Robert Bratton

Wave propagation in laminated composite plates

A stiffness method has been used in this article to study dispersive wave propagation in a laminated anisotropic plate. The advantage of this method is in its usefulness in obtaining numerical results for the dispersion characteristics of waves propagating in a plate with an arbitrary number of arbitrarily anisotropic laminae. This method has been applied here, as a way of illustration, to a plate made up of transversely isotropic laminae with the axis of isotropy of each lamina lying in the plane of the lamina. Results thus obtained are shown to agree well with the exact solutions for isotropic and transversely isotropic single layered plates. Numerical results are presented for cross‐ply (0°/90°/0°) laminated composite plates and show that the frequency spectrum in this case differs considerably from that for a single layered (0°) plate.

Transient response of a laminated composite plate : results from homogenization and discretization

Abstract Transient response of a multilayered laminated plate has been studied in this paper. The objective of this study is to analyze the effect of layering on the response of the laminated plate in both time and frequency domains to a line source on the surface of the plate. For simplicity of analysis, attention has been focused on the two-dimensional (plane strain) motion. It is shown that for a cross-ply plate when the number of plies is small the response of the plate is quite different than that of an equivalent homogeneous plate. For short pulses the response is fairly complicated due to the reflections from the interfaces between the plies. Dispersion of waves in the plate is also analyzed. It is found that the homogenized model predictions for the low-order modes agree with those of the layered model. However, they diverge when high-order modes are considered. This is consistent with the transient response comparisons

Scattering of Lamb waves in a composite plate

Recent investigations of space construction techniques have explored the use of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. Examples of these materials are laminates of graphite fibers in an epoxy or a metal (Al, Mg) matrix and boron fibers in an aluminum matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in [1] and [2]. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation. Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements. This method was used for out-of-plane (SH) wave scattering in an isotropic plate[3]. A combined analytical and finite element formulation for a single layered isotropic plate in the state of plane strain was investigated in [4]. In this study the authors considered only the lowest symmetric mode and geometrically symmetric cracks. In [5] a variational approach was used to investigate scattering by a symmetric pair of surface breaking thin slots. Employing standard elastostatic crack solutions as trial functions the authors examined the scattering by the first symmetric mode. A finite difference method was used in [6] to calculate the scattering of Lamb and shear waves from surface breaking cracks. In [7] a modified Wiener-Hopf technique was used to analyze scattering of Lamb waves by a crack. Applying this technique, the authors in [8] studied quantitative sizing of spot welds in joined sheets. Besides the finite difference and finite element techniques, the analytical approaches are not suitable for analyzing arbitrarily shaped defects and anistropic media. In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different material. Recently, using the hybrid method, the scattering by surface-breaking cracks in isotropic homogeneous and welded plates has been examined in [9].

Analysis of Guided Waves in a Bilayered Plate

Inspection of coated material is vital in order to ensure the integrity of the protective barrier. In some cases, the inspection process is complicated by the fact that the surface of the protective coating may not be accessible, thus the inspection must proceed with only access to the surface of the opposite side (this will be referred to as the inner surface). One method which can be applied in such a situation is the excitation of guided waves or Lamb waves in the coated material. Lamb waves excited from the inner surface will sense the variation in the coating conditions as well as flaws in the steel plate. Therefore for a correct and unambiguous interpretation of Lamb wave data for corrosion-related flaws, the effects of the coating and how they differ from the effects of corrosion-related flaws must be understood. To this end this paper will concentrate on the effects of the coating and its influence on dispersive characteristics of a soft layer bonded to a steel plate. By calculating the dispersion relations for a bare and coated steel plate and comparing the calculated results, unique new modes are seen to emerge in the coated plate. In addition, the coated plate is also modeled as a thin layer on a halfspace allowing a comparison between the problem of a coated halfspace and a coated plate. The comparison demonstrates that only limited information can be obtained by treating the problem as a layered halfspace. More detailed information can be obtained by treating the problem as a coated plate of finite thickness.

Anisotropy Effects on Lamb Waves in Composite Plates

There is currently considerable interest in metal matrix composites for applications in space structures. Both particle and fiber reinforced materials are under investigation. Our recent studies [1,2] have shown that these materials can usually be characterized as transversely isotropic having five distinct elastic stiffnesses. Using a wave scattering formalism, models of their rheology were derived for predicting these five elastic stiffnesses. Manufactured parts (plates, tubes, etc.) containing these materials have unique properties, which are subjects of considerable interest for ultrasonic nondestructive evaluations, impact response, and vibrations. In this paper we have studied guided wave propagation in plates of two different materials: SiC particle-reinforced aluminum alloy and graphite fiber-reinforced magnesium. As was shown in previous investigations [1,2], both of these materials show transverse isotropic symmetry. Here it has been assumed that the axis of symmetry lies in the plane of the plate. Thus for propagation in an arbitrary direction parallel to the plate, the motion is three dimensional, i.e., the equations governing the three components of displacement are coupled. This causes considerable complexity in the dispersion equation. Here we have presented solutions to this equation showing different behaviors for the two materials.

Elastic Wave Dispersion in Laminated Composite Plate

In the past dynamic behavior of infinite periodically laminated medium has been studied extensively. A review of the literature on exact and approximate analyses of this problem can be found in [1,2].

Transient Response of a Laminated Composite Plate

Propagation of guided waves in a laminated plate is of interest for ultrasonic nondestructive evaluation of defects and for material characterization. There is a need for a thorough understanding of the wave propagation characteristics in such a plate in order to use ultrasonic means to determine the material properties, assess damage, and characterize defects. The problem is also of interest for study of acoustic emission.

Scattering of SH Waves by Cracks and Delaminations in a Cladded Plate

Recent investigations of space construction have explored the use of Al cladded graphite/epoxy materials for space platforms. Characterization of potential flaws and joints in the cladded material by non-destructive evaluation (NDE) methods ensures the reliability of the structure. One possible NDE method is to use anti-plane shear (SH) waves generated and detected by electromagnetic-acoustic transducers (EMATs). There have been some investigations on the interactions of SH waves with delamination defects in a bimaterial plate. References to some of these can be found in Kundu[l,2]. Scattering of SH waves by cracks in a homogeneous plate was studied by Abduljabbar, et al. [3–5].

Surface and Interface Waves in a Sandwich Plate with Interface Soft Layers

In the past, dynamic behavior of periodically laminated medium has been studied extensively. A review of the literature on exact and approximate analyses of this problem can be found in [1,2].