Author:

Keywords:

Thermoplastic honeycomb panels, stochastic model updating, design parameter variability, correlation length, thermoplastic honeycomb, random fields

Abstract:

Honeycomb panels are sandwich structures. They combine a high specific strength and stiffness with a low areal mass. Consequently, these structures are ideally suited for ground transportation vehicle purposes. They have a complex but regular geometry. A first part of this paper describes the specific type of glass fibre reinforced thermoplastic honeycomb panels used in this study. A set of seven virtually identical panels (length: 2500 mm, width: 1200 mm and thickness: 25 mm) are used in this study. It is discussed which design parameters govern the dynamic behavior of freely suspended panels. A number of the design parameters can be determined experimentally. Special attention goes to the measured variability on these parameters. Some parameters cannot be measured easily so they have to be determined indirectly. A second part in this article discusses the full process of experimental modal analysis. It is discussed how the measurements are set up and how the modal parameters of interest are estimated for each of the seven test panels. Experimental modal analysis is a process that is subjected to many error sources which lead to some variability on the obtained modal parameters (resonance frequencies, mode shapes and damping factors). Consequently, focus is laid on the estimation of the modal parameter variability. Both measurement errors and modal parameter estimation errors are discussed. The third part of the paper explaines how a suitable FE – model is constructed to calculate resonance frequencies and mode shapes of honeycomb panels with free boundary conditions. It is briefly outlined how the (elastic) parameters of the homogenized FE – model (using orthotropic material properties for both skin faces and honeycomb core) are obtained from the real physical parameters of skin faces and honeycomb core. The panel model is devided into a number of intervals, each interval having constant values for the mass and elastic material properties. In this case, 240 intervals are considered in the model. For each of them, six elastic material properties are the parameters of interest. These are the Young’s moduli of both skin faces in lenght and width direction and the two relevant out-of-plane shear moduli of the homogenized honeycomb core. With respect to the considered sets of elastic parameters, the FE – models of the different test panels are updated using resonance frequencies and mode shapes obtained through experimental modal analysis. In this study the number of FE – model parameters to be updated, is much greater than the number of available update targets (resonance frequencies and mode shapes). This leads to an underdetermined model updating problem. It is discussed how stochastic model updating is applied to deal with this specific problem. Through this stochastic model updating process, databases are obtained for each considered elastic parameter and for each of the test panels. The fourth part of the article describes how the dynamic behaviour of a honeycomb panel can be regarded as a stochastic process that is governed by a set of stochastic variables, each having some variability. Taking into account the whole set of test samples, each of the considered elastic model parameters is treated as a stochastic random field. Two types of uncertainty are discussed and estimated for the random fields. The epistemic uncertainty is the uncertainty that arises from the fact that only limited experimental data (seven panels) is available for the estimation of probability density functions of the considered elastic parameters. The aleatory uncertainty is the uncertainty that is related to the inherent physical variabilty of the elastic parameters. It is also outlined how the implementation of the random field method is validated by means of a number of tests. An important factor to relate the variability of a model parameter with its underlying physical variable quantities is the correlation length. It is estimated from the covariance matrix, estimated by means of the random field method, using a suitable correlation function. The correlation length describes at what scale the considered parameter of interest is varying. In the paper it is outlined how the correlation length is estimated for the different elastic parameters. Finally, the variability of the elastic model parameters is related to the variability of the underlying geometrical parameters of both skin faces and honeycomb core. The estimated correlation lengths are a tool for this purpose.