Experimental case studies for uncertainty quantification in structural dynamics

Abstract

The consideration of uncertainties in numerical models to obtain the probabilistic descriptions of vibration response is becoming more desirable for industrial-scale finite element models. Broadly speaking, there are two aspects to this problem. The first is the quantification of parametric and non-parametric uncertainties associated with the model and the second is the propagation of uncertainties through the model. While the methods of uncertainty propagation have been extensively researched in the past three decades (e.g., the stochastic finite element method), only relatively recently has quantification been considered seriously. This paper considers uncertainty quantification with the aim of gaining more insight into the nature of uncertainties in medium- and high-frequency vibration problems. This paper describes the setup and results from two experimental studies that may be used for this purpose. The first experimental work described in this paper uses a fixed–fixed beam with 12 masses placed at random locations. The total ‘random mass’ is about 2% of the total mass of the beam and this experiment simulates ‘random errors’ in the mass matrix. The second experiment involves a cantilever plate with 10 randomly placed spring-mass oscillators. The oscillating mass of each of the 10 oscillators is about 1% of the mass of the plate. One hundred nominally identical dynamical systems are created and individually tested for each experiment. The probabilistic characteristics of the frequency response functions are discussed in the low, medium and high frequency ranges. The variability in the amplitude of the measured frequency response functions is compared with numerical Monte Carlo simulation results. The data obtained in these experiments may be useful for the validation of uncertainty quantification and propagation methods in structural dynamics.