A. H. Shah

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.

Tuned liquid dampers for controlling earthquake response of structures

Numerical simulations of a single-degree-of-freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both real and artificially generated earthquake ground motions, show that a properly designed TLD can significantly reduce the structures response to these motions. The TLD is a rigid, rectangular tank with shallow water in it. Its fundamental linear sloshing frequency is tuned to the structures natural frequency. The TLD is more effective in reducing structural response as the ground excitation level increases. This is because it then dissipates more energy due to sloshing and wave breaking. A larger water-depth to tank-length ratio than previous studies suggested, which still falls within the constraint of shallow water theory, is shown to be more suitable for excitation levels expected in strong earthquake motions. A larger water-mass to structure-mass ratio is shown to be required for a TLD to remain equally effective as structural damping increases. Furthermore, the reduction in response is seen to be fairly insensitive to the bandwidth of the ground motion but is dependent on the structures natural frequency relative to the significant ground frequencies. Finally, a practical approach is suggested for the design of a TLD to control earthquake response. Copyright

Impedance curves for an elastic pile

An extensive parametric study is conducted to investigate the impedance characteristics of a single elastic pile embedded in an elastic soil medium. A recently developed semi-analytical model based on Greens functions for a system of buried harmonic loading configurations is used in this study. The applicability of different compatibility conditions and force configurations are investigated. Accuracy of existing solutions based on simplified continuum models and finite element method are verified. Numerical solutions for axial, lateral, rocking, coupled and torsional impedances are presented as a system of non-dimensional curves over a wide range of governing parameters of the elastic soil-pile system.

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.

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.

Application of a three-dimensional mixed finite element model to the flexure of sandwich plate

Abstract The bending analysis of sandwich plates consisting of very stiff face sheets and a comparatively flexible core material offers challenge due to large variation in the magnitude of stress and strain components in the face and in the core regions of the plate. Similarly, the displacement fields do vary in zigzag manner at the layer interface of stiff face sheet and the soft core, thereby making the transverse strains highly discontinuous at such layer interfaces. All these behavioural aspects indicate that only an individual layerwise model can appropriately analyze sandwich plates. A layerwise (three-dimensional), mixed, 18-node finite element (FE) model developed by Ramtekkar et al. [Mech. Adv. Mater. Struct. 9 (2002) 133] has been employed for the accurate evaluation of transverse stresses in sandwich laminates. The FE model consists of six degrees-of-freedom (three displacement components and three transverse stress components τ xz , τ yz , σ z , where z is the thickness direction) per node which ensures the through thickness continuity of transverse stress and displacement fields. Results obtained by using the FE model have shown excellent agreement with the available elasticity solutions for sandwich plates. Additional results on the variation of transverse strains have also been presented to highlight the magnitude of discontinuity in these quantities due to difference in properties of the face and the core materials of sandwich plates.

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.

Wave Propagation in a Multilayered Laminated Cross-Ply Composite Plate

Dispersion of guided waves in a cross-ply laminated plate has been studied here using a stiffness method and an exact method. It is shown that the number of laminae strongly influences the dispersion behavior. Further, it is found that when the number of laminae is sufficiently large, then the dispersion behavior can be predicted by treating the plate as homogeneous with six stiffness constants obtained by using an effective modulus method.

Axisymmetric guided wave scattering by cracks in welded steel pipes

Scattering of axisymmetric guided waves by cracks and weldments of anisotropic bonding material in welded steel pipes is investigated in this paper by a hybrid method employing finite element and modal representation techniques. The study is motivated by the need to develop a quantitative ultrasonic technique to distinguish flaws and bonding materials in welded cylindrical structures. Numerical results for reflection coefficients are presented for a steel pipe with cracks and V-shaped weldments with and without cracks at the interface between the weldment and the steel pipe. It is shown that as the frequency increases, the coefficients of reflection exhibit resonant peaks at the cutoff frequencies of higher guided modes. These peaks become increasingly pronounced as the slope and the length of the crack increase. Numerical results presented have important applications in quantitative nondestructive evaluation.