Abstract
The damping effect of a boundary feedback mechanism on torsional vibrations of a homogeneous viscoelastic rod is examined. A characteristic equation is derived for the oscillatory modes, and the solutions of this equation are studied by analytic and numerical methods, as functions of the feedback gain parameter and of a parameter for feedback delay. Results are compared to recent studies of elastic materials, where a feedback delay can cause exponential instability; here this phenomenon depends significantly on the short-time behavior of the viscoelastic memory kernel. Finally, an existence result is given, showing that the behavior of a weak solution corresponds in the expected way to the location of the characteristic roots.
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