Date of Award

2017

Document Type

Open Access Dissertation

Department

Mechanical Engineering

Sub-Department

College of Engineering and Computing

First Advisor

V. Giurgiutiu

Abstract

To predict guided wave dispersion curves, it is common to use different solution approaches depending on the material type (isotropic or anisotropic) of the medium in which the wave propagates. The two different solution methods are defined in different domains, frequency-phase velocity domain for isotropic materials and wavenumber-phase velocity domain for anisotropic materials. This may lead to difficulties and unsatisfying results when predicting the dispersion curves for hybrid laminates which contain both isotropic and anisotropic materials. Therefore, a unified formulation defined in the wavenumber-phase velocity domain to accomodate both isotropic and anisotropic materials, as well as hybrid combinations, is desired. The unified analytic method (UAM) proposed in this dissertation is a simple and mathematically straightforward formulation that utilizes Christoffel’s equation for a lamina to obtain the eigenvalues and eigenvectors. The eigenvalues and eigenvectors are used to set up the field matrix from which the dispersion curves could be retrieved using a newly developed approach called the phase approach. As last, the dispersion curves are grouped and sorted using a modeshape analysis.

It is important to realize that predictions depend on the accuracy of the stiffness matrix input for the UAM. Common practice is to determine the required material properties using destructive mechanical testing procedures in combination with assumption based on the material type. However, when the predicted dispersion curves varied significantly from those obtained experimentally, the source of error was identified as the accuracy of the stiffness matrix. A new non-destructive characterization method that combines the best features of several existing ultrasonic immersion techniques is implemented. This LAMSS ultrasonic immersion technique is demonstrated to retrieve the stiffness matrix for a unidirectional and woven fabric composite.

The retrieved stiffness matrix using the LAMSS ultrasonic immersion technique was compared to the stiffness matrix reported in the literature. In the case of the woven fabric, in-house mechanical testing was performed as well. Differences between the stiffness matrices retrieved using the different methods were explained.

To validate the UAM predictions, the different stiffness matrices obtained with our methods as well as from literature were used to predict the wavenumber-frequency dispersion curves and compared to the experimentally obtained dispersion curves. The experimental dispersion curves were obtained using a hybrid setup consisting of a piezoelectric wafer active sensor exciter and a scanning laser Doppler vibrometer wave measuring system. A good correlation was observed between the predicted and experimental wavenumber-frequency dispersion curves when using the material properties obtained through the LAMSS ultrasonic immersion approach for both the unidirectional and woven fabric composite material. However, when stiffness matrix values obtained through destructive mechanical testing procedures were used, the error between the predicted and experimental wavenumber-frequency dispersion curves was increased.

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