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Peter G. Malischewsky - One of the best experts on this subject based on the ideXlab platform.
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A special relation between Young's modulus, Rayleigh-Wave Velocity, and Poisson's ratio.
The Journal of the Acoustical Society of America, 2009Co-Authors: Peter G. Malischewsky, Tran Thanh TuanAbstract:Bayon et al. [(2005). J. Acoust. Soc. Am. 117, 3469–3477] described a method for the determination of Young’s modulus by measuring the Rayleigh-Wave Velocity and the ellipticity of Rayleigh Waves, and found a peculiar almost linear relation between a non-dimensional quantity connecting Young’s modulus, Rayleigh-Wave Velocity and density, and Poisson’s ratio. The analytical reason for this special behavior remained unclear. It is demonstrated here that this behavior is a simple consequence of the mathematical form of the Rayleigh-Wave Velocity as a function of Poisson’s ratio. The consequences for auxetic materials (those materials for which Poisson’s ratio is negative) are discussed, as well as the determination of the shear and bulk moduli.
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IMPROVED APPROXIMATIONS FOR THE Rayleigh Wave Velocity IN [-1, 0.5]
Vietnam Journal of Mechanics, 2008Co-Authors: Pham Chi Vinh, Peter G. MalischewskyAbstract:In the present paper we derive improved approximations for the Rayleigh Wave Velocity in the interval \(\nu \in \) [−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.
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Improved Approximations of the Rayleigh Wave Velocity
Journal of Thermoplastic Composite Materials, 2008Co-Authors: Pham Chi Vinh, Peter G. MalischewskyAbstract:In this article we have derived some approximations for the Rayleigh Wave Velocity in isotropic elastic solids which are much more accurate than the ones of the same form, previously proposed. In p...
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Some new considerations concerning the Rayleigh-Wave Velocity in auxetic materials
physica status solidi (b), 2008Co-Authors: Fabrizio Scarpa, Peter G. MalischewskyAbstract:The Rayleigh Wave Velocity as examined in isotropic and non-isotropic auxetic (negative Poisson's ratio) solids. A novel approximation of the Rayleigh Wave speed c versus the Poisson's ratio of an isotropic solid is derived using the concept of ellipticity. The Rayleigh Wave propagation is investigated also for anisotropic incomprehensible solids, such as thick composite balanced symmetric cross-ply lamintes, exhibiting through-the-thickness negative Poisson's ratio. The results show increased Wave speed for auxetic laminate configurations, as well as increased sensitivity of the Wave speed in the cross-ply regions corresponding to NPR values.
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An improved approximation of Bergmann's form for the Rayleigh Wave Velocity.
Ultrasonics, 2007Co-Authors: Pham Chi Vinh, Peter G. MalischewskyAbstract:In the present paper an improved approximation for the Rayleigh Wave Velocity in isotropic elastic solids is obtained using the method of least squares. It is of Bergmann's form, i.e. the form of the ratio of two binomials. It is shown that this approximation is the best one of the Rayleigh Wave Velocity, in the sense of least squares, with respect to the class of functions whose elements are the ratio of two binomials. This approximation is much more accurate than Bergmann's one. Its maximum percentage error is 10 times smaller than that of Bergmann's. It is 7.6 times better than the one obtained recently by Royer and Clorennec [D. Royer, D. Clorennec, An improved approximation for the Rayleigh Wave equation, Ultrasonics 46 (2007) 23-24]. An approximation of Bergmann's form for the squared Rayleigh Wave Velocity is also derived and its maximum percentage error is 5 times smaller than that of Royer and Clorennec's approximation. Some polynomial approximations with very high accuracy are also obtained.
Pham Chi Vinh - One of the best experts on this subject based on the ideXlab platform.
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On formulas for the Rayleigh Wave Velocity in pre-stressed compressible solids
Wave Motion, 2011Co-Authors: Pham Chi VinhAbstract:Abstract In this paper, formulas for the Velocity of Rayleigh Waves in compressible isotropic solids subject to uniform initial deformations are derived using the theory of cubic equation. They are explicit, have simple algebraic forms, and hold for a general strain energy function. Unlike the previous investigations where the derived formulas for Rayleigh Wave Velocity are approximate and valid for only small enough values of pre-strains, this paper establishes exact formulas for Rayleigh Wave Velocity being valid for any range of pre-strains. When the prestresses are absent, the obtained formulas recover the Rayleigh Wave Velocity formula for compressible elastic solids. Since obtained formulas are explicit, exact and hold for any range of pre-strains, they are good tools for evaluating nondestructively prestresses of structures.
