On the parametric model of loose bonding between poroelastic half-spaces

2011 ◽  
Vol 18 (9) ◽  
pp. 1261-1274 ◽  
Author(s):  
C Nageswara Nath ◽  
M Tajuddin ◽  
JM Kumar
Keyword(s):  
Wave Propagation ◽  
Viscous Liquid ◽  
Liquid Layer ◽  
Shear Viscosity ◽  
Secular Equation ◽  
Parametric Model ◽  
Interfacial Waves ◽  
Bonded Interface ◽  
Special Cases ◽  
Loose Bonding

Wave propagation in a Newtonian viscous liquid layer of thickness ‘ h’ and of shear viscosity ‘ η’ bounded by two poroelastic half-spaces is studied. Possible bonding between the poroelastic half-spaces is discussed by considering the limiting forms of the secular equation, when h→0: (1) η is finite or η→0 such that η/h → ∞, (2) η→0 such that η/h → 0, (3) η → 0 such that η/h is a finite nonzero quantity, for each permeable and impermeable surface. It is shown that these three forms respectively represent welded, smooth and loosely bonded interface of poroelastic half-spaces. The secular equation for the interfacial waves for each of the above three types of bonding for infinite wavelength is derived as a particular case. It is observed that this secular equation is the same for all three types of bonding for each permeable and impermeable surface. Several other special cases are obtained.

Analysis of wave motion in transversely isotropic elastic material with voids under a inviscid liquid layer

2009 ◽  
Vol 87 (4) ◽  
pp. 377-388 ◽  
Author(s):  
Rajneesh Kumar ◽  
Rajeev Kumar
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Liquid Layer ◽  
Elastic Material ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Inviscid Liquid ◽  
Isotropic Elastic Material ◽  
Special Cases

The present investigation is to study the surface wave propagation in a semi-infinite transversely isotropic elastic material with voids under a homogeneous inviscid liquid layer. The frequency equation is derive after developing the mathematical model. The dispersion curves giving the phase velocity and attenuation coefficients versus wave numbers are plotted graphically to depict the effects of voids for (i) a transversely isotropic elastic half-space with voids under a homogeneous inviscid liquid layer and (ii) a transversely isotropic elastic half-space with voids. The particle path is also obtained for Rayleigh wave propagation in a transversely isotropic elastic half-space with voids, i.e., case (ii). The amplitudes of the displacements, the volume fraction field, and the normal stresses in both the media are obtained and are shown graphically for a particular model to depict the voids and anisotropy effects. Some special cases are also deduced from the present investigation.

On a technique for deriving explicit transfer matrices of orthotropic layers

2015 ◽  
Vol 37 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Half Space ◽  
Transfer Matrix ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Transfer Matrices ◽  
Orthotropic Layer ◽  
Wave Propagation Problem ◽  
Arbitrary Thickness

This paper presents  a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

scholarly journals The information complexity of learning tasks, their structure and their distance

2021 ◽  
Author(s):  
Alessandro Achille ◽  
Giovanni Paolini ◽  
Glen Mbeng ◽  
Stefano Soatto
Keyword(s):  
Kolmogorov Complexity ◽  
Large Scale ◽  
Parametric Model ◽  
Training Dataset ◽  
Optimization Scheme ◽  
Learning Tasks ◽  
Asymmetric Distance ◽  
Special Cases ◽  
Scale Models ◽  
Real World Datasets

Abstract We introduce an asymmetric distance in the space of learning tasks and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task, and then fine tuned for another. The framework we develop is non-asymptotic, captures the finite nature of the training dataset and allows distinguishing learning from memorization. It encompasses, as special cases, classical notions from Kolmogorov complexity and Shannon and Fisher information. However, unlike some of those frameworks, it can be applied to large-scale models and real-world datasets. Our framework is the first to measure complexity in a way that accounts for the effect of the optimization scheme, which is critical in deep learning.

Wave Propagation in the Linear Theory of Elastic Shells

1976 ◽  
Vol 43 (2) ◽  
pp. 281-285 ◽  
Author(s):  
H. Cohen
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Linear Theory ◽  
Wave Mode ◽  
Mode Shapes ◽  
Elastic Shells ◽  
Special Cases ◽  
Cosserat Surface ◽  
Singular Wave ◽  
The Right

The problem of wave propagation in elastic shells within the framework of a linear theory of a Cosserat surface is treated using the method of singular wave curves. The equations for determining the speeds of propagation and their associated wave mode shapes are obtained in a form involving the speeds of propagation in Cosserat plates and the curvature of the shell. A number of special cases in which the speeds and mode shapes simplify are considered. In particular, these special cases are shown to include as examples, certain systems of waves in elastic shells whose middle surfaces are the surface of revolution, the circular cylinder, the sphere, and the right helicoid.

scholarly journals Motion of a Viscous Liquid Layer Covered by a Thin Plate Subject to Gas Stream

1982 ◽  
Vol 25 (199) ◽  
pp. 32-37
Author(s):  
Eiji HASEGAWA ◽  
Masaru TANABE
Keyword(s):  
Viscous Liquid ◽  
Thin Plate ◽  
Liquid Layer

Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shishir Gupta ◽  
Rishi Dwivedi ◽  
Smita Smita ◽  
Rachaita Dutta
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Rayleigh Wave ◽  
Penetration Depth ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Rayleigh Surface Wave ◽  
Content Type

Purpose The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Design/methodology/approach The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves. Findings The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Originality/value Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

scholarly journals Precise Determination of Liquid Layer Thickness with Downward Annular Two-Phase Gas-Very Viscous Liquid Flow

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6529
Author(s):  
Krystian Czernek ◽  
Stanisław Witczak
Keyword(s):  
Viscous Liquid ◽  
Liquid Layer ◽  
Liquid Flow ◽  
Liquid Films ◽  
Measuring System ◽  
Image Analysis System ◽  
Oil Viscosity ◽  
Two Phase ◽  
Study Results

The paper presents the characteristics of the original optoelectronic system for measuring the values of hydrodynamics of two-phase downward gas-very viscous liquid flow. The measurement methods and results of the research on selected values describing gas–oil two-phase flow are presented. The study was conducted in vertical pipes with diameters of 12.5, 16, 22, and 54 mm. The research was conducted with the superficial velocities of air jg = 0–29.9 m/s and oil jl = 0–0.254 m/s, which corresponded to the values of gas stream density gg = (0–37.31) kg/(m2s) and of liquid gl = (0.61–226.87) kg/(m2s), in order to determine the influence of air and oil streams on the character of liquid films. The variations in oil viscosity were applied in the range ηl = (0.055–1.517) Pas. The study results that were obtained with optical probes along with computer image analysis system revealed vast research opportunities in terms of the identification of gas–liquid two-phase downward flow structures that were generated as well as the determination of the thickness of liquid film with various level of interfacial surface area undulation. The designed and constructed proprietary measuring system is also useful for testing the liquid layer by determining the parameters of the resulting waves. It is considered that the apparatus system that is presented in the article is the most effective in examining the properties of liquid layers of oil and other liquids with low electrical conductivity and a significant degree of monochromatic light absorption. In view of noninvasive technique of measuring characteristic values of liquid films being formed, the above measuring system is believed to be very useful for industry in the diagnostics of the apparatus employing such flows.

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