Search

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]

Dispersion analysis of acoustic guided waves, propagating in a stratified medium, containing an internal sandy layer in contact with the isotropic elastic substrate and the upper elastic isotropic layer, is developed by applying the modified Cauchy formalism coupled with the exponential fundamental matrices and the Thomson–Haskell transfer matrix method. The developed approach is suitable for analyzing dispersion properties of guided waves at the broad variation of the sandy parameter. Several phenomena, concerning anomalous dispersion of guided waves at varying sandy parameter, are observed, revealing the possibility of nondestructive evaluation of sandy layers within the upper crust. [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]

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]

Nonlinear torsional waves propagating in cylindrical shells made of hyperelastic material obeying Ogden model, are studied by a combined approach comprising theoretical and finite element analysis. It was found, apparently for the first time, that delta-like pulses of torsional waves attenuate with distance due to the appearance of shock wave fronts. Moreover, both strain and kinetic mechanical energy dissipate due to the release of thermal energy. • Nonlinear torsional waves are analyzed. • Ogden hyperelastic potential is introduced. • Delta-like pulse propagation in a thin cylindrical shell is analyzed. • The appearance of shock wave fronts is observed. • Finite element approach is used. [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]

The exact solutions of the linear Pochhammer–Chree equation for propagating harmonic waves in a cylindrical rod are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed and analytical expressions for displacement fields are obtained. The variation of wave polarization on the free surface due to the variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear speed all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer–Chree waves can propagate at this phase speed. [ABSTRACT FROM AUTHOR]

The exact solutions of the linear Pochhammer - Chree equation for propagating harmonic waves in a cylindrical rod, are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of wave polarization on the free surface due to variation of Poisson's ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear wave speed all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer - Chree wave can propagate at this phase speed. [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]

SUMMARY The manuscript presents a dispersive nonlinear continuum theory for the case where the shortest wavelength is several times larger than the characteristic size of the microstructure and the observation window is large. We develop a general purpose computational framework, which is valid for nonlinear problems and requires standard C 0 continuous formalism. The fine-scale inertia effect is accounted for by formulating a quasi-dynamic unit cell problem where the fine-scale inertia effect is represented by so-called inertia induced eigenstrain. The solution of the nonlinear quasi-dynamic unit cell problem gives rise to the modification of either coarse-scale mass matrix in the implicit solvers or internal force in the explicit solvers. Similarly to the classical homogenization theory, scale-separation is assumed, but higher order homogenization is not pursued to avoid higher order coarse-scale gradients, higher order continuity, and higher order boundary conditions. Numerical examples for both the one-dimensional model problem and three-dimensional heterogeneous medium with layered and fibrous composite microstructure are used to validate the computational framework proposed. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]