Abstract
A probability model for symmetric positive-definite real random matrices is constructed using the maximum entropy principle which allows only the available information to be used. The result obtained differs from the known results concerning Gaussian and circular ensembles for random matrices. The probability distribution of such a random matrix and the probability density function of its random eigenvalues are explicitely constructed. A fundamental mathematical result concerning convergence properties as the dimension of the random matrix approaches infinity is presented. An algebraic representation of the probability model has been obtained and is very well suited to Monte Carlo numerical simulation. This random matrix theory is used to construct a new nonparametric method for modeling random uncertainties in transient elastodynamics. The information used does not require the description of the local parameters of the mechanical model. The 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. The fundamental properties related to the convergence of the stochastic transient response in elastodynamics is analyzed. Finally, an example is presented.a)Present address: Ing. 2000, Bat. Copernic, Univ. de Marne-la-Vallée, 5 Bd. Descartes, 77454 Marne-la-Vallée, France.
Published Version
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