The dynamic response of a deformable curved solid body is investigated as it interacts with a flow field. The fluid is assumed to be viscous and the flow is nearly incompressible. Fluid dynamics is predicted through a lattice Boltzmann solver. Corotational beam finite elements undergoing large displacements are adopted to idealize the submerged body, whose presence in the lattice fluid background is handled by the immersed boundary method. The attention focuses on the solid’s deformation and a numerical campaign is carried out. Findings are reported in terms of deformation energy and deformed configuration. On the one hand, it is shown that the solution of the problem is strictly dependent on the elastic properties of the body. On the other hand, the encompassing flow physics plays a crucial role on the resultant solid dynamics. With respect to the existing literature, the present problem is attacked by a new point of view. Specifically, the author proposes that the problem is governed by four dimensionless parameters: the Reynolds number, the normalized elastic modulus, the density and aspect ratii. The formulation and the solution strategy for curved solid bodies herein adopted are introduced for the first time in this paper.
@article{bwmeta1.element.doi-10_1515_cls-2015-0018, author = {Alessandro De Rosis}, title = {Non-linear flow-induced vibrations in deformable curved bodies: A lattice Boltzmann-immersed boundary-finite element study}, journal = {Curved and Layered Structures}, volume = {2}, year = {2015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_cls-2015-0018} }
Alessandro De Rosis. Non-linear flow-induced vibrations in deformable curved bodies: A lattice Boltzmann-immersed boundary-finite element study. Curved and Layered Structures, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_cls-2015-0018/
[1] Qin Z., Batra R.C. Local slamming impact of sandwich composite hulls. Int. J. Solids Struct., 2009, 46, 2011-2035. [Crossref] | Zbl 1215.74018
[2] Panciroli R., Abrate S., Minak G., Zucchelli A. Hydroelasticity in water-entry problems: Comparison between experimental and SPH results. Compos. Struct., 2012, 94, 532-539. [Crossref]
[3] Panciroli R., Abrate S., Minak G. Dynamic response of flexible wedges entering the water. Compos. Struct., 2013, 99, 163-171.
[4] Shrivastava S., Mohite P.M. Redesigning of a canard control surface of an advanced fighter aircraft: Effect on buckling and aerodynamic behavior. Curved and Layer. Struct., 2015, 2, 183-193.
[5] Ke L., Yang J., Kitipornchai S. An analytical study on the nonlinear vibration of functionally graded beams. Meccanica, 2010, 45, 743-752. [Crossref] | Zbl 1258.74104
[6] Tornabene F., Fantuzzi N., Bacciocchi M. Free vibrations of freeform doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories. Compos. Part B, 2014, 67, 490-509.
[7] Amabili M. Nonlinear vibrations of laminated circular cylindrical shells: comparison of different shell theories. Compos. Struct., 2011, 94, 207-220. [Crossref]
[8] Viola E., Tornabene F., Fantuzzi N. General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels. Compos. Struct., 2013, 95, 639-666. [Crossref]
[9] Natarajan S., Ferreira A.J.M., Nguyen-Xuan H. Analysis of crossply laminated plates using isogeometric analysis and unified formulation. Curved and Layer. Struct., 2015, 1, 1-10.
[10] Sahoo S. Free vibration behavior of laminated composite stiffened elliptic parabolic shell panel with cutout. Curved and Layer. Struct., 2015, 2, 162-182.
[11] Liu B., Xing Y.F., Qatu M.S., Ferreira A.J.M. Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells. Compos. Struct., 2012, 94, 484-493.
[12] Pellicano F., Amabili M., Paidoussis M.P. Effect of the geometry on the non-linear vibration of circular cylindrical shells. Int. J. Nonlin. Mech., 2002, 37, 1181-1198. [Crossref] | Zbl 05138098
[13] Gonçalves P.B., Del Prado Z.G. Effect of non-linear modal interaction on the dynamic instability of axially excited cylindrical shells. Comput. Struct., 2004, 82, 2621-2634.
