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AbstractAn explicit equation is derived for the condition of non-semisimple degeneracy of the fundamental matrix and, hence, the occurrence of anomalous guided waves propagating along the crystallographic axes of a cubic crystal. It is revealed that the observed non-semisimple degeneracy appears at a certain phase velocity in any cubic crystal of type I, but this kind of degeneracy is not possible in cubic crystals of type II. The analysis is based on the Cauchy sextic formalism combined with the spectral analysis of the fundamental matrix. [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]

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]

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]