Abstract
In this work one discusses a uniform observability of a semi-discrete Timoshenko beam model. We established an observability inequality to a particular class of solutions given by Fourier’s development and we prove that there exists a lack of numerical observability to the spectral problem in the setting of the spatial finite difference, i.e., the observability constant blows-up as the mesh-size h tends to zero. The semi-discrete system in finite difference avoids a numerical anomaly known as locking phenomenon on shear force and, in addition, such system raises an important problem in theoretical numerical analysis consisting in the determination of the Fourier’s solution that takes into account the parity of a sequence of the vibration modes.
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Funding
A. J. A. Ramos thanks the CNPq for financial support through the projects “Asymptotic stabilization and numerical treatment for carbon nanotubes” (CNPq Grant 310729/2019-0)
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Júnior, D.S.A., Ramos, A.J.A. & Filho, E.L.M.B. An inverse inequality for Timoshenko system and some properties related to the finite-difference space semidiscretization. Rend. Circ. Mat. Palermo, II. Ser 71, 381–395 (2022). https://doi.org/10.1007/s12215-021-00598-7
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DOI: https://doi.org/10.1007/s12215-021-00598-7