S. K. Datta

Scattering of an Impact Wave by a Crack in a Composite Plate

Ultrasonic waves provide an efficient means of characterizing defects in structures. For this purpose it is necessary to analyze scattering by such defects. However, scattering by crack-like defects in a plate-like structure is a complicated phenomenon and the problem is made more difficult if it is a composite plate. In recent years considerable progress has been made toward understanding wave propagation in anisotropic composite plates [1–5], but not much work has been done on the scattering by cracks in a composite plate. Recently Karim and Kundu [6] and Karim et al. [7] studied scattering of elastic waves in a layered half-space and in layered fiber-reiforced composite plates by interface cracks using a boundary integral formulation. They considered antiplane motions. Although this method can be extended to plane strain motion the computional effort is considerably amplified if one considers a plate geometry. Besides, the method used by these authors is limited to planar defects. For arbitrarily shaped scatterers Sanchez-Sesma [8] reviewed various applicable methods. Most of these numerical methods require considerable computational effort to evaluate the response. Their applicability to layered and anisotropic medium is also limited.

Reflection of Waves at the Free Edge of a Laminated Circular Cylinder

A wave function expansion is used. Wave function are obtained using a propagator matrix approach for laminated isotropic cylinders and by a Rayleigh Ritz type approximation for laminate composite cylinders. The least square technique as well as the variational method are employed to evaluate the complex amplitudes and the energy flux associated with the reflected waves

Three dimensional dynamics of pipelines buried in backfilled trenches due to oblique incidence of body waves

Abstract Dynamic response of pipelines buried in a back-filled rectangular trench in a semi-infinite medium has been investigated. The pipelines are modelled as long cylindrical shells of small thickness. By using the boundary integral representation and finite element method, we have studied the three-dimensional response to account for either plane P or SV wave incident at an arbitrary angle to the pipe-axis. Numerical results are presented for the normal displacements, displacements along pipe-axis, and the hoop stresses in the pipe wall. It is shown that the response depends critically on the back-filled material as well as on the directions of propagation of the incident waves.

Wave propagation in laminated composite circular cylinders

Abstract A stiffness method is used to study the dispersion characteristics of waves propagating in laminated composite cylinders. Each lamina of the cylinder can possess distinct anisotropic properties, mass density and thickness. The objective of the study is to analyze the effects of the circumferential wave number, ply lay up configuration, number of layers, and the thickness-toradius ratio on the dispersion characteristics. A Rayleigh-Ritz type of approximation of the throughthickness variation of the displacements which maintains the continuity of displacements and tractions at the interfaces between the layers has been used. The numerical results are compared with those obtained from the method using quadratic interpolation functions and also with the analytical solutions to illustrate the accuracy and efficiency of the method. Frequency spectra for four ply [+30−30], and [+15−15]. sixteen ply [+ 15−15]. and twelve ply [O 2 +45−45O 2 ], graphite/epoxy laminated composite cylinders are also presented Numerical results show strong influence of anisotropy on the guided waves.

Mode-Coupling of Waves in Laminated Tubes:

The dispersive and modal behavior of specially orthotropic fiber-rein forced laminated tubes is investigated over a range of frequencies. A wave propagation based method with finite element discretization in the radial direction is used to allow modeling which includes the radial variation of the constitutive properties of such lami nated tubes. Tubes with different numbers of total plies are compared in order to determine at what frequencies the ply lay-up affects the character of the propagating modes and cou pling between these modes. In particular, coupling between predominantly longitudinal (axial-radial and radial-axial) and predominantly torsional modes is examined.

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

Elastic wave scattering by surface-breaking planar and nonplanar cracks

Abstract : At present ultrasonic techniques for characterizing defects are being explored vigorously at various research centers around the world. Currently, the ultrasonic approach to defect sizing and characterization is beginning to find great favor for in- or out-of-service use. A recent review of practical ultrasonic nondestructive evaluation is referred. Because of recent advances in experimental ultrasonic technology, increasing demands are being put on quantitative theoretical modeling of scattering of ultrasonic (elastic) waves by cracks, cavities and other material inhomogeneities in an elastic medium. With a view to obtain detailed information about signals scattered from complex defects various analytical and numerical techniques have emerged. In this article we present a combined finite elements and eigenfunction expansion technique for solving scattering problems involving multiple scattering as well as complex geometries. Numerical results obtained by this method are compared with recent experimental results. In the following we first summarize the theoretical treatment. Then we present the finite elements and eigenfunction expansion technique (FEEET). Numerical and experimental results are presented next. Although the results presented here are for homogeneous materials, the method can readily be extended to composite materials.

Transient Scattering of Rayleigh-Lamb Waves by Surface-Breaking and Buried Cracks in a Plate

The evaluation of integrity of critical structures and parts is of vital importance for the maintenance of quality and safety. Quantitative nondestructive evaluation (QNDE) techniques provide the means to detect a flaw and to determine its location, size, shape and orientation. Ultrasonic technique is one of such commonly used ones. Comprehensive discussions of ultrasonic QNDE methods can be found in recent review papers by Thompson and Thompson [1] and a recent symposium volume edited by Datta et al. [2].

Dynamics of buried pipes in back-filled trench

Abstract Dynamic response of pipelines lying in a back-filled trench in a semi-infinite medium is investigated. The pipelines are modelled as circular cylindrical shells of small thickness. The problems associated are the ones of plane strain, in which it is assumed that the waves are propagating perpendicular to the pipe-axes. Since no exact solution is obtainable for the problems considered here, a numerical technique that combines the finite element method with multipolar representation of the scattered field is used. Numerical results are presented for the normal displacements, as well as the hoop stress in the pipewall either in the presence or absence of another pipe lying nearby.

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.