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Anomalous guided waves appearing at a non-semisimple degeneracy of the fundamental matrix are observed and analyzed in the framework of the Cauchy sextic formalism. The non-semisimple degeneracy condition is explicitly constructed for the most general case of Lamb waves propagating in a traction-free layer with arbitrary elastic anisotropy. A new type of dispersion equation and the corresponding dispersion solution are obtained. The connection with surface waves of the non-Rayleigh type is discussed. [ABSTRACT FROM AUTHOR]

It is known that Lamb waves in homogeneous traction-free plates can propagate with arbitrary phase velocity, spanning the admissible speed interval (0; + ∞) . However, as the current research shows, Lamb waves propagating in two-layered traction-free plates may have 'forbidden' phase velocities, at which no Lamb waves can propagate. The analysis is based on the approach comprising Cauchy complex formalism and the exponential fundamental matrix method. [ABSTRACT FROM AUTHOR]

The analytical and geometrical conditions for the possible appearance of the infinite group velocity (IGV) points belonging to the dispersion curves of Lamb waves propagating in traction-free plates are studied by a combined method comprising Cauchy sextic formalism and the exponential fundamental matrix method. According to the obtained geometrical condition, the IGV corresponds to the coincidence of a tangent line to any of the dispersion curves with a straight line passing through the origin. The developed technique is demonstrated by applying to the analysis of Lamb wave dispersion in three-layered plates with a soft inner core. [ABSTRACT FROM AUTHOR]

The current research is concerned with the study of Lamb waves propagating in a traction-free plate with cubic anisotropy along the crystallographic axes. Splitting all cubic crystals into two non-intersecting classes revealed either the appearance or disappearance of the crossing points of the fundamental branches. The spectral analysis of the resolvent matrix in the vicinity of the crossing points showed existence of a two-fold degeneracy with two distinct kernel eigenvectors and absence of the non-semisimple degeneracy, meaning stability of the flexural and symmetric fundamental branches passing through the crossing point. [ABSTRACT FROM AUTHOR]

The constructed closed form solutions for the long-wave limits for guided waves propagating in anisotropic crystals reveal a principal ability for existence of several long-wave limiting velocities exhibiting dependence on the wave normal. Numerical examples for guided waves propagating on the (1,0,0)-plane of several cubic crystals indicate existence of two distinct long-wave limiting velocities for all directions of the wave normal, except a possible discrete number of directions where two long-wave limiting velocities may coincide. [ABSTRACT FROM AUTHOR]

The closed form expressions for the low frequency velocity limits of Lamb waves propagating in anisotropic homogeneous, stratified and functionally graded (FG) plates with arbitrary elastic anisotropy and arbitrary (continuous) transverse variation of physical properties are constructed. The applied method is based on Cauchy sextic formalism coupled with the stratification convergence theorem for FG plates. The constructed solutions are obtained in the form of vanishing auxiliary determinants related to derivatives of the closed form solutions of dispersion equations. [ABSTRACT FROM AUTHOR]

Lamb waves propagating in anisotropic functionally graded (FG) plates with an arbitrary continuous transverse inhomogeneity are considered. Along with the FG plates, stratified ones with the homogeneous physical properties inside the individual layers, are considered. Theorem on convergence of dispersion curves in stratified plates to the corresponding dispersion curves in the FG plates is proved, allowing one to analyze dispersion of Lamb waves in FG plates by constructing the less complicated solutions related to stratified plates. Numerical examples for isotropic FG and stratified plates are considered. [ABSTRACT FROM AUTHOR]

Dispersion of Lamb waves propagating in stratified and functionally graded (FG) plates is analyzed by a newly developed variant of Cauchy sextic formalism. Comparative analysis of Lamb wave dispersion in stratified, FG, and homogenized plates reveals a substantial discrepancy in dispersion properties of the studied media, making the use of homogenization techniques almost meaningless, with the only exception at the limiting phase velocity that corresponds to vanishing frequency. At the same time, dispersion curves in the stratified plates converge to the corresponding curves in the FG plate at the increasing number of the stratification layers. [ABSTRACT FROM AUTHOR]

Propagation of Lamb waves in both laminated and functionally graded (FG) composites is analyzed. Anomalous dispersion at high frequencies is observed revealing substantial discrepancy in the high frequencies asymptotes for quasi-flexural and quasi-symmetric fundamental modes. The applied methodology is based on a variant of sextic complex formalism. [ABSTRACT FROM AUTHOR]

Propagation of harmonic Lamb waves in plates made of functionally graded materials with transverse inhomogeneity is analyzed by applying Cauchy six-dimensional formalism previously developed for the study of Lamb wave propagation in homogeneous or stratified anisotropic plates. For anisotropic plates with arbitrary transverse inhomogeneity a closed form implicit solution for the dispersion equation is derived and analyzed. [ABSTRACT FROM AUTHOR]

