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首页> 外文期刊>Mechanical systems and signal processing >Approximate critical curves in exponentially damped nonviscous systems
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Approximate critical curves in exponentially damped nonviscous systems

机译：指数阻尼非粘性系统的近似临界曲线

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摘要

In this paper a new approximate numerical method to obtain critical curves in exponentially damped nonviscous systems is proposed. The assumed viscoelastic forces depend on the past history of the velocity response via convolution integrals over exponential kernel functions. Critical surfaces are manifolds in the multidimensional domain defined by the damping parameters, depicting thresholds between the induced oscillatory and non-oscillatory motion. If these surfaces are formed by two parameters, then they are named critical curves. The available method in the literature to construct these curves involves the analytical manipulation of the transcendental matrix determinant, something that can become highly inefficient for large systems. In this paper, it is proved that approximate critical curves can be constructed eliminating the Laplace parameter from two eigenvalue problems: the original one controlled by the dynamical stiffness matrix and another one defined by its derivative respect to the Laplace parameter. The theoretical background of the approach is derived with help of the implicit function theorem. It turns out that the so-found approximate overdamped regions are enclosed by a set of critical curves, which can be derived in parametric form. The proposed method is validated through two numerical examples involving multiple degrees of freedom. (C) 2018 Elsevier Ltd. All rights reserved.
机译：本文提出了一种新的近似数值方法来获得指数阻尼非粘性系统的临界曲线。假定的粘弹性力取决于速度响应的过去历史，该速度响应是通过指数核函数上的卷积积分实现的。关键表面是由阻尼参数定义的多维域中的歧管，描绘了诱导的振荡运动和非振荡运动之间的阈值。如果这些表面由两个参数形成，则将它们称为临界曲线。文献中可用于构造这些曲线的可用方法涉及先验矩阵行列式的分析操作，这对于大型系统可能会变得非常低效。在本文中，证明了可以构造近似临界曲线，从而从两个特征值问题中消除了拉普拉斯参数：原始的一个由动态刚度矩阵控制，而另一个由其相对于拉普拉斯参数的导数定义。该方法的理论背景是借助隐函数定理得出的。事实证明，如此发现的近似过阻尼区域被一组临界曲线所包围，这些临界曲线可以参数形式导出。通过两个涉及多个自由度的数值示例验证了该方法的有效性。 （C）2018 Elsevier Ltd.保留所有权利。

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