A stochastic modal decomposition framework for the analysis of structural dynamics under uncertainties
A stochastic modal decomposition framework for the analysis of structural dynamics under uncertainties
复制标题
用于分析不确定性下结构动力学的随机模态分解框架
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Ghanem
中科院分区：
文献类型：
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作者：
H. Meidani;R. Ghanem
讨论了结构在几何特性、材料特性不确定以及外载荷随机性作用下动力响应的不确定性量化问题。当基于相关的谱行为进一步减少相应悬臂梁模型的有限元离散化时，可以使用所提出的形式进行风力机叶片的动力学分析。采用一种计算效率高的随机特征值问题求解算法，量化了几何和材料特性的不确定性对光束光谱特性的影响。该算法将幂迭代和子空间迭代的思想推广到随机算子中，在此基础上构造了基于随机特征值的低维优势子空间，并计算了特征向量，从而方便了随机响应的计算。数值结果验证了该框架的有效性。
The uncertainty quantification in the dynamic response of structures under uncertainties in the geometric and material properties as well as the randomness in the external loading is discussed. The dynamics analysis of the wind turbine blades can be performed using the proposed formalism when the finite element discretization of the corresponding cantilever beam model is further reduced based on the associated spectral behavior. The impact of the uncertainties in the geometry and material properties on the spectral property of the beam is quantified using a computationally efficient solution algorithm for the stochastic eigenvalue problem. The algorithm extends the ideas of power iteration and subspace iteration to the stochastic operators, based on which the a lower dimensional dominant subspace is constructed based on the random eigenvalues and eigenvectors are calculated which subsequently facilitates the computation of the random response. Numerical results are then shown to verify the efficiency of the proposed framework.