Propagation of harmonic Lamb waves in plates made of functionally graded materials with transverse inhomogeneity is studied by the modified Cauchy six-dimensional formalism. For arbitrary transverse inhomogeneity, a closed-form dispersion equation is derived. Dispersion relations for materials with different kinds of inhomogeneity are obtained and compared. [ABSTRACT FROM AUTHOR]

Lamb waves propagating in a layered structure consisting of layers with equal acoustic impedances, is studied by a variant of Cauchy sextic formalism and the exponential fundamental matrix method. It is shown that the dispersion portraits provide enough information to distinguish individual layers, even if their acoustic impedances are identical, making such layers indistinguishable by the pulse – echo method. It is revealed that the developed methodology is adequate for determining geometrical and physical properties of the individual layers with equal acoustic impedances. [ABSTRACT FROM AUTHOR]

Dispersion of guided waves propagating in layered media containing layers with equal acoustic impedances is analyzed by Cauchy sextic formalism coupled with the exponential fundamental matrix method. The cases of layers with equal acoustic impedances apparently have not been studied yet. However, dispersion in such a medium exhibits several peculiarities that may be essential for developing the acoustic non-destructive testing methods. • Dispersion of guided waves propagating in layered media containing layers with equal acoustic impedances is analyzed. • Cauchy sextic formalism coupled with the exponential fundamental matrix method is used. • The cases of layers with equal acoustic impedances are studied. • Dispersion exhibits the anomalous behavior. • The outer layers become invisible. [ABSTRACT FROM AUTHOR]

Propagation of Lamb waves in multilayered elastic anisotropic plates is studied in the framework of combination of the six dimensional Cauchy formalism and the transfer matrix method. The closed form secular equations for dispersion curves of Lamb waves propagating in multilayered plates with arbitrary elastic anisotropy are obtained. [ABSTRACT FROM AUTHOR]

A six-dimensional complex formalism for analysis of Lamb waves propagating with subsonic speed in anisotropic plates is formulated. Conditions for nonexistence of certain Lam'' waves in anisotropic plates are obtained. An example of transversely isotropic plate having "forbidden" speed at which no subsonic Lamb wave propagates is presented. [ABSTRACT FROM AUTHOR]

This paper presents an efficient hybrid asynchronous three-dimensional (3D) perfectly matched layer (PML) for modeling unbounded domains. The proposed unsplit explicit or implicit 3D PML formulation is implemented in the framework of a heterogeneous asynchronous time integrator. It is fully versatile in terms of time integrators and time step sizes according to partitions while conserving classical finite element formulations in the elastic domain without complex-valued stretched coordinates. Examples of a semi-infinite bar, Lamb's test, and a soil-structure interaction problem with PML-truncated semi-infinite heterogeneous media are investigated to illustrate the efficiency of the proposed PML in terms of accuracy and CPU time. [ABSTRACT FROM AUTHOR]

The establishment of reliable correlations between parameters of damage and a sensor response during automatic NDI is first aim of present paper. Second, and it is main aim, is estimation of efficiency different approaches of the fatigue crack prediction at use of scalar parameters of a signal-response. Investigation of ultrasonic Lamb wave interaction with a fatigue crack has been executed on flat samples from an aluminum alloy 2024-?3 by thickness 1??. Three parameters of response were selected for their efficiency comparison. Standard deviation of a predicted fatigue crack was used for comparison. Quite definitely it is possible to conclude, that the given technology of NDT over use of ultrasonic waves is quite capable to provide high stability and necessary accuracy at the continuous integrated SHM of thin-walled aluminum components of aircraft. Result of this research shows that multi-parametric criterion can be used. It is shown also the accuracy of damage predicting is one of the most significant parameter of SHM efficiency. It can be used as the main criterion at selection of diagnostic parameters for continuous integrated monitoring of structural elements of aircraft. [ABSTRACT FROM AUTHOR]

This paper presents a benchmark for three-dimensional explicit asynchronous absorbing layers for modeling unbounded domains through a standard displacement-based finite element method: Three-dimensional Perfectly Matched Layers (PML) is compared to recently proposed Absorbing Layers with Increasing Damping (ALID) based on Rayleigh and Kosloff damping formulations. The coupled problem, including the interior subdomain and the absorbing layers, is implemented in the framework of Heterogeneous Asynchronous Time Integrator (HATI), enabling the absorbing layers to be handed with an explicit Central Difference scheme, with fine time steps, independently from the time stepping procedure adopted in the interior subdomain. Simple 3D Lamb's tests are considered by using different kinds of absorbing layers. The superiority of the PML in terms of the accuracy and computation time is highlighted. Finally, realistic 3D applications are investigated, such as the Lamb's test and the study of the screening effect provided by a horizontal wave barrier in mitigating the ground surface vibration generated by an excited plate. [ABSTRACT FROM AUTHOR]