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In the Timoshenko beam equation model, the displacement field and the cross-sectional rotation are treated independently. The Timoshenko Beam Theory accounts for inertial rotation and shear effects, aspects not considered in the Euler-Bernoulli theory. We prove that the spatial part of the loading can be uniquely identified, provided the observation of the displacement of the beam over a small part of it is long enough. To our best knowledge it is a new result in the literature. Additionally, we provide numerical results that compare the identification when the beam is modeled by the Timoshenko equation versus the classical Euler-Bernoulli equation.

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Identification of Out-of-plane Loads Over Timoshenko Beams

  • 会议论文

  • 发表日期：

    2025年

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  • Alexandre Kawano

摘要

In the Timoshenko beam equation model, the displacement field and the cross-sectional rotation are treated independently. The Timoshenko Beam Theory accounts for inertial rotation and shear effects, aspects not considered in the Euler-Bernoulli theory. We prove that the spatial part of the loading can be uniquely identified, provided the observation of the displacement of the beam over a small part of it is long enough. To our best knowledge it is a new result in the literature. Additionally, we provide numerical results that compare the identification when the beam is modeled by the Timoshenko equation versus the classical Euler-Bernoulli equation.