Journal of Sound and Vibration, (2007), 231-245.
doi: 10.1016/j.jsv.2007.07.032. |
[12] |
A. E. Green and J. E. Adkins, "Large Elastic Deformations," Clarendon Press (Oxford), 1970. |
[13] |
H. W. Haslach, J. D. Humphrey, Dynamics of biological soft tissue or rubber: Internally pressurized spherical membranes surrounded by a fluid, Int J Nonlin Mech, 39 (2004), 399-420. |
[14] |
J. D. Humphrey, "Cardiovascular Solid Mechanics," Springer, 2002. |
[15] |
A. I. Ibragimov and P. Koola, The dynamics of wave carpet, P. 2288, OCEAN 2003 MTS/IEEE, proceedings. |
[16] |
R. A. Ibrahim, Nonlinear vibrations of suspended cables, Part III: Random excitation and interaction with fluid flow, Applied Mechanics Reviews, 57 (2004), 515-549.
doi: 10.1115/1.1804541. |
[17] |
J. E. Lagnese, Modelling and stabilization of nonlinear plates, International Series of Numerical Mathematics, 100 (1991), 247-264. |
[18] |
C. L. Lou and D. L. Sikarskie, Nonlinear Vibration of beams using a form-function approximation, ASME Journal of Applied Mechanics, 42 (1975), 209-214.
doi: 10.1115/1.3423520. |
[19] |
C. Mei, Finite element displacement method for large amplitude free flexural vibrations of beams and plates, Computers and Structures, 3 (1973), 163-174. |
[20] |
J. Padovan, Nonlinear vibrations of general structures, Journal of Sound and Vibration, 72 (1980), 427-441. |
[21] |
J. Peradze, A numerical alghorithm for Kirchhoff-Type nonlinear static beam, Journal of Applied Mathematics, in Press (2009).
doi: 10.1155/2009/818269. |
[22] |
J. N. Reddy, Finite element modeling of structural vibrations: A review of recent advances,, The Shock Vibration Digest, 11 (): 25.
|
[23] |
J. N. Reddy, An introduction to Nonlinear Finite Element Analysis, Oxford University, 2004.
doi: 10.1093/acprof:oso/9780198525295.001.0001. |
[24] |
D. L. Russel, A comparison of certain dissipation mechanisms via decoupling and projection techniques, Quart. Appl. Math., XLIX (1991), 373-396. |
[25] |
P. Seshaiyer and J. D. Humphrey, A sub-domain inverse finite element characterization of hyperelastic membranes, including soft tissues, ASME J Biomech Engr., 125 (2003), 363-371.
doi: 10.1115/1.1574333. |
[26] |
W. Shyy, Y. Lian, J. Tang, D. Viieru and H. Liu, Aerodynamics of Low Reynolds Number Flyers, Cambridge University Press, 2007.
doi: 10.1017/CBO9780511551154. |
[27] |
G. Singh, G. V. Rao and N. G. R. Iyengar, Reinvestigation of large amplitude free vibrations of beams using finite elements, Journal of Sound and Vibration, 143 (1990), 351-355. |
[28] |
H. Wagner and V. Ramamurti, Beam vibrations-A review, The Shock and Vibration Digest, 9 (1977), 17-24. |
[29] |
O. C. Zienkiewicz and R. L. Taylor, "The Finite Element Method," McGraw-Hill, 1993, |
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