Two non-probabilistic set-theoretical models to predict the transient vibrations of cross-ply plates with uncertainty
Two non-probabilistic set-theoretical models to predict the transient vibrations of cross-ply plates with uncertainty
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DOI：
10.1016/j.apm.2007.10.016
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发表时间：
2008-12
影响因子：
5
通讯作者：
Z. Qiu;Juxi Hu
中科院分区：
文献类型：
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作者：
Z. Qiu;Juxi Hu
在实际工程和科学研究中，所有的工程分析和设计问题都不同程度地涉及到不确定性。作用在结构上的动态载荷往往具有不确定性，这是由于难以预测这些载荷的大小。本文提出了一种非概率的集合理论模型-区间分析法，用于预测正交铺设板在不确定激励下的瞬态振动。动态载荷包括力函数和初始条件的确定性和不确定性分量。这些函数中的无量纲化要求在L2范数上有界，并用有限个本征模表示。算例分析表明，用区间分析方法计算的临界屈曲载荷的上、下界宽度比用凸模型计算的临界屈曲载荷的上、下界宽度更窄。此外，区间分析具有更少的计算成本比凸模型。考虑到具体情况，各参数和不确定性水平对正交铺设板响应的影响是不同的。
In practical engineering and scientific researches, all engineering analysis and design problems involve uncertainties to various degrees. Dynamic loads acting on a structure are usually with uncertain nature due to the difficulty of predicting the magnitudes of such loads. In this paper, a non-probabilistic and set-theoretical model named interval analysis method is developed to predict the transient vibrations of cross-ply plates with uncertain excitations. The dynamic loads involve deterministic and uncertain components of force function and initial conditions. Uncertainties in these functions are required to be bounded on the L2norm and expressed by finite eigenmodes. Analyzed by a numerical example, the width of the upper and lower bounds of the critical buckling loads that calculated by the interval analysis method is sharper than those are obtained by convex models. Moreover, the interval analysis has less computational cost than convex models. Considering specific cases, the effect of various parameters and the level of uncertainty on the response of the cross-ply plates are different.