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ON THE DISCRETIZATION OF AN ELASTIC ROD WITH DISTRIBUTED SLIDING FRICTION

✍ Scribed by C.M. JUNG; B.F. FEENY

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
327 KB
Volume
252
Category
Article
ISSN
0022-460X

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✦ Synopsis

A one-dimensional elastic system with distributed contact under "xed boundary conditions is investigated in order to study dynamic behavior under sliding friction. A partial di!erential 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 "xed boundary conditions is neutrally stable when the coe$cient 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.

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