Frequency-Independent Modal Damping for Flexural Structures via a Viscous "Geometric" Damping Model
Frequency-Independent Modal Damping for Flexural Structures via a Viscous "Geometric" Damping Model
复制标题
通过粘性“几何”阻尼模型实现弯曲结构的频率无关模态阻尼
DOI：
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发表时间：
2010
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通讯作者：
G. Lesieutre
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作者：
G. Lesieutre
* 本文考虑弯曲结构的阻尼横向振动。迄今为止，粘性阻尼模型的不足之处在于预测的模态阻尼是强烈的频率依赖性，这种情况在建筑结构的实验中并不常见。基于应变的粘滞阻尼对应于刚度比例阻尼的情况，产生随频率线性增加的模态阻尼。基于运动的粘性阻尼，这对应于质量比例阻尼的情况下，产生模态阻尼，随频率线性下降。该模型引入了一个粘性的“几何”阻尼项，其中抵抗剪切力与斜率的时间变化率成正比。在离散化（有限元）的情况下，得到的阻尼矩阵类似于几何刚度矩阵，用于解释膜荷载对横向刚度的影响。以简支梁为例，该模型产生与频率无关的常模态阻尼。对于某些边界条件，相应的振型是真实的。通过有限元分析验证了这些结论。这样的粘性阻尼模型应该证明是有用的研究人员和工程师谁需要一个时域阻尼模型，表现出现实的频率无关的阻尼。
*This paper considers the damped transverse vibration of flexural structures. Viscous damping models available to date suffer from the deficiency that predicted modal damping is strongly frequency-dependent, a situation not often encountered in experiments with builtup structures. Strain-based viscous damping, which corresponds to the case of stiffnessproportional damping, yields modal damping that increases linearly with frequency. Motion-based viscous damping, which corresponds to the case of mass-proportional damping, yields modal damping that decreases linearly with frequency. The proposed model introduces a viscous “geometric” damping term in which a resisting shear force is proportional to the time rate of change of the slope. In a discretized (finite element) context, the resulting damping matrix resembles the geometric stiffness matrix used to account for the effects of membrane loads on lateral stiffness. For an illustrative example of a simplysupported beam, this model yields constant modal damping that is independent of frequency. For some boundary conditions, the corresponding mode shapes are real. These conclusions are verified through additional finite element analysis. Such a viscous damping model should prove useful to researchers and engineers who need a time-domain damping model that exhibits realistic frequency-independent damping.