Rayleigh wave propagation in human skin: A multiphysics model of a natural fibrous composite incorporating nonlocal, micropolar, and thermal-memory effects

In an attempt to include the effects of natural porosity of lung parenchyma into the mathematical study of lung diagnostics, a model describing the propagation of low-frequency Rayleigh waves in relation to the porous architecture of the lung parenchyma is presented. The wave motion is analyzed by assuming that the lung parenchyma behaves as an isotropic elastic half-space containing a distribution of vacuous pores with the visceral pleura as a taut elastic membrane in smooth contact with the half-space. The thinness of the pleural membrane in comparison with the large surface area of contact enables it to be modeled as a material surface in contact with the parenchyma. Utilizing the perturbation technique, an approximate formula for the Rayleigh wave velocity in the parenchyma with allowance for surface tension, mass density, and porosity is derived. In addition, the effect of the tension in the pleural membrane and the porosity in the parenchyma on the propagation of the low-frequency Rayleigh waves is brought out through the dispersion spectrum. It is hoped that the results of this paper would enable a better understanding of the porosity and surface-tension effects on lung parenchyma.

The present paper investigates the propagation of anti-plane Rayleigh waves in an elastic three-layered inhomogeneous plate in the presence of viscous damping. The core layer is sandwiched between skin layers with appropriate perfect interfacial boundary conditions, while traction-free conditions are prescribed on the outer faces. The eigenfunctions expansion method is employed for the study. Various cases of damped and undamped situations have been examined in connection to the obtained displacements and shear stresses. Finally, the effects of viscous damping on the propagation of Rayleigh waves are reported graphically using some physical available data.

Propagation of Rayleigh waves on curved surfaces

In this paper the effects of heat conduction upon the propagation of Rayleigh surface waves in a semi-infinite elastic solid are studied theoretically in two special cases: (i) when the surface of the solid is maintained at constant temperature (case 1); and (ii) when the surface is thermally insulated (case 2). The investigation is carried out within the framework of the linear theory of thermoelasticity, a principal objective being the clarification of the relation between so-called thermoelastic Rayleigh waves and the Rayleigh waves of classical elastokinetics. The secular equation for thermoelastic Rayleigh waves is shown to define a many-valued algebraic function μ(X ) (X being a dimensionless frequency) the branches of which represent possible modes of surface wave propagation. Two different types of surface mode are recognized: E-modes, which resemble classical Rayleigh waves but are subject to damping and dispersion; and T-modes, which are essentially diffusive in character. Necessary and sufficient conditions for the existence of a surface wave are formulated, and questions of the existence and multiplicity of Rayleigh E- and T-modes in particular situations are resolved by submitting the branches of μ(X) to these requirements. The algebraic function μ(X ) has singular points at X = 0 and X = ∞, and approximations, valid at sufficiently low or at sufficiently high frequencies, to the speed of propagation v and the attenuation coefficient q of a given surface mode are obtainable from series representations of the appropriate branch of μ(X) in neighbourhoods of these singularities. The singular point X = 0 is associated with adiabatic deformations of the solid, and hence with classical Rayleigh waves, and the singularity at X = ∞ with isothermal deformations. Particular attention is devoted to the Rayleigh E-modes and the main conclusions reached are as follows. In case 1 there exists a single E-mode (mode 2) at low frequencies and two distinct E-modes (modes 1 and 2) at high frequencies. For mode 2, v/vR = 1 + O(X½), q = O(X3/2) Xdistinct 0 (vR being the speed of propagation of classical Rayleigh waves), and for both modes v and q approach finite limits as X → ∞. In case 2 the converse situation applies, there being two distinct E-modes (modes 1 and 2) at low frequencies and only one (mode 1) at high frequencies. For both modes, v/vR = 1 + O(X3/2), q = O(X2) as X → 0, and for mode 1, v and q approach finite limits as X → ∞. Detailed numerical results referring to a medium of worked pure copper at a reference temperature of 20 °C are given. In particular the frequency dependence of the speeds of propagation and attenuation coefficients of the various E-modes are exhibited, and the frequencies at which mode 1 appears in case 1 and at which mode 2 disappears in case 2 are determined.

Propagation and attenuation of Rayleigh waves in a partially-saturated porous solid with impervious boundary

Propagation of harmonic plane waves is considered in an orthotropic elastic medium in the presence of initial stress and gravity. Roots of a quadratic equation define the propagation of one quasi-longitudinal wave and one quasi-transverse wave in a symmetry plane in this medium. These two waves are coupled in the identical phase to define the propagation of Rayleigh waves at the boundary of the medium. Two conditions at the stress-free boundary translate into a complex frequency equation, which explains the dispersive behavior of this Rayleigh wave. For the presence of radical terms, this complex equation is rationalized into a real algebraic equation. Only one root of this algebraic equation satisfies the mother frequency equation and hence represents the propagation of dispersive Rayleigh waves at the boundary of the orthotropic solid. The influence of initial stress and gravity on velocity and polarization of Rayleigh waves is observed through a numerical example.

