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Vibrations of a simply supported beam with a fractional viscoelastic material model -supports movement excitation

机译：具有分数粘弹性材料模型的简支梁的振动-支持运动激励

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摘要

The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann - Liouville fractional derivative of order 0 ＜α ≤ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann - Liouville fractional derivative with lower terminal at -∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.
机译：本文提出了具有分数阶粘弹性材料模型的简单支撑梁的振动分析。考虑了伯努利-欧拉梁模型。支撑架运动激发了光束。应用0 ＜α≤1的Riemann-Liouville分数阶导数。在第一阶段，分析梁的稳态振动，因此假设下端为-∞的Riemann-Liouville分数阶导数。该假设简化了分数阶微分方程的求解，并使我们能够直接获得所检查系统的幅频特性。对于α阶分数导数的各种值和Voigt材料模型参数的值，可以获得特性。研究表明，与使用整数阶导数阻尼模型相比，选择合适的阻尼系数和分数阶阻尼模型可以使我们更加准确地拟合梁的动力特性。

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