Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)


 The spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background. The aim of this article is to formulate the H/V technique in terms of the characteristics of Rayleigh and Love waves, and to contribute to improve the technique. The improvement includes use of not only peaks but also troughs in the H/V ratio for reliable estimation of the period and use of a newly proposed smoothing function for better estimation of the amplification factor. The formulation leads to a simple formula for the amplification factor expressed with the H/V ratio. With microtremor data measured at 546 junior high schools in 23 wards of Tokyo, the improved technique is applied to mapping site periods and amplification factors in the area.

Ground Motion Characteristics Estimated from Spectral Ratio between Horizontal and Verticcl Components of Mietremors.

The English-language dictionary defines wrinkles as "small furrows, ridges, or creases on a normally smooth surface, caused by crumpling, folding, or shrinking". In this paper we review the scientific aspects of wrinkling and the related phenomenon of buckling. Specifically, we discuss how and why wrinkles/buckles form in various materials. We also describe several examples from everyday life, which demonstrate that wrinkling or buckling is indeed a commonplace phenomenon that spans a multitude of length scales. We will emphasize that wrinkling is not always a frustrating feature (e.g., wrinkles in human skin), as it can help to assemble new structures, understand important physical phenomena, and even assist in characterizing chief material properties.

Soft matter with hard skin : From skin wrinkles to templating and material characterization

A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress-strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of particular value. It enables the limiting values of all nine fourth-order elastic constants in the incompressible limit to be evaluated precisely and rigorously. In particular, it is explained why the three constants of fourth-order incompressible elasticity μ, Ā, and D are of the same order of magnitude. Several examples of application of the results follow, including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation.

/pdf/on-the-third-and-fourth-order-constants-of-incompressible-1jy1wjrxfn.pdf

On the third- and fourth-order constants of incompressible isotropic elasticity.

In this paper, the propagation of Lamb waves in an orthotropic elastic sandwich plate is investigated. The surface layers and the core layer may be compressible or incompressible. The main aim of t...

Lamb waves in sandwich orthotropic elastic plates

Correction to: The incompressible limit method and Rayleigh waves in incompressible layered nonlocal orthotropic elastic media

In this paper, the following new results related to Rayleigh waves in incompressible elastic media under the influence of gravity are presented: (i) the exact formulas for the velocity of Rayleigh waves propagating along the free-surface of an incompressible isotropic elastic half-space under the gravity are derived, and (ii) two approximate formulas for the velocity of the Rayleigh waves are established and it is shown that their accuracy is very high. To derive the exact formulas, we use the theory of cubic equation, and to establish the approximate formulas, we employ the best approximate second-order polynomials of the cubic power. The obtained formulas are powerful tools for analyzing the effect of gravity on the propagation of Rayleigh waves and for solving the inverse problem.

New results on Rayleigh waves in incompressible elastic media subjected to gravity

This paper studies the propagation of Rayleigh waves in an orthotropic elastic half-space coated by a thin orthotropic elastic layer. The half-space and the layer are assumed to be either compressible or incompressible and they are in sliding contact with each other. The main aim of the paper is to establish approximate secular equations of the wave for all (four) possibilities of a compressible or incompressible half-space covered with a compressible or incompressible thin layer, except the case of a compressible half-space coated by a compressible layer that has been considered [19]. In order to do that, the effective boundary condition method is employed and the approximate third-order secular equations regarding the dimensionless thickness of the layer are derived. It is shown that these approximate secular equations have a high accuracy. Based on the obtained secular equations, the effect of incompressibility on the Raleigh wave propagation is considered through some numerical examples. It is shown that incompressibility strongly affects the Raleigh wave velocity and the effect becomes stronger when the coating is incompressible.

http://am.ippt.pan.pl/am/article/viewFile/v67p477/pdf

Effective boundary condition method and Rayleigh waves in orthotropic half-spaces coated by a thin layer with sliding contact

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

/pdf/homogenization-of-very-rough-three-dimensional-interfaces-1a2p8suudq.pdf

Pham Chi Vinh

Papers

Lamb waves in sandwich orthotropic elastic plates

Correction to: The incompressible limit method and Rayleigh waves in incompressible layered nonlocal orthotropic elastic media

New results on Rayleigh waves in incompressible elastic media subjected to gravity

Effective boundary condition method and Rayleigh waves in orthotropic half-spaces coated by a thin layer with sliding contact

Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model