Abstract
In the present work, we study biaxial vibrations of elasto-plastic beamswith a prescribed rigid-body motion. Exemplarily, we treat the case of ahinged-hinged beam with a rotation about a fixed hinge. Such a problemis frequently to be encountered in machine dynamics. The deformations ofthe beam are assumed to remain small. In order to describe the beamvibrations, we utilize the Bernoulli–Euler beam theory. Axial vibrationsof the beam are neglected. We study cases, in which the flexuralstiffness of the beam is considerably lowered due to catastrophicenvironmental influences, such that the deformations relative to therigid-body motion, albeit small, reach the plastic regime. In thepresent paper, special emphasis is laid upon including the effect ofgeometric stiffening due to a comparatively fast rigid-body rotation.The equations of motion are derived by Hamilton's principle. The biaxialdeflections are discretized in space by means of Legendre polynomials.The plastic strains are discretized over length, height and width of thebeam by small plastic cells. Galerkin's procedure, together with aproper implicit midpoint rule is used for integration of the equationsof motion. The plastic strains are computed in every time-step by asuitable iterative procedure. Linear elastic/perfectly plastic behavioris exemplarily treated in a numerical study.
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References
Gerstmayr, J., ‘Modeling and simulation of elastoplastic multibody systems with damage’, Mechanics Based Design of Structures and Machines 31(2), 2003, 201–227.
Gerstmayr, J., Holl, H., and Irschik, H., ‘Development of plasticity and damage in vibrating structural elements performing guided rigid-body motion’, Archive of Applied Mechanics 71, 2001, 135–145.
Gerstmayr, J. and Irschik, H., ‘Vibrations of the elasto-plastic pendulum’, International Journal of Non-Linear Mechanics 38, 2003, 111–122.
Irschik, H., ‘Biaxial dynamic bending of elastoplastic beam’, Acta Mechanica 62, 1986, 155–167.
Rubin, H. and Schneider, K. J., Baustatik. Theorie I. und II. Ordnung, 3rd edition, Werner-Verlag, 1999.
Dibold, M., Gerstmayr, J., and Irschik, H., ‘Biaxial vibrations of an elasto-plastic beam with a prescribed rigid-body rotation’, in Proceedings of DETC'03, ASME 2003 Design Engineering Technical Conference, Chicago, IL, ASME, New York, 2003, Paper No. VIB-48324.
Schiehlen, W., Technische Dynamik, BG Teubner, Stuttgart, 1986.
Shabana, A. A., Dynamics of Multibody Systems, 2nd edition, Cambridge University Press, Cambridge, UK, 1988.
Schwertassek, R., Wallrapp, O., and Shabana, A. A., ‘Flexible multibody simulation and choice of shape functions’, Nonlinear Dynamics 20, 1999, 361–380.
Parkus, H., Mechanik der festen Körper, 2nd edition, Springer, New York, 1995.
Hairer, E. and Wanner, G., Solving Ordinary Differential Equations, II, Springer, Berlin, 1991.
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Dibold, M., Gerstmayr, J. & Irschik, H. Biaxial Vibrations of an Elasto-Plastic Beam with a Prescribed Rigid-Body Rotation Including the Effect of Stiffening. Nonlinear Dynamics 34, 147–157 (2003). https://doi.org/10.1023/B:NODY.0000014557.32797.c1
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DOI: https://doi.org/10.1023/B:NODY.0000014557.32797.c1