Boundary stabilization of an Euler-Bernoulli beam with viscoelastic damping

Boundary feedback schemes for stabilizing flexural vibrations in a linear viscoelastic beam are studied. It is shown that in the Euler-Bernoulli model an arbitrarily small feedback delay can cause unbounded vibrations with arbitrarily large exponential growth rates. For the Timoshenko beam, in the purely elastic case, a contrasting result is given, and formulas for decay rates of high frequency modes are developed for the case of no feedback delay. Numerical results for various no-delay cases are summarized.