[14] Ferreira A.J.M., Carrera E., Cinefra M., Viola E., Tornabene F., Fantuzzi N., Zenkour A.M. Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a unified formulation. Compos. Part B, 2014, 58, 544-552.
[15] Kubenko V.D., Kovalchuk P.S., Kruk L.A.. Nonlinear vibrations of cylindrical shells filledwith a fluid and subjected to longitudinal and transverse periodic excitation. Int. Appl. Mech., 2010, 46, 186-194. [Crossref] | Zbl 1272.74279
[16] Firouz-Abadi R.D., Noorian M.A., Haddadpour H. A fluidstructure interaction model for stability analysis of shells conveying fluid. J. Fluid Struct., 2010, 26, 747-763. [Crossref]
[17] Amabili M., Pellicano F., Paidoussis M.P. Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part I: stability. J. Sound Vib., 1999, 225, 655-699.
[18] Amabili M., Pellicano F., Paidoussis M.P. Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part II: large-amplitude vibrations without flow. J. Sound Vib., 1999, 228, 1103-1124.
[19] Amabili M., Pellicano F., Paidoussis M.P. Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part III: truncation effect without flow and experiments. J. Sound Vib., 2000, 237, 617-640.
[20] Amabili M., Pellicano F., Paidoussis M.P. Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part IV: large-amplitude vibrationswith flow. J. Sound Vib., 2000, 237, 641-666.
[21] Karagiozis K.N., Amabili M., Paidoussis M.P., Misra K. Nonlinear vibrations of fluid-filled clamped circular cylindrical shells. J. Fluid Struct., 2005, 21, 579-595. [Crossref]
[22] Karagiozis K.N., Amabili M., Paidoussis M.P., Misra K. Effect of geometry on the stability of cylindrical clamped shells subjected to internal fluid flow. Comput. Struct., 2007, 85, 645-659.
[23] Del Prado Z.J.G.N. , Gonçalves P.B., Paidoussis M.P. Non-linear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow. J. Sound Vib., 2009, 327, 211-230.
[24] Amabili M., Karagiozis K.N., Paidoussis M.P. Effect of geometric imperfections on non-linear stability of circular cylindrical shells conveying fluid. Int. J. Nonlin. Mech., 2009, 44, 276-289. [Crossref]
[25] Iakovlev S., Seaton C.T., Sigrist J.F. Submerged circular cylindrical shell subjected to two consecutive shockwaves: Resonancelike phenomena. J. Fluid Struct., 2013, 42, 70-87.
[26] Iakovlev S., Mitchell M., Lefieux A., Murray R.. Shock response of a two-fluid cylindrical shell system containing a rigid core. Comput. Fluids, 2014, 96, 215-225. [Crossref]
[27] Bochkarev S.A., Lekomtsev S.V., Matveenko V.P.. Natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid. Thin Wall. Struct., 2015, 90, 12-22.
[28] Fu Y, Price W.G.. Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid. J. Sound Vib., 1987, 118, 495-513.
[29] Kovalchuk P.S., Podchasov N.P. Stability of elastic cylindrical shells interacting with flowing fluid. Int. Appl. Mech., 2010, 46, 60-68. [Crossref] | Zbl 1272.74313
[30] Breslavsky I.D., Strelnikova E.A., Avramov K.V. Dynamics of shallow shells with geometrical nonlinearity interacting with fluid. Comput. Struct., 2011, 89, 496-506.
[31] Kubenko V.D., Kovalchuk P.S., Podchasov N.P. Analysis of nonstationary processes in cylindrical shells interacting with a fluid flow. Int. Appl. Mech., 2011, 46, 1119-1131. | Zbl 1272.74429
[32] Kovalchuk P.S., Podchasov N.P. Influence of initial deflections on the stability of composite cylindrical shells interacting with a fluid flow. Int. Appl. Mech., 2011, 46, 902-911. [Crossref]
[33] Kovalchuk P.S., Kruk L.A., Pelykh V.A. Stability of differently fixed composite cylindrical shells interactingwith fluid flow. Int. Appl. Mech., 2014, 50, 664-676. [Crossref] | Zbl 1314.74049
[34] Avramov K.V., Strelnikova E. A., Pierre C. Resonant manymode periodic and chaotic self-sustained aeroelastic vibrations of cantilever plates with geometrical non-linearities in incompressible flow. Nonlinear Dynam., 2012, 70, 1335-1354.
