doi:10.3850/978-981-08-7619-7_P039

ABSTRACT

A preliminary investigation is presented in this work regarding Dynamic Variability Response Functions (DVRF) which are obtained for a linear beam with random material properties under dynamic excitation. An integral form for the variance of the dynamic response of stochastic systems is considered, involving a DVRF and the spectral density function of the stochastic field modeling the uncertain system properties. As in the case of static systems, the independence of the DVRF to the spectral density and the marginal probability density function of the stochastic field modeling the uncertain parameters have to be assumed. This assumption is here validated using brute-force Monte Carlo simulations as well as a series of different moving power spectral density functions for the calculation of the VRF. The uncertain system property considered is the inverse of the elastic modulus (flexibility). It is shown numerically that DVRF is a function of the standard deviation of the stochastic field modeling flexibility. The same integral expression can be used to calculate the mean response of a dynamic system using the concept of the so called Dynamic Mean Response Function (DMRF), which is a function similar to the DVRF. These integral forms can be used to efficiently compute the mean and variance of the transient system response at any time of the dynamic response together with spectral-distribution-free upper bounds. They also provide an insight into the mechanisms controlling the dynamic mean and variability response.

Keywords: Variability Response Function, Stochastic finite element analysis, Upper bounds, Stochastic dynamic systems.

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