Analysis of Coupled Bending Torsional Vibration of Beams in the Presence of Uncertainties

Abstract

Several methods are presented for the modeling and analysis of uncertain beams and other structural elements/systems. By representing each uncertain parameter as an interval number, the vibration problem associated with any uncertain system can be expressed in the form of a system of nonlinear interval equations. The resulting equations can be solved using the exact or a truncationbased interval analysis method. An universal grey numberbased approach and an intervaldiscretization method are proposed to obtain more efficient and/or more accurate solutions. Specifically, the problem of the coupled bendingtorsional vibration of a beam involving uncertainties is considered. It is found that the range of the solution (response) increases with increasing levels of uncertainty in all the methods. Numerical examples are presented to illustrate the computational aspects of the methods presented and also to indicate the high accuracy of the intervaldiscretization approach in finding the solution of practical uncertain systems. The results given by the different interval analysis methods (including the universal grey numberbased analysis) are compared with those given by the Monte Carlo method (probabilistic approach) and the results are found to be in good agreement with those given by the interval analysisbased methods for similar data.