[35] Avramov K.V., Strelnikova E. A. Chaotic oscillations of plates interacting on both sides with a fluid flow. Int. Appl. Mech., 2014, 50, 303-309. [Crossref] | Zbl 1314.74019
[36] Higuera F.J. , Succi S., Benzi R.. Lattice gas dynamics with enhanced collisions. Europhys. Lett., 1989, 9, 345-349. [Crossref]
[37] Benzi R., Succi S., Vergassola M. The lattice Boltzmann equation: theory and applications. Phys. Rep., 1992, 222, 145-197.
[38] Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Clarendon, 2001.
[39] Chen H., Chen S.,MatthaeusW.H. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. Lett., 1992, 5, R5339-R5342.
[40] Fadlun E.A., Verzicco R., Orlandi P., Mohd-Yusof J. Combined immersed-boundary finite-difference methods for threedimensional complex flow simulations. J. Comput. Phys., 2000, 161, 35-60. | Zbl 0972.76073
[41] Peskin C.S. The immersed boundary method. Acta Num., 2002, 11, 479-517.
[42] Wu J. and Shu C. Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications. J. Comput. Phys., 2009, 228, 1963-1979. | Zbl 1243.76081
[43] Sotiropoulos F., Yang X.. Immersed boundary methods for simulating fluid-structure interaction. Progr. Aerosp. Sci., 2014, 65, 1-21.
[44] Filippova O., Hanel D. Lattice Boltzmann simulation of gasparticle flow in filters. Comput. Fluids, 1997, 26, 697-712. [Crossref] | Zbl 0902.76077
[45] De Rosis A. Harmonic oscillations of laminae in non-Newtonian fluids: A lattice Boltzmann-immersed boundary approach Adv. Wat. Resour., 2014, 73, 97-107.
[46] Felippa C.A., Haugen B. A unified formulation of small-strain corotational finite elements: I. Theory. Comput. Method. Appl. M., 2005, 194, 2285-2335. | Zbl 1093.74055
[47] Garcea G., Madeo A., Zagari G., Casciaro R. Asymptotic postbuckling fem analysis using corotational formulation. Int. J. Solids Struct., 2009, 46, 377-397. [Crossref] | Zbl 1168.74350
[48] De Rosis A. A lattice Boltzmann model for multiphase flows interacting with deformable bodies. Adv. Wat. Resour., 2014, 73, 55-64.
[49] De Rosis A. On the dynamics of a tandem of asynchronous flapping wings: Lattice Boltzmann-immersed boundary simulations. Physica A, 2014, 410, 276-286.
[50] De Rosis A. Fluid forces enhance the performance of an aspirant leader in self-organized living groups. PloS ONE, 2014, 9, e114687.
[51] De Rosis A. Ground-induced lift enhancement in a tandem of symmetric flapping wings: Lattice Boltzmann-immersed boundary simulations Comput. Struct., 2015, 153, 230-238.
[52] De Rosis A., Falcucci G., Ubertini S., Ubertini F. A coupled lattice Boltzmann-finite element approach for two-dimensional fluidstructure interaction. Comput. Fluids, 2013, 86, 558-568. [Crossref] | Zbl 1290.76120
[53] Geuzaine C., Remacle J.F. Gmsh: A 3-d finite element mesh generator with built-in pre-and post-processing facilities. Int J. Numer. Meth. Eng., 2009, 79, 1309-1331. | Zbl 1176.74181
[54] FLUENT User Guide. Fluent inc. Lebanon NH, 2005, 3766.