Mechanics of Nano, Micro and Macro Composite Structures
Politecnico di Torino, 18-20 June 2012
A. J. M. Ferreira, E. Carrera (Editors)
http://paginas.fe.up.pt/~icnmmcs/
STUDYING DESIGN PARAMETER VARIABILITY OF HONEYCOMB
SANDWICH BEAMS BY MEANS OF EXPERIMENTAL MODAL
DATA: A STOCHASTIC APPROACH
Stijn Debruyne†, Dirk Vandepitte†, Loujaine Mehrez†, Eric Debrabandere*
† Department of Mechanical Engineering
Katholieke Universiteit Leuven (KUL)
Celestijnenlaan 300b, 3001 Heverlee, Belgium
e-mail: stijn.debruyne@khbo.be,
dirk.vandepitte@mech.kuleuven.be,loujaine.mehrez@mech.kuleuven.be
*
Department of Industrial Science
Katholieke Hogeschool Brugge Oostende
Zeedijk 101, Oostende, Belgium
e-mail: eric.debrabandere@khbo.be
Key words: Thermoplastic honeycomb beams, design parameter variability, Random Fields,
Modal Analysis, measurement uncertainty.
Summary. This paper relates design parameter variability of thermoplastic honeycomb
sandwich beams to their experimentally determined dynamic behaviour in case of free
boundary conditions. This paper describes how two independent elastic material properties
are chosen as design parameters of interest, treated as Random Fields, are linked to
experimentally determined variability of resonance frequencies and mode shapes.
Abstract.
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
S.Debruyne, D.Vandepitte, L.Mehrez and E.Debrabandere
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.
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