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Application of the polynomial chaos approximation to a stochastic parametric vibrations problem

Brząkała A.

Archives of Civil and Mechanical Engineering

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2013

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Vol. 13, no. 2

220--228

EN

In the paper the application of the polynomial chaos expansion in case of parametric vibrations problem is presented. Hitherto this innovative approach has not been applied to such a stochastic problem. The phenomenon is described by a nonlinear ordinary differential equation with periodic coefficients. It can be observed among others in cable-stayed bridges due to periodic excitation caused by a deck or a pylon. The analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben–Ahin bridge). The characteristic of the viscous damper is considered as a log-normal random variable. The results obtained by the use of the polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation. The convergence of both methods is discussed. It is found that the polynomial chaos yields a better convergence then the Monte Carlo simulation, if resonant vibrations appear.

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Eksperymentalna i teoretyczna analiza dynamiczna konstrukcji

Wójcicki Z., Grosel J., Sawicki W., Majcher K., Pakos W., Brząkała A.

Inżynieria i Budownictwo

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2010

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R. 66, nr 12

706-709

PL

Opisano aparaturę do pomiarów dynamicznych wielkich konstrukcji inżynierskich i budowlanych. Przedstawiono przykłady jej wykorzystania do dynamicznych analiz różnych konstrukcji i modeli fizycznych. Stwierdzono, że w analizie konstrukcji inżynierskich i budowlanych powinny być jednocześnie prowadzone analizy teoretyczne i eksperymentalne w celu weryfikacji i walidacji modeli MES.

EN

Especially was presented an equipment for nondestructive research i.e. system for dynamic measurements of giant engineering structures. In paper is also some illustrative examples of usage of this system to dynamical analysis of different structures and models of structures. The authors propose that a new approach become the recommended standard in the analysis of engineering and building structures. According to them, both theoretical and experimental research should be carried out simultaneously in order to verify and validate FEM models.

3

Badanie drgań dużej konstrukcji przemysłowej

Wójcicki Z., Grosel J., Mironowicz W., Sawicki W., Brząkała A., Majcher K., Pakos W.

Materiały Budowlane

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2009

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nr 3

132-136