This study considers the propagation of Rayleigh waves in a generalized thermoelastic half-space with stress-free plane boundary. The boundary has the option of being either isothermal or thermally insulated. In either case, the dispersion equation is obtained in the form of a complex irrational expression due to the presence of radicals. This dispersion equation is rationalized into a polynomial equation, which is solvable, numerically, for exact complex roots. The roots of the dispersion equation are obtained after removing the extraneous zeros of this polynomial equation. Then, these roots are filtered out for the inhomogeneous propagation of waves decaying with depth. Numerical examples are solved to analyze the effects of thermal properties of elastic materials on the dispersion of existing surface waves. For these thermoelastic Rayleigh waves, the behavior of elliptical particle motion is studied inside and at the surface of the medium. Insulation of boundary does play a significant role in changing the speed, amplitude, and polarization of Rayleigh waves in thermoelastic media.

Three dimensional magneto-elastic equations pertaining to the problem of propagation of axial Rayleigh waves on the surface of elastic cylinder of isotropic material have been solved. Two cases have been considered — first, when the density varies linearly and second, when it varies inversely as the radius vector and frequency equations for both the cases have been obtained.

Theoretical and experimental work on magnetoacoustic surface waves in ferro- and antiferromagnets is reviewed. Results on the propagation of Rayleigh and Lamb magnetoelastic waves in a plate are presented within the framework of a rotation- and translation-invariant theory. Spectra of the shear surface magnetoacoustic waves (SSMAWs) caused by effects of magnetostriction and piezomagnetism are also considered with emphasis on the vicinity of reorientation phase transitions. The problem types of soft modes involved in phase transitions is discussed in detail. A comparison is made of experimental results and theoretical predictions on the propagation of Rayleigh waves in magnetic materials.

According to thermoviscoelastic theory, the relations of laser-generated Rayleigh waves in viscoelastic plates with thermophysical and viscoelastic properties are investigated quantitatively. The displacement spectra are calculated in the frequency domain using the finite element method, and the temporal displacement waveforms are obtained by applying inverse fast Fourier transforms. And then, the effects of the laser parameters, including the laser spot radius, pulse rise time, and optical penetration depth, on the propagation of laser-generated Rayleigh waves are studied. In addition, the influence of the increase of each elastic modulus and viscous modulus of the viscoelastic plates on laser-generated Rayleigh waves is investigated in detail.

Nonlocal scale effect on Rayleigh wave propagation in porous fluid-saturated materials

Magneto-thermoelastic surface waves phenomenon with voids, gravity, initial stress, and rotation under four theories

This paper evaluates the response of the seven‐story instrumented building, Holiday Inn Hotel, during the 1994 Northridge earthquake through the wave propagation dynamic analysis. The building has been instrumented during other earthquakes, the most important of these was the 1971 San Fernando earthquake, where the building was located only 22 [km] from the epicenter and didn't showing structural damage. From the accelerograms analysis is detected the propagation of Rayleigh and soil waves in the building, where the first has a polarized particle motion on a vertical plane and the second has a coupled particle motion in the horizontal plane. Both waves impose their frequencies to the building response, whose fundamental frequency (1.4 [Hz] according to ambient vibration test) is less than the frequencies of the identified waves. Due to the impact that these observations have in the seismic design of buildings, as a first attempt, a simple method is proposed to estimate the drift produced by the propagation of a Rayleigh wave in buildings.

Generation of rayleigh waves by picosecond laser pulses

Bone is a inhomogeneous hierarchical material with different microstructure at different length scales. On the other hand, the constituent materials (mineral, proteins, water and polysaccharides) and the fluid in bone pores give rise of viscoelastic behavior. In the present work, the effect of bones mi-crostructure and its viscoelastic properties on the propagation of Rayleigh waves is investigated. Microstructural effects are taken into account through Mindlin's general gradient elastic theory. A composite material model proposed by Ben-Amoz is employed for the determination of the intrinsic parameters imposed by Mindlin's theory. Viscoelasticity is introduced via convolution integrals and proper relaxation functions valid for bones. All the gradient viscoelastic problems are solved via the Boundary Element Method and exploiting the correspondence principle. The results reveal that both microstructure and viscoelastic properties affect significantly the propagation and dispersion of Rayleigh waves in long bones.