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Dynamics of an Euler beam with unilateral constraints

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Free Boundary Problems and Related Topics

We study the vibrations of an elastic beam between rigid obstacles. The non penetrability condition leads to a description of the dynamics as a hyperbolic fourth order variational inequality. For this free boundary problem we construct a sequence of approximate solutions by combining some classical space discretizations with time-stepping schemes especially suited to unilateral contact problems for discrete mechanical systems. We prove the stability and the convergence of these numerical methods and we obtain an existence result for our original problem under very general assumptions on the geometry of the obstacles.

This talk is part of the Isaac Newton Institute Seminar Series series.

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