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On the Discretization of an Elastic Rod with Distributed Sliding Friction

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Abstract:

A one-dimensional elastic system with distributed contact under fixed boundary conditions is investigated in order to study dynamic behavior under sliding friction. A partial differential equation of motion is established and its exact solution is presented. Due to the friction the eigenvalue problem is non-self-adjoint. Mathematical methods for handling the non-self-adjoint system, such as the non-self-adjoint eigenvalue problem and the eigenvalue problem with a proper inner product, are reviewed and applied. The exact solution showed that the undamped elastic system under fixed boundary conditions is neutrally stable when the coefficient of friction is a constant. The assumed mode approximation and the lumped-parameter discretization method are evaluated and their solutions are compared with the exact solution. As a cautionary example the assumed modes approximation leads to false conclusions about stability. The lumped-parameter discretization algorithm generates reliable results.

Document Type: Research Article

DOI: http://dx.doi.org/10.0000/014186399255818

Affiliations: Digital Appliance Research Laboratory, 327-23 Gasan-dong, Kumchon-gu Seoul, 153-023, South Korea

Publication date: May 1, 2002

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