Ken L. Kuttler, Serge Kruk, Pawel Marcinek, Meir Shillor
Abstract:
This work models, analyses and simulates a one-dimensional process of
debonding of a structure made of two viscoelastic bonded slabs that is
described by a rod-beam system. It is motivated, primarily, by the
degradation of adhesively bonded plates in automotive applications and
studies the effects of the humidity, horizontal and vertical vibrations
and temperature on the debonding process.
The existence of a weak solution to the model is established by using
approximate problems, existence theorems for differential inclusions,
and a fixed point theorem. An implicit finite differences algorithm for
the problem is developed and used to simulate the system dynamics.
It is found that the qualitative behavior of the system correlates
well with experimental results. Moreover, it indicates that using the
shifts in the spectrum, as described by the FFT of one component of the
solution, may be used to measure nondestructively the integrity of the
bonds and their deterioration.
Submitted October 16, 2017. Published December 6, 2017.
Math Subject Classifications: 74K10, 74F25, 74M99, 35L86, 74H15.
Key Words: Rod-beam system; debonding; single lap joint; differential inclusions;
existence; simulations; spectrum shifts.
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Ken L. Kuttler Brigham Young University Department of Mathematics Provo, UT 84602, USA email: klkuttler@gmail.com |
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Serge Kruk Oakland University Department of Mathematics and Statistics Rochester, MI 48309, USA email: kruk@oakland.edu |
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Pawel Marcinek Oakland University Department of Mathematics and Statistics Rochester, MI 48309, USA email: pbmarcin@oakland.edu |
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Meir Shillor Oakland University Department of Mathematics and Statistics Rochester, MI 48309, USA email: shillor@oakland.edu |
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