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The restitution coefficient for a linear elastic rod. (English) Zbl 1122.74429
Summary: We consider a linear elastic rod that comes to impact with a rigid obstacle under the action of a constant body force. The restitution coefficient is defined as the ratio between the rebound velocity and the approaching velocity at the impact end of the rod. We derive an explicit formula that computes the restitution coefficient in terms of the physical parameters of the problem.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74M20 Impact in solid mechanics
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[1] Johnson, K.L., Contact mechanics, (1987), Cambridge University Press · Zbl 0599.73108
[2] Schatzman, M.; Bercovier, M., Numerical approximation of a wave equation with unilateral constraints, Math. comput., 53, 55-79, (1989) · Zbl 0683.65088
[3] Lebeau, G.; Schatzman, M., A wave problem in a half-space with a unilateral constraint at the boundary, J. diff. eq., 53, 309-361, (1984) · Zbl 0559.35043
[4] C.M. Elliott and T. Qi, A dynamic contact problem in thermoelasticity, Euro. J. Appl. Math., (to appear). · Zbl 0818.73061
[5] Andrews, T.; Shillor, M.; Wright, S., A hyperbolic-parabolic system modelling the thermoelastic impact of two rods, Math. meth. appl. sci., 17, 901-918, (1994) · Zbl 0808.35080
[6] Martins, J.A.C.; Pires, E.B., A class of impact problems in linear elasticity, (), 323-328 · Zbl 0713.73083
[7] Kim, J., A boundary thin obstacle problem for a wave equation, Commun. partial diff. eq., 14, 1011-1026, (1989) · Zbl 0704.35101
[8] Chang, K.C., The obstacle problem and partial differential equations with discontinuous nonlinearities, Commun. pure. appl. math., 33, 117-146, (1980) · Zbl 0405.35074
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