Energy decay of damped Timoshenko–type beams on two-parameter elastic foundations

Abstract

This work is devoted to the analysis of well-posedness and stabilization properties of both the classical and truncated Timoshenko beam models resting on a two-parameter elastic foundation. We rigorously investigate the effects of the elastic subgrade on the dynamic behavior of the systems and consider the influence of viscous damping mechanisms acting on the angular rotation. For each model, we establish the existence, uniqueness, and continuous dependence of solutions. Moreover, we analyze the long-time behavior of the solutions, proving exponential or polynomial energy decay depending on the parameters of the wave speeds. The results highlight the differences in stability between the classical and truncated models and contribute to the mathematical theory of damped elastic structures interacting with elastic media.

Keywords

Timoshenko beam / two-parameter elastic foundation / energy decay / exponential stability / polynomial stability / viscous damping / well-posedness / stabilization

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