STUDY OF AN ELASTIC BEAM, IN CENTRIFUGAL FIELD, USING FINITE ELEMENT METHOD

Maria Luminiţa SCUTARU, Eliza CHIRCAN, Marin MARIN

Abstract


The finite element method (FEM) has been applied mainly to the study of the behavior of different elastic bodies, whether static or dynamic. The case of rigid motion of bodies analyzed with MEF, involving new terms due to the effects of inertia and relative motions, has not yet been incorporated into the classic MEF software. Papers to analyze this behavior arose in the 70's for the plane beam and later for a three-dimensional general motion. The present paper aims to develop models previously studied by other researchers and study the influences that the geometric parameters of the bar can have on the dynamic response. The case study is that of a moving bar in a rotation around a fixed axis. The shape functions used are of degree five.


Key words: Finite Element Method, beam, eigenvalues, eigenmodes, rotation, centrifugal


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References


Deu, J.-F., Galucio, A.C., Ohayon, R., Dynamic responses of flexible-link mechanisms with passive/active damping treatment. Comput. Struct. 86(35), 258–265, 2008.

Erdman, A.G., Sandor, G.N., Oakberg, A., A general method for kineto-elastodynamic analysis and synthesis of mechanisms. J. Eng. Ind. ASME Trans. 94(4), 1193–1203, 1972.

Fanghella, P., Galletti, C., Torre, G., An explicit independent-coordinate formulation for equations of motion of flexible multibody systems. Mech. Mach. Theory 38, 417–437, 2003.

De Falco, D., Pennestri, E., Vita, L., An investigation of the influence of pseudoinverse matrix calculations on multibody dynamics by means of the Udwadia–Kalaba formulation. J. Aerosp. Eng. 22(4), 365–372, 2009.

Gerstmayr, J., Schberl, J., A 3D finite element method for flexible multibody systems. Multibody Syst. Dyn. 15(4), 305–320, 2006.

Hou, W., Zhang, X., Dynamic analysis of flexible linkage mechanisms under uniform temperature change. J. Sound Vib. 319(12), 570–592, 2009.

Ibrahimbegovic, A., Mamouri, S., Taylor, R.L., Chen, A.J., Finite element method in dynamics of flexible multibody systems: modeling of holonomic constraints and energy conserving integration schemes. Multibody Syst. Dyn. 4(2–3), 195–223, 2000.

Khang, N.V., Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems. Mech. Res. Commun. 38(4), 294–299, 2011.

Khulief, Y.A., On the finite element dynamic analysis of flexible mechanisms. Comput. Methods Appl. Mech. Eng. 97(1), 23–32, 1992.

Marin, M., Oechsner, A., The effect of a dipolar structure on the Holder stability in Green-Naghdi thermoelasticity, Contin Mech Thermodyn, 29(6) 1365-1374, 2017.

Marin, M., Cesaro means in thermoelasticity of dipolar bodies, Acta Mech, 122(1-4), 155-168, 1997.

Marin, M., Öchsner, A., Complements of Higher Mathematics. Springer, Cham (2018)

Mayo, J., Dominguez, J., Geometrically non-linear formulation of flexible multibody systems in terms of beam elements: geometric stiffness. Comput. Struct. 59(6), 1039–1050, 1996.

Negrean I., New Formulations in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue I, pp. 49-56, 2017.

Negrean I., Mass Distribution in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue II, pp. 175-184, 2017.

Negrean I., Generalized Forces in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue III, pp. 357-368, 2017.

Negrean I., Advanced Notions in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue IV, pp. 491-502, 2017.

Negrean I., Advanced Equations in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue IV, pp. 503-514, 2017.

Negrean I., New Approaches on Notions from Advanced Mechanics, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 61, Issue II, pp. 149-158, 2018.

Neto, M.A., Ambrosio, J.A.C., Leal, R.P., Composite materials in flexible multibody systems. Comput. Methods Appl. Mech. Eng. 195(5051), 6860–6873, 2006.

Öchsner, A., Computational Statics and Dynamics: An Introduction Based on the Finite Element Method. Springer, Singapore, 2016.

Piras, G., Cleghorn, W.L., Mills, J.K., Dynamic finite-element analysis of a planar high speed, high-precision parallel manipulator with flexible links. Mech. Mach. Theory 40(7), 849–862, 2005.

Shi, Y.M., Li, Z.F., Hua, H.X., Fu, Z.F., Liu, T.X., The modelling and vibration control of beams with active constrained layer damping. J. Sound Vib. 245(5), 785–800, 2001.

Simeon, B., On Lagrange multipliers in flexible multibody dynamic. Comput. Methods Appl. Mech. Eng. 195(50–51), 6993–7005, 2006.

Sung, C.K., An experimental study on the nonlinear elastic dynamic response of linkage mechanism. Mech. Mach. Theory 21, 121–133, 1986.

Thompson, B.S., Sung, C.K., A survey of finite element techniques for mechanism design. Mech. Mach. Theory 21(4), 351–359, 1986.

Vlase, S., A Method of eliminating Lagrangian-Multipliers from the Equation of Motion of Interconnected Mechanical Systems. Journal of Applied Mechanics-Transactions of the ASME, Vol. 54, Issue: 1, pp: 235-237, 1987.

Vlase, S., Elimination of Lagrangian multipliers. Mech. Res. Commun. 14(1), 17–22, 1987.

Vlase, S., Teodorescu, P. P., Elasto-Dynamics of a Solid with a General "Rigid" Motion using FEM Model Part I. Theoretical Approach. Romanian Journal of Physics, Vol. 58, 7-8, pp. 872-881,2013.

Vlase, S., Teodorescu, P. P., Itu, C. et al., Elasto-Dynamics of a Solid with a General "Rigid" Motion using FEM Model Part II. Analysis of a Double Cardan Joint. Romanian Journal of Physics, Vol. 58, 7-8, pp. 882-892,2013.

Vlase, S., Marin, M., Öchsner, A. et al. Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system. Continuum Mech. Thermodyn. 31: 715. https:// doi.org/10.1007 /s00161-018-0722-y, 2019.

Vlase, S., Finite element analysis of the planar mechanisms: numerical aspects. Appl. Mech. 4, 90–100, 1992.

Vlase, S., Dynamical response of a multibody system with flexible element with a general three-dimensional motion. Rom. J. Phys. 57(3–4), 676–693, 2012.

Vlase, S., Danasel, C., Scutaru, M.L., Mihalcica, M., Finite element analysis of two-dimensional linear elastic systems with a plane rigid motion. Rom. J. Phys. 59(5–6), 476–487, 2014.


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