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On Formulas for the Velocity of Rayleigh Waves in Prestrained Incompressible Elastic Solids
Journal of Applied Mechanics, 2009Co-Authors: Pham Chi VinhAbstract:In the present paper, formulas for the Velocity of Rayleigh Waves in incompressible isotropic solids subject to a general pure homogeneous prestrain are derived using the theory of cubic equation. They have simple algebraic form and hold for a general strainenergy function. The formulas are concretized for some specific forms of strain-energy function. They then become totally explicit in terms of parameters characterizing the material and the prestrains. These formulas recover the (exact) value of the dimensionless speed of Rayleigh Wave in incompressible isotropic elastic materials (without prestrain). Interestingly that, for the case of hydrostatic stress, the formula for the Rayleigh Wave Velocity does not depend on the type of strain-energy function. © 2010 by ASME. Author Keywords: Incompressible; Prestrains; Prestresses; Rayleigh Wave Velocity; Rayleigh Waves Index Keywords: Cubic equations; Elastic materials; Elastic solids; Hydrostatic stress; Isotropic solids; Parameters characterizing; Pre-strain; Prestrains; Prestresses; Rayleigh Wave Velocity; Strain energy functions; Acoustic Wave Velocity; Strain energy; Wave propagation; Rayleigh Waves
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IMPROVED APPROXIMATIONS FOR THE Rayleigh Wave Velocity IN [-1, 0.5]
Vietnam Journal of Mechanics, 2008Co-Authors: Pham Chi Vinh, Peter G. MalischewskyAbstract:In the present paper we derive improved approximations for the Rayleigh Wave Velocity in the interval \(\nu \in \) [−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.
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Improved Approximations of the Rayleigh Wave Velocity
Journal of Thermoplastic Composite Materials, 2008Co-Authors: Pham Chi Vinh, Peter G. MalischewskyAbstract:In this article we have derived some approximations for the Rayleigh Wave Velocity in isotropic elastic solids which are much more accurate than the ones of the same form, previously proposed. In p...
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An improved approximation of Bergmann's form for the Rayleigh Wave Velocity.
Ultrasonics, 2007Co-Authors: Pham Chi Vinh, Peter G. MalischewskyAbstract:In the present paper an improved approximation for the Rayleigh Wave Velocity in isotropic elastic solids is obtained using the method of least squares. It is of Bergmann's form, i.e. the form of the ratio of two binomials. It is shown that this approximation is the best one of the Rayleigh Wave Velocity, in the sense of least squares, with respect to the class of functions whose elements are the ratio of two binomials. This approximation is much more accurate than Bergmann's one. Its maximum percentage error is 10 times smaller than that of Bergmann's. It is 7.6 times better than the one obtained recently by Royer and Clorennec [D. Royer, D. Clorennec, An improved approximation for the Rayleigh Wave equation, Ultrasonics 46 (2007) 23-24]. An approximation of Bergmann's form for the squared Rayleigh Wave Velocity is also derived and its maximum percentage error is 5 times smaller than that of Royer and Clorennec's approximation. Some polynomial approximations with very high accuracy are also obtained.
S. Sathish - One of the best experts on this subject based on the ideXlab platform.
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Quantitative imaging of Rayleigh Wave Velocity with a scanning acoustic microscope
IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2002Co-Authors: S. Sathish, R. W. MartinAbstract:An acoustic microscope operating with impulse excitation has been used to perform measurements of the Rayleigh Wave Velocity by measuring the time difference between the direct reflected signal and the Rayleigh Wave signal. The accuracy and precision of the methodology have been examined by performing measurements at a single location on an elastically isotropic sample of E6 glass. The accuracy of the Rayleigh Wave Velocity measurement has been determined to be better than 0.5%. The measured Rayleigh Wave Velocity of (3035/spl plusmn/5) m/s differs by 0.3% from measurements reported in the literature for a similar sample, using two different techniques. The methodology has been extended to acquire the Rayleigh Wave Velocity while raster scanning the sample to develop a quantitative Velocity image. The background noise in the Rayleigh Wave Velocity image has been investigated by mapping the Velocity on elastically isotropic E6 glass. Possible reasons for background noise in the images is discussed. The methodology has been extended to acquire quantitative Rayleigh Wave Velocity images on Ti-6Al-4V. The contrast in the images is attributed to the variation of the Rayleigh Wave Velocity in individual grains or regions. Applicability of the technique to investigate crystallographic texture in materials is discussed.
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Elastically isotropic Al-Li-Cu quasicrystal
Solid State Communications, 1991Co-Authors: S. Sathish, Andrzej J. Kulik, Gérard GremaudAbstract:Angular dependence of Rayleigh Wave Velocity has been measured in single grain quasi-crystals of Al-Li-Cu using a continuous Wave scanning acoustic microscope. The observed variation is quite small. This indicates the elastically isotropic nature of quasi-crystals.
