Interval analysis for free vibration of composite laminated beams

A new method named interval analysis method, which solves the free vibration of composite laminated beams with uncertain parameters, was presented. Based on interval mathematics and Taylor series expansion, uncertain parameters were described by interval numbers. Instead of conventional probabilistic approach, interval analysis method could get the variation intervals of the natural frequencies of structure, in which the bounds on the magnitude of uncertain parameters were only required, not necessarily knowing other information of statistics. From the comparison between the non-probabilistic interval analysis method and the probabilistic approach in the numerical examples, it could be seen that the region of the natural frequency of structures with uncertain parameters obtained by the interval analysis method contained that produced by the probabilistic approach. In other words, the width of the maximum or upper and minimum or lower bounds on the natural frequency yielded by the probabilistic approach was tighter than that produced by the interval analysis method. The result illustrates the feasibility and the efficiency of the interval analysis method.