Impact of an elastic rod on a deformable barrier: analytical and numerical investigations on models of a valve and a rod-shaped stamping tool |
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Authors: | Cornelia Schwarz Franz D Fischer Ewald Werner Hans J Dirschmid |
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Institution: | 1. Institute of Materials Science and Mechanics of Materials, Technische Universit?t München, Boltzmannstr. 15, 84747, Garching, Germany 2. Institute of Mechanics, Montanuniversit?t Leoben, Franz-Josef-Strasse 18, 8700, Leoben, Austria 3. Institute of Analysis and Scientific Computing, Technische Universit?t Wien, Wiedner Hauptstr. 8, 1040, Vienna, Austria
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Abstract: | The longitudinal motion of an elastic rod is studied for the case that the rod is suddenly elastically fixed at one end and
is hit by a mass at its other end. This configuration represents real settings e.g. as a valve impacts an elastic valve-seat
or as a stamping device used in forging is hit by a large mass. The solution of the problem is formulated in the Laplace transformation
space. The inverse transformation into the time domain is performed by engaging the so-called Laguerre polynomial technique.
This method allows to calculate exact solutions for finite times from a finite number of series elements. Rigorous mathematical
proofs not established up to now are given with respect to the convergence of the series encountered and the validity of exchanging
the order of inversion of the Laplace transformation and summation of the established series. For comparison also a numerical
solution of the problem is presented. An analysis of the energy transfer between rod, impacting mass and elastic barrier elucidates
the marked influence of the deformability of the elastic barrier on the stress state in the rod. |
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