<p>In this paper, we investigate the stabilization of Timoshenko beam with localized fractional damping of order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\frac{1}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></EquationSource> </InlineEquation>. Using frequency domain approach combined with the multiplier method, we prove that the energy of our system decays polynomially with different rates.</p>

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Energy decay of a Timoshenko beam with localized fractional damping of order 1/2

  • Haidar Badawi

摘要

In this paper, we investigate the stabilization of Timoshenko beam with localized fractional damping of order \(\frac{1}{2}\) 1 2 . Using frequency domain approach combined with the multiplier method, we prove that the energy of our system decays polynomially with different rates.