Probabilistic free vibration analysis of beams subjected to axial loads

A stochastic finite-element-based algorithm for the probabilistic free vibration analysis of beams subjected to axial forces is proposed in this paper through combination of the advantages of the response surface method, finite element method and Monte Carlo simulation. Uncertainties in the structural parameters can be taken into account in this algorithm. Three response surface models are proposed. Model I: star experiment design using a quadratic polynomial without cross-terms; Model II: minimum experiment design using a quadratic polynomial with cross-terms; Model III: composite experiment design using a quadratic polynomial with cross-terms. A separate set of finite element data is generated to verify the models. The results show that the Model II is the most promising one in view of its accuracy and efficiency. Probabilistic free vibration analysis of a simply supported beam is performed to investigate the effects of various parameters on the statistical moments of the frequency response of beams. It is found that the geometric properties of beams have significant effects on the variation of frequency response. (C) 2006 Elsevier Ltd. All rights reserved.