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Nonlinear vibrations of beams and plates with fractional derivative elements subject to combined harmonic and random excitations
Probabilistic Engineering Mechanics ( IF 2.6 ) Pub Date : 2020-01-01 , DOI: 10.1016/j.probengmech.2020.103043
Pol D. Spanos , Giovanni Malara

Abstract This paper proposes an efficient approach for estimating reliably the second order statistics of the response of continua excited by combinations of harmonic and random loads. The problem is relevant in several engineering applications, where, for instance, the harmonic load is influenced by significant noise that cannot be neglected when computing the response statistics. The considered problems pertain to the vibration of beams and of plates endowed with fractional derivative elements. In both cases, it is shown that by representing the system response by the linear modes of vibration, systems of nonlinear fractional ordinary differential equations describing the time-dependent variation of the modes amplitudes are obtained. These equations are coupled and are treated by combining the harmonic balance and statistical linearization techniques, leading to the determination of the second-order statistics of the response. Relevant Monte Carlo data demonstrate the reliability of the proposed solution approach. The specific numerical examples considered pertain to simply supported beams, and plates with simply supported stress-free edges conditions.

中文翻译:

具有分数阶导数单元的梁和板在谐波和随机激励下的非线性振动

摘要 本文提出了一种有效的方法来可靠地估计由谐波和随机载荷组合激发的连续体响应的二阶统计量。该问题与多个工程应用相关,例如,在计算响应统计数据时,谐波负载受到显着噪声的影响,这些噪声不能被忽略。所考虑的问题与梁和具有分数阶导数单元的板的振动有关。在这两种情况下,都表明通过用线性振动模式表示系统响应,可以获得描述模式振幅随时间变化的非线性分数阶常微分方程组。这些方程是耦合的,并通过结合谐波平衡和统计线性化技术进行处理,从而确定响应的二阶统计量。相关的蒙特卡罗数据证明了所提出的解决方案方法的可靠性。所考虑的具体数值示例与简支梁和具有简支无应力边缘条件的板有关。
更新日期:2020-01-01
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