Abstract
In order to study dynamics of multibody system (MBS) moving in ambient fluid, we adopt geometric modeling approach of fully coupled MBS-fluid system, incorporating boundary integral method and time integrator in Lie group setting. By assuming inviscid and incompressible fluid, the configuration space of the MBS-fluid system is reduced by eliminating fluid variables via symplectic reduction without compromising any accuracy. Consequently, the equations of motion for the submerged MBS are formulated without explicitly incorporating fluid variables, while effect of the fluid flow to MBS overall dynamics is accounted for by ‘added mass’ effect to the submerged bodies. In such approach, the ‘added masses’ are expressed as boundary integral functions of the fluid density and the flow velocity potential. In order to take into account additional viscous effects and include fluid vorticity and circulation in the system dynamics, vortex shedding and evolution mechanism is incorporated in the overall model by unsteady potential flow method, enforcing Kutta conditions on MBS sharp edges. In summary, presented approach exhibits significant computational advantages in comparison to the standard numerical procedures that - most commonly - comprise finite volume discretization of the whole fluid domain and (loosely coupled) solving fluid and MBS dynamics on different meshes.
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References
Vazquez, J.G.V.: Fluid-Structure Interaction Analysis. VDM Verlag Dr. Müller, Saarbrücken (2008)
Arnold, V.I., Khesin., B.A.: Topological Methods in Hydrodynamics. Springer-Verlag, Berlin, Heidelberg (1998). https://doi.org/10.1007/b97593
Kanso, E., Marsden, J.E., Rowley, C.W., Melli-Huber, J.B.: Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15(4), 255–289 (2005)
Leonard, N.E.: Stability of a bottom-heavy underwater vehicle. Automatica 33(3), 331–346 (1997)
Vankerschaver, J., Kanso, E., Marsden, J.E.: The geometry and dynamics of interacting rigid bodies and point vortices. J. Geom. Mecha. 1 (2009)
García-Naranjo, L.C., Vankerschaver, J.: Nonholonomic ll systems on central extensions and the hydrodynamic chaplygin sleigh with circulation. J. Geom. Phys. 73, 56–69 (2013)
Fedorov, Y.N., García-Naranjo, L.C.: The hydrodynamic chaplygin sleigh. J. Phys. A: Math. Theor. 43(43), 434013 (2010)
Arnold, V.: Sur la géométrie différentielle des groupes de lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits. Annales de l’Institut Fourier 16(1), 319–361 (1966)
Terze, Z., Müller, A., Zlatar, D.: Lie-group integration method for constrained multibody systems in state space. Multibody Sys. Dyn. 34(3), 275–305 (2015)
Shashikanth, B.N., Marsden, J.E., Burdick, J.W., Kelly, S.D.: The hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with n point vortices. Phys. Fluids 14(3), 1214–1227 (2002)
Marsden, J.E., Misiolek, G., Ortega, J.-P., Perlmutter, M., Ratiu, T.: Hamiltonian Reduction by Stages. Springer-Verlag, Berlin, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72470-4
Munthe-Kaas, H.: Runge-Kutta methods on Lie groups. BIT Numer. Math. 38(1), 92–111 (1998)
Sutradhar, A., Paulino, G., Gray, L.J.: Symmetric Galerkin Boundary Element Method. Springer-Verlag, Berlin, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68772-6
Terze, Z., Pandža, V., Kasalo, M., Zlatar, D.: Discrete mechanics and optimal control optimization of flapping wingdynamics for Mars exploration. Aerosp. Sci. Technol. 106, 106131 (2020)
Terze, Z., Pandža, V., Kasalo, M., Zlatar, D.: Optimized flapping wing dynamics via DMOC approach. Nonlinear Dynamics. (accepted)
Yongliang, Y., Binggang, T., Huiyang, M.: An analytic approach to theoretical modeling of highly unsteady viscous flow excited by wing flapping in small insects. Acta Mechanica Sinica 19(6), 508–516 (2003)
Pollard, B., Fedonyuk, V., Tallapragada, P.: Swimming on limit cycles with nonholonomic constraints. Nonlinear Dyn. 97, 2453–2468 (2019)
Katz, J., Plotkin, A.: Low-Speed Aerodynamics, 2nd edn. Cambridge Aerospace Series. Cambridge University Press (2001)
Vankerschaver, J., Kanso, E., Marsden, J.E.: The dynamics of a rigid body in potential flow with circulation. Regul. Chaotic Dyn. 15, 606–629 (2010)
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This work has been fully supported by Croatian Science Foundation under the project IP-2016-06-6696.
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Terze, Z., Pandža, V., Andrić, M., Zlatar, D. (2021). Computational Dynamics of Reduced Coupled Multibody-Fluid System in Lie Group Setting. In: Barbaresco, F., Nielsen, F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning. SPIGL 2020. Springer Proceedings in Mathematics & Statistics, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-030-77957-3_15
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