ESTIMATION OF STIFFNESS PARAMETER VARIABILITY OF HONEYCOMB SANDWICH STRUCTURES BY MEANS OF EXPERIMENTAL MODAL DATA: A STOCHASTIC APPROACH

Honeycomb panels are sandwich structures with a high specific strength and stiffness, together with a low areal mass. They are complex but regular structures with a high number of design parameters that govern their dynamic behaviour, which is this case resonance frequencies and mode shapes of beam samples with free boundary conditions. A first part of this paper gives a quick overview of how the Thermoplastic honeycomb beams are built up and what the various design parameters are that influence the resonance frequencies and mode shapes considered. The considered dynamic behaviour of the honeycomb sandwich beams is considered as a stochastic process, governed by a set of parameters, each having some kind of randomness. Because of the complexity of the honeycomb geometry this governing set of parameters is elaborate. Therefore by means of a suitable Finite Element model two independent elastic material properties are selected from the total set of design parameters, namely the Young’s modulus of the skin in length direction and the out of plane core shear modulus. These two parameters are important factors in governing the resonance behaviour of the considered honeycomb sandwich beams. The skin Young’s modulus determines the bending stiffness of the beam across the frequency range of interest. With increasing frequency the core out of plane modulus has an increasing effect. The goal of this paper is to describe the relation between the variability of these two independent design parameters and the experienced variability in mode shapes and resonance frequencies. These are experimentally determined for a set of 22 honeycomb samples, each having 17 measurement points. Each beam sample is thus divided into 17 intervals with the two considered parameters having a constant value within each interval. The two material constants are in their turn each regarded as a one dimensional Random Field with realizations in the measurement points. The considered variability is split into alleatory and epistemic uncertainty. Alleatory uncertainty arises from the inherent physical variability of the design parameters of interest and variability arising from the process of Experimental Modal Analysis. Epistemic uncertainty arises from the fact that only limited experimental data is available for a statistical evaluation; only 22 beam samples are used. Each Random Field is described in terms of a Karhunen – Loève series expansion with a Polynomial Chaos decomposition of its random coefficients; the realisations of these Random Fields are the quantities of these two parameters at the 17 measurement points. Describing the two design variables as Random Fields involves solving an inverse problem. This is done by means of a direct model updating of the Finite Element model using the measured resonance frequencies and mode shapes. The paper outlines the implementation of the Random Field method along with its extension to estimate the epistemic uncertainty. The errors that occur during the whole process of Experimental Modal Analysis may lead to a certain variability on the considered design parameters which is not physically related to the design parameter variability itself. The way how this is tackled in the study is also outlined in the paper. As a result of this study the unknown probability distributions of two important independent design parameters at the 17 considered measurement locations are estimated, including an estimation of the uncertainty due to the lack of sufficient statistical data. Hereby the influence of measurement uncertainty is addressed. Finally the paper gives a prospect to the following phases in the research, namely the adoption of the methods on two-dimensional structures.

Publication year:2012

Accessibility:Open