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Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control

机译:受轴向谐波力和时滞控制的粘弹性柱的参数分叉

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We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu-Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge-Kutta method, numerical results are obtained and compared with analytical solutions for verification.
机译:我们研究受轴向谐波激励的简单支撑粘弹性柱的稳态响应。粘弹性材料以分数导数开尔文(Kelvin)方式建模。运动方程式通过Galerkin近似推导并离散化,从而得到具有时间延迟的广义Mathieu-Duffing方程式。可以通过适当的反馈增益和时间延迟来消除参量激励中的分叉。还研究了不同分数阶和材料比的分叉行为。建立了确定稳定性的新标准。基于Runge-Kutta方法,可以获得数值结果,并将其与分析解决方案进行比较以进行验证。

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