Soize C
Structural Dynamics and Coupled Systems Department, ONERA, Chatillon, France.
J Acoust Soc Am. 2001 May;109(5 Pt 1):1979-96. doi: 10.1121/1.1360716.
A new approach is presented for analyzing random uncertainties in dynamical systems. This approach consists of modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics. The information used does not require the description of the local parameters of the mechanical model. The probability model is deduced from the use of the entropy optimization principle, whose available information is constituted of the algebraic properties related to the generalized mass, damping, and stiffness matrices which have to be positive-definite symmetric matrices, and the knowledge of these matrices for the mean reduced matrix model. An explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to Monte Carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads. The fundamental properties related to the convergence of the stochastic solution with respect to the dimension of the random reduced matrix model are analyzed. Finally, an example is presented.
提出了一种分析动力系统中随机不确定性的新方法。该方法包括通过非参数模型对随机不确定性进行建模，从而能够在线性结构动力学的背景下预测承受冲击载荷的机械系统的瞬态响应。所使用的信息不需要描述机械模型的局部参数。概率模型是根据熵优化原理推导出来的，其可用信息由与广义质量、阻尼和刚度矩阵相关的代数性质组成，这些矩阵必须是正定对称矩阵，以及关于平均简化矩阵模型的这些矩阵的知识。已经获得了概率模型的显式构造和表示，并且非常适合代数计算和蒙特卡罗数值模拟，以便计算承受冲击载荷的结构的瞬态响应。分析了与随机解相对于随机简化矩阵模型维度的收敛性相关的基本性质。最后给出了一个例子。
