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<p>We investigate laminated Timoshenko beams with structural damping subject to a nonlinear frictional damping on the effective rotation angle with a variable exponent <i>m</i>(<i>x</i>) and a time-dependent coefficient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha (t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Using the multipliers method, we obtain energy decay rates, depending on both <i>m</i> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>, without imposing restrictions on the physical parameters of the system. Also, we establish stability results for the system in the absence of the structural damping provided that the wave speeds are equal.</p>

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Weakly Damped Laminated Beams with a Variable-Exponent Nonlinearity

  • 期刊论文

  • 发表日期：

    2026年2月12日

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  • Muhammad I. Mustafa

摘要

We investigate laminated Timoshenko beams with structural damping subject to a nonlinear frictional damping on the effective rotation angle with a variable exponent m(x) and a time-dependent coefficient \(\alpha (t)\) α ( t ) . Using the multipliers method, we obtain energy decay rates, depending on both m and \(\alpha \) α , without imposing restrictions on the physical parameters of the system. Also, we establish stability results for the system in the absence of the structural damping provided that the wave speeds are equal.