J.-h Tong - One of the best experts on this subject based on the ideXlab platform.
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On the study of elastic Wave scattering and Rayleigh Wave Velocity measurement of concrete with steel bar
NDT & E International, 2000Co-Authors: Jia-hong Sun, J.-h TongAbstract:This paper presents results on a study of the Rayleigh Wave scattering and Rayleigh Wave Velocity measurement in concrete with a steel bar using transient elastic Waves. To study the characteristics of the scattered Waves induced by a steel bar in concrete, a three-dimensional heterogeneous finite difference formulation with staggered grids was adopted. The cases for both elastic Wave propagation parallel and perpendicular to the steel bar are discussed. The effect of the cover thickness and steel bar spacing on the Rayleigh Wave Velocity measurement was studied. To confirm the numerical investigations, a concrete specimen containing steel bar was made and the corresponding transient elastic Wave experiments were conducted. The numerical results are in good accordance with those of the measured. We note that the result of this study can serve as an important reference in the Rayleigh Wave Velocity measurement of concrete with steel bar.
Lluis Pujades - One of the best experts on this subject based on the ideXlab platform.
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First two-station Rayleigh-Wave Velocity measurements for the northern Iberian region
Bulletin of the Seismological Society of America, 1992Co-Authors: G. Payo, José Badal, V. Corchete, Francisco J. Serón, J. A. Canas, Lluis PujadesAbstract:Abstract Up to now, dispersion analysis of surface Waves across the Iberian Peninsula and adjacent zones has been based on analog data recorded at the long-period Iberian stations. Also, the northern region of the peninsula has never been investigated due to the lack of seismological stations. With the ILIHA data set now available, it is possible to investigate the northern part of Iberia from quality digital records. To efficiently remove higher-mode interference and to improve isolation of the fundamental-mode Rayleigh Wave from the seismograms, time-variable filtering is employed. Once the signal is filtered, multiple filtering is then used to compute group velocities at each station. The interstation Rayleigh-Wave group Velocity can thus be easily calculated. Frequency-domain Wiener deconvolution is used to determine the interstation phase Velocity. We carried out inversion of Velocity dispersion data containing both Rayleigh-Wave phase velocities and group velocities according to the generalized inversion theory by means of the stochastic inverse operator. The theoretical 2-D Earth models determined by joint inversion allow us to obtain for the first time the distribution of the shear-Wave Velocity both laterally and with depth for the northern Iberian region, and to emphasize the main features of the crust-mantle structure of this area.
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Deep structure of the Iberian Peninsula determined by Rayleigh Wave Velocity inversion
Geophysical Journal International, 1992Co-Authors: José Badal, V. Corchete, G. Payo, Francisco J. Serón, J. A. Canas, Lluis PujadesAbstract:SUMMARY A rigorous study of Velocity dispersion of surface Waves generated by teleseismic events propagating across the Iberian Peninsula and traversing main geological units, has been carried out from a set of selected analogue data, as digital records have only become available recently. Dispersed seismic signals have been obtained over a period of 16 years, between 1967 and 1982, at the five Iberian stations having long-period instruments. In our study, we have considered many earthquakes thus obtaining a fairly good path coverage of most of the peninsula for two-station Rayleigh Wave Velocity measurements. In all cases, the approach azimuths of the Wavefronts were carefully checked. Several digital filtering techniques have been employed to remove the effects of multipathing and modal contamination, and to isolate the fundamental mode from Rayleigh Wavetrains. Thus, we have obtained good estimates for both phase and group velocities. A time-variable filter has reduced the influence of noise and removed higher mode interference. Multiple filtering is then used to compute group Velocity. Frequency-domain Wiener deconvolution is used to compute the interstation phase Velocity. The determined average Rayleigh Wave velocities reveal differences in the propagation conditions of the seismic energy across the peninsula. A mapping of velocities for various periods of reference, together with a mapping of errors in Velocity, are the basis for obtaining the Rayleigh Wave Velocity distribution in the peninsula. Theoretical 2-D layered earth models are obtained by joint inversion of phase and group Velocity dispersion curves using the stochastic inverse operator. In our inversion scheme, we use velocities corrected for anelastic effects. Finally, a 3-D mapping of S Velocity is performed. This study shows important regional features of the deep structure of Iberia; we see small lateral inhomogeneities and also two low-Velocity layers: one with shear velocities usually ranging from 4.23 to 4.31 km s-1 directly under the Moho, and another, the asthenosphere, with a negative Velocity gradient for depths between 81 and 181 km, terminated at the bottom by a sharp discontinuity.
