Abstract:
The dynamic behavior of rod systems under the action of external force factors described by multivalued (subdifferential) relations is studied. The mathematical formulation of the problem is given in the form of a dynamic quasivariational inequality. With the use of the Newmark difference scheme, successive approximations, and finite-element discretization, the problem is reduced to minimization of a convex nonsmooth finite-dimensional functional with respect to velocities at each time step. Introduction of auxiliary variables by the method of a modified Lagrangian reduces the problem of minimization of this functional to a sequence of smooth problems of nonlinear programming. The algorithm is verified using the numerical solution for a problem with one degree of freedom. The algorithm proposed is used to calculate the rods of deep-well pumps.
Keywords:
dynamic problems, rod systems, finite-element discretization.
Citation:
I. N. Vasserman, I. N. Shardakov, “Formulation and solution of dynamic problems of elastic rod systems subjected to boundary conditions described by multivalued relations”, Prikl. Mekh. Tekh. Fiz., 44:3 (2003), 124–135; J. Appl. Mech. Tech. Phys., 44:3 (2003), 406–414
\Bibitem{VasSha03}
\by I.~N.~Vasserman, I.~N.~Shardakov
\paper Formulation and solution of dynamic problems of elastic rod systems subjected to boundary conditions described by multivalued relations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2003
\vol 44
\issue 3
\pages 124--135
\mathnet{http://mi.mathnet.ru/pmtf2505}
\elib{https://elibrary.ru/item.asp?id=17274797}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2003
\vol 44
\issue 3
\pages 406--414
\crossref{https://doi.org/10.1023/A:1023493425848}
Linking options:
https://www.mathnet.ru/eng/pmtf2505
https://www.mathnet.ru/eng/pmtf/v44/i3/p124
This publication is cited in the following 5 articles:
Zengshi Chen, Luther W. White, Huimin Zhang, “Predicting Behavior of Sucker-Rod Pumping Systems With Optimal Control”, Journal of Dynamic Systems, Measurement, and Control, 140:5 (2018)
Li-ming Lao, Hua Zhou, “Application and effect of buoyancy on sucker rod string dynamics”, Journal of Petroleum Science and Engineering, 146 (2016), 264
Gang Sheng Chen, Xiandong Liu, Friction Dynamics, 2016, 211
Handbook of Friction-Vibration Interactions, 2014, 153
I.N. Shardakov, I.N. Wasserman, “Numerical modelling of longitudinal vibrations of a sucker rod string”, Journal of Sound and Vibration, 329:3 (2010), 317
Citation in format AMSBIB
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