In this paper we consider damping mechanisms in the context of dynamic beam models. We summarize previous efforts on various damping models (strain rate or Kelvin-Voigt, time hysteresis (Boltzmann), spatial hysteresis, bending rate/square root) for the Euler-Bernoulli beam theory. The Euler-Bernoulli theory is known to be inadequate for experiments in which high frequency modes have been excited. In such cases the Timoshenko theory may be more appropriate; we consider a number of damping hypotheses for this theory. Corresponding models are proposed and compared to experimental data in the context of parameter estimation or identification problems formulated in the frequency domain. Theoretical results related to the convergence of approximations to these infinite dimensional distributed parameter system estimation problems are presented. Associated computational findings for specific beam experiments are discussed.

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