What question did this study set out to answer?

The aim is to investigate the long-term behavior of shear beams subjected to rotational damping and determine optimal energy decay rates.

April 1, 2026Open Access

On the optimal polynomial decay of shear beams under rotational damping

Key Points

The aim is to investigate the long-term behavior of shear beams subjected to rotational damping and determine optimal energy decay rates.
Analyzed the shear beam model without rotational inertia.
Focused on the energy decay of the rotations of cross-sections.
Utilized resolvent estimates on the imaginary axis for analysis.
Proved that energy decays at a sharp polynomial rate.
Established the optimality of the decay rate through mathematical arguments.
Contributed to the stabilization theory of partially damped beam models.

Abstract

Abstract In this paper, we study the long-time behavior of solutions to the Shear beam model without rotational inertia, where a dissipative mechanism acts only on the equation governing the rotations of the cross-sections. Owing to the elliptic-hyperbolic structure of the system, we prove that the energy decays at a sharp polynomial rate. The optimality is established through resolvent estimates on the imaginary axis based on important arguments of 7. This result contributes to the stabilization theory of partially damped beam models and settles an important open question concerning the asymptotic behavior in this class of systems.

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