Unilateral dynamic contact of two beams.

*(English)*Zbl 0991.74046Summary: We investigate the dynamic unilateral contact between two beams. The contact is modeled with Signorini or normal compliance conditions. The model is given in the form of a variational inequality, for which we establish an existence theorem. A numerical algorithm for the problem is obtained by using the method of lines in which the problem is approximated by a system of ordinary differential equations. Simulation results are given when one of the beams is driven periodically. We also investigate numerically the characteristics of vibration transmission across the joint between the beams.

##### MSC:

74M15 | Contact in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74H20 | Existence of solutions of dynamical problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |

##### Keywords:

two viscoelastic beams; weak solutions; Signorini condition; normal compliance condition; dynamic unilateral contact; variational inequality; existence theorem; method of lines; vibration transmission##### Software:

VODE
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\textit{K. L. Kuttler} et al., Math. Comput. Modelling 34, No. 3--4, 365--384 (2001; Zbl 0991.74046)

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##### References:

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