Vibration bounding of uncertain thin beams by using an extreme value model based on statistical moments

Abstract

The paper introduces an extreme value model based on statistical moments to predict modal and vibration response bounds for stochastic structures. The approach is applied to a thin beam having two input uncertain parameters: elasticity modulus and specific volume (inverse of the mass density). The input parameters are controllably generated with random shifted normal distributions that have positive statistics. Then the first two statistical moments, mean and standard deviation of natural frequency, and bending vibration displacement are predicted by solving stochastic differential equation of bending vibration of thin beams. Here, the differential equation is solved by utilizing a powerful numerical technique, discrete singular convolution. The accuracies of the discrete singular convolution method and the statistical moment approach are separately ensured with analytical comparisons and experimental and numerical Monte Carlo simulations. These statistical moments are then processed by an extreme value model to predict uncertainty bounds for modal and vibration displacement responses. Predicted bounds are compared with random responses obtained by numerical Monte Carlo simulations. The proposed approach estimates very accurate results with less computation memory and time compared to Monte Carlo solutions. Therefore, the approach proves its efficiency in the use of uncertainty propagation problems governed by partial differential equations.