Designed short-time observations for rotational damping recovery in Timoshenko beams
Abstract
We study the recovery of spatial rotational damping in a clamped Timoshenko beam. The coefficient belongs to a prescribed bounded finite-dimensional family. One fixed spatial average of rotation is recorded in separately labelled experiments with known initial rotational velocities. We construct these velocities so that the leading coefficient-to-data map is an invertible Gram matrix. Testing the equations against the smooth observation kernel gives a uniform parameter-Lipschitz remainder without differentiating the damping coefficient. A weighted temporal moment then yields global injectivity, Lipschitz stability and a globally convergent projected fixed-point reconstruction for sufficiently short observation times. Upper and deterministic two-point lower bounds give the same noise-amplification order T−5/2 for L2 time-history errors. A second sensitivity estimate supplies a separate sufficient condition for strong convexity and global projected-gradient convergence. We derive continuous and exact discrete adjoints, prove finite-time convergence of a conforming finite-element midpoint scheme, and propagate forward error into coefficient error. Reproducible synthetic experiments examine symmetry, gradient accuracy, noise and discretization bias.
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BibTeX
@misc{elhindi2026designed,
title = {{Designed short-time observations for rotational damping recovery in Timoshenko beams}},
author = {Mohammad El-Hindi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34786},
eprint = {2610.34786},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34786},
}
RIS
TY - UNPB
TI - Designed short-time observations for rotational damping recovery in Timoshenko beams
AU - Mohammad El-Hindi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34786
UR - https://arxiv.org/abs/2610.34786
AB - We study the recovery of spatial rotational damping in a clamped Timoshenko beam. The coefficient belongs to a prescribed bounded finite-dimensional family. One fixed spatial average of rotation is recorded in separately labelled experiments with known initial rotational velocities. We construct these velocities so that the leading coefficient-to-data map is an invertible Gram matrix. Testing the equations against the smooth observation kernel gives a uniform parameter-Lipschitz remainder without differentiating the damping coefficient. A weighted temporal moment then yields global injectivity, Lipschitz stability and a globally convergent projected fixed-point reconstruction for sufficiently short observation times. Upper and deterministic two-point lower bounds give the same noise-amplification order T^−5/2 for L^2 time-history errors. A second sensitivity estimate supplies a separate sufficient condition for strong convexity and global projected-gradient convergence. We derive continuous and exact discrete adjoints, prove finite-time convergence of a conforming finite-element midpoint scheme, and propagate forward error into coefficient error. Reproducible synthetic experiments examine symmetry, gradient accuracy, noise and discretization bias.
ER -