https://hal-upec-upem.archives-ouvertes.fr/hal-00686285Soize, ChristianChristianSoizeLaM - Laboratoire de Mécanique - UPEM - Université Paris-Est Marne-la-ValléeTransient responses of dynamical systems with random uncertaintiesHAL CCSD2001uncertainty quantificationrandom uncertaintiesdynamical systemsstructural dynamicstransient responseimpulsive loadmaximum entropy principlenonparametric probabilistic methodmodeling errorsmodel uncertaintiesrandom matrix[SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph][PHYS.MECA.VIBR] Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph][MATH.MATH-PR] Mathematics [math]/Probability [math.PR][MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]Soize, Christian2012-04-09 18:48:322022-01-15 04:04:272012-04-10 14:53:44enJournal articleshttps://hal-upec-upem.archives-ouvertes.fr/hal-00686285/document10.1016/S0266-8920(01)00026-1application/pdf1A new approach is presented for 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 probability model is deduced from the use of the entropy optimization principle whose available information involves 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. Finally, a simple example is presented.