A comparison of certain elastic dissipation mechanisms via decoupling and projection techniques
David L. Russell · Quarterly of Applied Mathematics · 1991
In this paper we study the Euler-Bernoulli elastic beam model, modified in a variety of ways to achieve an asymptotically linear relationship between damping rate and frequency. We review the so-called spatial hysteresis model and then introduce the thermoelastic/shear diffusion model, which is obtained by coupling the originally conservative elastic equations to two different diffusion processes. We then use a decoupling/triangulation process to project the coupled system onto the subspace corresponding to the lateral displacements and velocities and show that the projected system agrees in many significant respects with the spatial hysteresis model. The procedure also indicates some possibly desirable modifications in the elastic term of the spatial hysteresis model.