Random Response of Indeterministic Structures Subjected to Stationary Random Excitation: a Practical Engineering Solution

✍ Scribed by G. Maymon

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 564 KB
• Volume: 172
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1994.1170

✦ Synopsis

A practical method for the determination of the dynamic random response of an indeterministic structure excited by a random stationary dynamic load is described. Random processes and random fields are approximated by random variables, under some simplifying assumptions justified by practical engineering considerations. Expressions for the root mean square values of the displacement and the stress are formulated, the latter by using the stress modes approach. As an example, closed form expressions are obtained for a simply supported beam and a simply supported rectangular plate. A numerical procedure is outlined for the very common practical cases in which dynamic properties can be calculated only numerically. This procedure is based on a Taylor expansion of the response around the mean value. The coefficients of the series are determined by a least mean squares error technique based on a relatively small number of numerical solutions for deterministic cases. A simple but general numerical example is solved by approximate analytical methods, by the Taylor series procedure and by a commercial probabilistic computer program (PROBAN). Very good agreement is obtained between the different methods. It is shown that displacements and stresses can be obtained which are considerably higher than those calculated by classical methods for deterministic structures. The effect of randomness in the structural parameters should therefore be taken into account in a practical design. The suggested numerical procedure can also be used for the analysis of the probability of failure of the indeterministic structure.