Stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion
Stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion
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DOI：
10.1016/j.jsv.2011.08.012
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发表时间：
2012-01
影响因子：
4.7
通讯作者：
K. Sepahvand;S. Marburg;H. Hardtke
中科院分区：
文献类型：
--
作者：
K. Sepahvand;S. Marburg;H. Hardtke
本文介绍了正交各向异性板随机自由振动的广义多项式混沌展开理论及其应用。具体地说，研究了弹性模量不确定条件下正交各向异性板的随机分析。用任意随机基的截断多项式混沌展开式表示板的不确定模、本征频率和本征模。将展开代入控制微分方程，计算本征频率和本征模态的多项式混沌系数。不确定模的分布函数由实验数据导出，其中使用Pearson模型来识别密度函数的类型。然后利用这一实现构造每个不确定参数的随机正交基。由于现有的试验模态分析数据，本文提供了一个有用的实例，将模态响应的统计矩和概率分布与试验结果进行了比较。
This paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates. Specifically, the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated. The uncertain moduli, eigen-frequencies and eigen-modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis. The expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen-frequencies and the eigen-modes. Distribution functions of the uncertain moduli are derived from experimental data where the Pearson model is used to identify the type of density functions. This realization then is employed to construct random orthogonal basis for each uncertain parameter. Because of available experimental modal analysis data, this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results.