An Exact Expression for the Distribution of Linear Combinations of Uniform Random Variables

by Chung-Chih Lin, Arizona State Univ, Tempe, AZ, USA,
Marc P. Mignolet, Arizona State Univ, Tempe, AZ, USA,

Abstract: Structural dynamic analysis have often in the past relied on the assumption that the system under consideration is well known ahd have been associated the unpredictability of the response with a lack of knowledge of the excitation. More recently, however, it has been found that a proper understanding of the behavior of certain mechanical systems can only be reached by considering some of the system parameters, such as mass, stiffness and/or damping to be random variables. The goal of the present paper is to partially address this problem by describing a new numerical technique for the evaluation of the probability that a linear combination of independent uniformly distributed random variables exceeds a given threhshold and also of some related conditional moments.

Subject Headings: Dynamic structural analysis | Structural dynamics | Linear functions | Excitation (physics) | Mechanical properties | Mechanical systems | Parameters (statistics) | Stiffening

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