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 the present paper we derive improved approximations for the Rayleigh wave velocity in the interval ν ∈ [−1, 0.5] using the method of least squares. In particular: (i) We create approximate polynomials of order 4, 5, 6 whose maximum percentage errors are 0.035 %, 0.015 %, 0.0083 %, respectively. (2i) Improved approximations in the form of the inverse of polynomials of order 3, 5 are also established. They are approximations with very high accuracy. (3i) By using the best approximate second-order polynomial of the cubic power in the space C[0.474572, 0.912622], we derive an approximation that is the best, so far, of the approximations obtained by approximating the secular equation.

/pdf/improved-approximations-for-the-rayleigh-wave-velocity-in-1-sfaic65gn0.pdf

Improved approximations for the rayleigh wave velocity in [-1, 0.5]

The main aim of this paper is to derive homogenized equations in explicit form of the linear piezoelectricity in two-dimensional domains separated by an interface which highly oscillates between two parallel straight lines. First, the basic equations of the linear theory of piezoelectricity are written down in matrix form. Then, following the techniques presented recently by these authors, the explicit homogenized equation and the associate continuity condition, for generally anisotropic piezoelectric materials, are derived. They are then written down in component form for some specific cases. Since the obtained equations are totally explicit, they are significant in practical applications.

Homogenization of very rough interfaces separating two piezoelectric solids

In this paper, the propagation of Stoneley waves along the interface between two orthotropic elastic half-spaces is investigated. The half-spaces are compressible or incompressible and they are in spring contact with each other. The main aim of the paper is to derive secular equations and formulas for the ratios of displacement components at the interface and to show that Stoneley waves are a good tool for evaluating the quality of imperfect bonds modeled as spring contacts. First, the secular equation and the formulas for the displacement-component ratios for the compressible case (two half-spaces are compressible) are derived. Then, those for the incompressible cases (one or both half-spaces are incompressible) are obtained by using the incompressible limit method. The obtained secular equations reveal that, while Stoneley waves are non-dispersive for the welded contact and the sliding contact, they are dispersive for the spring contact. Employing the obtained secular equations and formulas for the displacement-component ratios, two particular examples are carried out for determining the spring constants from the measured values of the displacement-component ratios and the wave velocity. It is shown that the ratios of displacement components at two sides of the interface are the best choice for evaluating the quality of imperfect bonds.

Stoneley waves with spring contact and evaluation of the quality of imperfect bonds

Rayleigh waves in anisotropic porous media and the polarization vector method

This paper concerns the propagation of Rayleigh waves in compressible and incompressible orthotropic elastic half-spaces. The main aim of the paper is to derive formulas for the H/V ratio (...

Pham Chi Vinh

Papers

Improved approximations for the rayleigh wave velocity in [-1, 0.5]

Homogenization of very rough interfaces separating two piezoelectric solids

Stoneley waves with spring contact and evaluation of the quality of imperfect bonds

Rayleigh waves in anisotropic porous media and the polarization vector method

Formulas for the H/V ratio (ellipticity) of Rayleigh waves in orthotropic elastic half-spaces