Three dimensional wave propagation characteristics in laminated plates are studied considering the anisotropic and viscoelastic properties of fiber reinforced composite material. A Rayleigh-Ritz based stiffness method is used to discretize the plate in the vertical direction to determine propagation characteristics (wave number, phase velocity, group velocity) and mode shapes for a plane wave front. For 3-dimesional cases, wave propagation problem is decomposed into a series of two-dimensional plane wave problems with three displacements coupled. Double Fourier transform integral transformations are used to get the governing equation in a transformed wave number domain. Steady state elastodynamic Green's functions for the laminated composite plates are constructed through summing the contribution of all two-dimensional problems and the application of modal summation technique. Numerical integration of double infinite integrals is performed by summations over a finite range. The wave propagation characteristics for a 16-layer unidirectional fibre reinforced laminated composite plate show the orthotropic nature of the plate reflected in its 3-D wave propagation characteristics. It is also seen that the Green's functions for 3D waves are very different from those for plane strain 2D waves. Furthermore, the direction of propagation has a significant effect on the Green's function for surface displacements.
In this study, the detection of delamination flaws in laminated composite plates is carried out using artificial neural networks (ANN) in a two-level cascading manner. The three damage parameters detected using ANN are the size of the delamination, its vertical location (across the plate thickness) and horizontal location (along the plate surface). The numerical data in the form of frequency domain Green's function for the displacement response on the surface of the plate containing the delamination flaw is generated first using an available numerical method. Pseudo-experimental data is generated adding artificial random noise into the numerical data. At the first level, a counterpropagation neural network (CPN) is trained for qualitatively classifying the damage parameters using the numerical data generated above. Next, a second level back-propagation network (BPN) is used for each subclass to quantify the damage parameters. An overlapping data set is used for the training of each class of the second level network. As a result, any pattern misclassified by the CPN due to its closeness to the boundary of any two classes is still quantified correctly. By feeding pseudo-experimental data to the trained networks, it is seen that the classification success rate and noise tolerance level of CPN is excellent. The quantification of damage by the second level BPN is also good. It is possible to stop after the first level if only a qualitative assessment of the damage and its approximate location is required. These cascaded networks show promise in providing a successful delamination damage detection tool.
In this paper, guided elastic Lamb wave propagation characteristics in laminated plates are studied using a proper phenomological model for the fiber reinforced composite material. It is well established that ultrasonic waves attenuate in FRP composite material. This is caused by the visco-elastic behavior of the resin ad scattering due to the fiber. The material here is, therefore, numerically modeled using complex material properties. Both the material and frequency-dependent damping for each layer of the laminated plate is incorporated in the formulation. A Rayleigh-Ritz based stiffness method is used to discretize the plate in the vertical direction to determine wave numbers. Furthermore, elasto-dynamic Green functions for both displacement and stress fields in the laminated composite plate are also derived. In this manner, the effect of guided wave attenuation on wave numbers and displacements and stress Green functions are studied. All wave numbers, including those for propagating modes, are complex. However, the relative value of the imaginary part of the wave number of the propagating modes are small, and it is seen that incorporation of damping has an insignificant effect on dispersion characteristics, irrespective of the excitation frequency. However, it significantly affects both displacement and stress fields, especially as the distance from the source increases. This effect is dependent on the excitation frequency. At relative low frequencies, the attenuation of the displacement and stress fields is small. The attenuation increases with excitation frequency, although seemingly the effects on the stress field are relatively less significant than those on the displacement field.
A recently developed Green's function and Hybrid method to analyze wave scattering problem in laminated composite plate have been employed and extended to include material damping and calculate the time domain response beyond the crack zone. Analysis has been carried out for through depth vertical crack only. Attention has been focused on plane-strain motion. Arbitrary values of damping factor have been introduced for numerical analysis to check the decaying phenomenon of the Lamb wave modes in layered composite plate. Experimental verification of the applicability of the simulation with the numerical analysis has also been carried out. It has been found that numerical analysis results are in good agreement with the experimental results.