Semiclassical analysis of elastic surface waves (original) (raw)

Surface waves of non-Rayleigh type

Quarterly of Applied Mathematics, 2003

Existence of surface waves of non-Rayleigh type propagating on some anisotropic elastic half-spaces is proved. Conditions for originating the non-Rayleigh type waves are analyzed. An example of a transversely isotropic material admitting a surface wave of the non-Rayleigh type is constructed.

Sh surface Waves in a Homogeneous Gradient-Elastic Half-Space with Surface Energy

1997

The existence of SH surface waves in a half-space of homogeneous material (i.e. anti-plane shear wave motions which decay exponentially with the distance from the free surface) is shown to be possible within the framework of the generalized linear continuum theory of gradient elasticity with surface energy. As is well-known such waves cannot be predicted by the classical theory of linear elasticity for a homogeneous half-space, although there is experimental evidence supporting their existence. Indeed, this is a drawback of the classical theory which is only circumvented by modelling the half-space as a layered structure (Love waves) or as having non-homogeneous material properties. On the contrary, the present study reveals that SH surface waves may exist in a homogeneous halfspace if the problem is analyzed by a continuum theory with appropriate microstructure. This theory, which was recently introduced by Vardoulakis and co-workers, assumes a strain-energy density expression containing, besides the classical terms, volume strain-gradient and surface-energy gradient terms.

A Hamiltonian Representation of Surface Waves

This paper presents an application of the Hamiltonian formalism to the study of the initial value water wave problem, aiming to develop numerical techniques for solving the complete nonlinear Hamilton equations. These equations belong to the class of functional differential equations (fde), i.e. to the class of differential equations having operator coefficients, which are dependent on the unknown liquid domain. The operator coefficient of the fde models the kinematical constrains of the system, while the fde itself models the dynamics of the system. The discrete system of dynamic equations was obtained with the aid of a specific canonical transformation fitting to the general scheme of the momentum representations. The main idea behind this treatment is to replace the continuous space variables represented by the free surface elevation and the velocity potential at the free surface with a discrete spectral expansion. In this context the normalized Cebycev-Hermite polynomials have b...

Surface waves in a periodic two-layered elastic half-space with the boundary normal to the layering

Acta Mechanica, 2009

The paper deals with the problem of surface waves in a vertically layered elastic half-space. The transmitting medium is composed of periodically repeated two-constituent laminae, and its boundary is assumed to be normal to the layering. The problem is solved using an approximate model proposed by Woźniak (Int J Eng Sci 25:483-499, 1987) and Matysiak and Woźniak (Int J Eng Sci 25: [549][550][551][552][553][554][555][556][557][558][559] 1987), which is referred to as the homogenized model with microlocal parameters. The velocity of the surface wave is obtained as a function of geometric and dynamic properties of the laminae. The variation of the surface wave velocity with respect to composite constituents is illustrated by numerical examples.

Laterally dependent surface waves in an elastic medium with a general depth dependence

Wave Motion, 2009

We consider waves in layered elastic structure with arbitrary vertical dependence of parameters, in assumption of rotation invariance of the problem. The goal is generalisation of the traditional form of the solution uðx; y; zÞ ¼ expðikxÞvðzÞ with z depth and ðx; yÞ lateral variables, to general lateral dependence. We derive a general integral representation for surface or interfacial wave field, and consider as its particular cases, waves with plane wavefronts and polynomial amplitudes and waves, showing Gaussian-type localisation with respect to ðx; yÞ. We mention a possibility of surface and interfacial waves, inhomogeneous with respect to lateral variables.

Surface waves in a periodic two-layered elastic half-space

Acta Mechanica, 1992

The paper deals with surface waves propagating through a periodic two-layered elastic half-space. The analysis is performed on the basis of a homogenized model with microlocal parameters. The velocity of the surface wave is obtained as a function of geometric and dynamic properties of the subsequent layers. The numerical examples illustrating the variations of the surface wave velocity are presented.

Cauchy Formalism in the Theory of Acoustic Surface Waves

Mechanics of Solids

To describe the propagation of acoustic surface waves in an anisotropic layer, a six-dimensional complex formalism is introduced, a Hamiltonian is constructed, an analogue of the Rayleigh dissipative function, and an exponential fundamental matrix. Dispersion equations are obtained for a multilayer plate with different conditions on the boundary surfaces. Examples of the application of the Cauchy formalism to the analysis of the dispersion of Lamb waves are given.

On the existence of surface waves in an elastic half-space with impedance boundary conditions

Wave Motion, 2012

In this work, the problem of surface waves in an isotropic elastic half-space with impedance boundary conditions is investigated. It is assumed that the boundary is free of normal traction and the shear traction varies linearly with the tangential component of displacement multiplied by the frequency, where the impedance corresponds to the constant of proportionality. The standard traction-free boundary conditions are then retrieved for zero impedance. The secular equation for surface waves with impedance boundary conditions is derived in explicit form. The existence and uniqueness of the Rayleigh wave is properly established, and it is found that its velocity varies with the impedance. Moreover, we prove that an additional surface wave exists in a particular case, whose velocity lies between those of the longitudinal and the transverse waves. Numerical examples are presented to illustrate the obtained results.

Non-principal surface waves in deformed incompressible materials

International Journal of Engineering Science, 2005

The Stroh formalism is applied to the analysis of infinitesimal surface wave propagation in a statically, finitely and homogeneously deformed isotropic half-space. The free surface is assumed to coincide with one of the principal planes of the primary strain, but a propagating surface wave is not restricted to a principal direction. A variant of Taziev's technique [Sov. Phys. Acoust. 35 (1989) 535] is used to obtain an explicit expression of the secular equation for the surface wave speed, which possesses no restrictions on the form of the strain energy function. Albeit powerful, this method does not produce a unique solution and additional checks are necessary. However, a class of materials is presented for which an exact secular equation for the surface wave speed can be formulated. This class includes the wellknown Mooney-Rivlin model. The main results are illustrated with several numerical examples. arXiv:1304.6235v1 [cond-mat.soft] 23 Apr 2013

Semiclassical inverse spectral problem for elastic Rayleigh waves in isotropic media

arXiv (Cornell University), 2019

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [6] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio is constant, we establish uniqueness and present a reconstruction scheme for the S-wave speed with multiple wells from the semiclassical spectrum of these waves.