Subhendu K. Datta

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.

Scattering of lamb waves by a normal rectangular strip weldment

Abstract A combined finite element and Lamb wave modal expansion method is presented here for analysing scattering of time harmonic Lamb waves by material and geometric irregularities in an isotropic linearly elastic infinite plate. All the irregularities are assumed to be contained in a bounded region. The method is to replace this region with a finite element mesh. A nodal force-displacement relation is developed to satisfy the continuity conditions along the artificial boundaries separating the inner finite element region from the exterior regular region. The method is illustrated by solving the problem of scattering of Lamb waves by a normal transversely anisotropic weldment. The reflection and transmission coefficients are computed for the first antisymmetric and symmetric incident modes. The validity and accuracy of the results are checked by satisfaction of the energy conservation principle.

Ultrasonic wave propagation in a random particulate composite

Abstract Ultrasonic wave propagation in a composite consisting of spherical glass inclusions distributed in a random homogeneous manner in an epoxy matrix has been studied in the frequency range of 0.3–5 MHz. The longitudinal and shear phase velocities, and the attenuation of longitudinal waves in the composite were determined as functions of frequency and the volume fraction of the inclusions. The results are compared with several theoretical analyses available in the literature. It is shown that the results of Datta are in very good agreement with the experimental observations. Further, the data satisfy the bounds due to Hashin and Shtrikman, and due to Miller. The phenomenon of cut-off frequencies—a characteristic of periodic composites—is not observed in the random particulate composities.

Scattering of SH waves by embedded cavities

Abstract Scattering of plane SH waves by sub-surface circular cavities and thin slits in a semi-infinite elastic medium is analyzed in this paper. Two methods of solution are used to obtain the displacements on the free-surface. One of these is a method of matched asymptotic expansion that is very effective when the wavelength is long compared to the dimensions of the cavity (or the crack). The other is a combined finite element and analytical technique, which is useful in the long to intermediate wavelength range. The results obtained by these two techniques are shown to agree quite well for long wave-lengths. Numerical results for the surface displacements for various incident wave angles are seen to depend significantly on the depth and size of the cavity and the crack. In the latter case the orientation of the crack has a significant influence on the scattered field.

Elastodynamic Scattering From Inclusions Surrounded by Thin Interface Layers

The scattering of elastic waves by elastic inclusions surrounded by interface layers is a problem of interest for nondestructive evaluation of interfaces in composites. In the present paper the scattering by a single elastic inclusion is studied. The scattering problem is solved by means of the null field approach and the properties of the interface layer enters through the boundary conditions on the inclusion

On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions

In this paper, effective boundary conditions for elastic wave propagation in plates with thin coatings are derived. These effective boundary conditions are used to obtain an approximate dispersion relation for guided waves in an isotropic plate with thin anisotropic coating layers. The accuracy of the effective boundary conditions is investigated numerically by comparison with exact solutions for two different material systems. The systems considered consist of a metallic core with thin superconducting coatings. It is shown that for wavelengths long compared to the coating thickness there is excellent agreement between the approximate and exact solutions for both systems. Furthermore, numerical results presented might be used to characterize coating properties by ultrasonic techniques.

Calculated elastic constants of composites containing anisotropic fibers

Abstract By a wave-scattering method, we derive dispersion relationships for waves propagating perpendicular to continuous fibers that are oriented unidirectionally. In the long-wavelength limit one obtains relationships that predict the composites effective static elastic constants. We compare these relationships with others derived by energy methods to obtain upper and lower bounds of the effective static moduli. We demonstrate them graphically by plotting for graphite-cpoxy the predicted composite constants over the full range of fiber volume fractions. We consider the fibers to be anisotropic, but transversely isotropic. Under special conditions, the energy-method upper and lower bounds compare identically with the results of this study. The static properties are, of course, special cases of the more general dispersion relationships. Graphs are given for nine elastic constants: axial and transverse Youngs and shear moduli, bulk and plane-strain bulk moduli, and three Poissons ratios.

Elastic guided waves in a layered plate with rectangular cross section

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated.

Transient ultrasonic guided waves in layered plates with rectangular cross section

Transient ultrasonic guided waves in anisotropic layered plates with finite and infinite width are presented in this article. A semianalytical finite-element method is adopted to study the guided waves in both infinite- and finite-width elastic plates. Three-noded beam elements in the thickness direction are used in infinite plate model, whereas the cross section of the finite-width plate is represented by nine-noded quadrilateral elements. Propagation in the axial direction is modeled by analytical wave functions. Elastodynamic Green’s functions are derived using modal summation in the frequency–wave number and time–space domains. Results for dispersion and transient analysis of guided waves in infinite nickel plates are presented and compared with those of finite-width plates. Group velocities are calculated and wave arrival times are computed for different plate cross sections. Numerical results show a significant influence of the plate aspect ratio on the dispersion and transient wave response. The co...

Scattering of Guided Waves by Circumferential Cracks in Steel Pipes

A novel numerical procedure is presented in this paper to study wave scattering problem by circumferential cracks in steel pipes. The study is motivated by the need to develop a quantitative ultrasonic technique to characterise properties of cracks in pipes. By employing wave function expansion in axial direction and decomposing the problem into a symmetry problem and an antisymmetry problem, a three-dimensional wave scattering problem is then reduced into two quasi-one-dimensional problems. This simplification greatly reduces the computational time. Numerical results for reflection and transmission coefficients of different incident wave modes are presented here for a steel pipe with cracks (may have arbitrary circumferential crack length and radial crack depth) and they are shown to agree quite closely with available but limited experimental data.