Random Eigenvalue Problems in Structural Dynamics

Abstract

An experimental investigation of uncertainty in natural frequencies of linear struc-tures estimated from measured frequency response function (FRF) under dynamic load-ing is presented. Experiments were conducted on one hundred nominally identical real-izations of a fixed-fixed beam; each realisation was obtained by placing twelve identical masses at random spatial locations (generated by a computer) along the length of the beam. The total random mass is about 2 % of the total mass of the beam. These ex-periments contain parametric uncertainty in the mass matrix, and hence may be useful for the validation of many random eigenvalue analysis and prediction methods currently available to structural dynamicist. Predictions from Monte Carlo simulation of deter-ministic finite elements model are compared with experiments. It is concluded that the method of estimation of natural frequencies from FRFs and the spatial location of the measurements has significant influence upon the first two moments (mean and standard deviation) of the natural frequency ensemble. Furthermore, whilst the Monte Carlo sim-ulation estimates of the mean and standard deviation are in reasonable agreement with experiments at higher frequencies, the probability density function differ appreciably, within the limits of the sample size investigated in this study.

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