Propagation of shear elastic waves in composites with a random set of spherical inclusions (effective field approach)

Kanaun, S. K.; Levin, V. M.

doi:10.1016/j.ijsolstr.2005.01.002

Cited by 29 publications

(11 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the long wave region, the method gives physically correct values of the velocities and attenuation factors of the mean wave field, and its predictions of the effective static elastic modules of particulate composites correspond to the numerical calculations and experimental data (see [10,13]). The error of the EFM in this region is essential for the composites with high contrast in properties of the matrix and inclusions and large volume concentrations of the latter ( p > 0.3).…”

Section: Resultsmentioning

confidence: 77%

“…Omitting long but evident calculations similar to the presented in Kanaun and Levin [13], we go to the long wave asymptotics of the coefficient M * in dispersion equation (4.27) in the form…”

Section: Solution Of the Dispersion Equation In The Long-wave Regionmentioning

confidence: 99%

“…The factor f and function (r ), depend only on geometrical properties of the random field of inclusions, and f ≥ 0 for any correlation function of a realizable spatially homogeneous random set of inclusions (see [13]). …”

Section: Solution Of the Dispersion Equation In The Long-wave Regionmentioning

confidence: 99%

“…This technique turned out to be more efficient for carrying out the averaging procedure. In the work of Kanaun and Levin [13], this technique was used for the solution of the problem of elastic shear wave propagation in particulate composites for arbitrary lengths of the propagating waves.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Propagation of longitudinal elastic waves in composites with a random set of spherical inclusions (effective field approach)

Kanaun

Levin

2007

Arch Appl Mech

View full text Add to dashboard Cite

The work is devoted to the problem of plane monochromatic longitudinal wave propagation through a homogeneous elastic medium with a random set of spherical inclusions. The effective field method and quasicrystalline approximation are used for the calculation of the phase velocity and attenuation factor of the mean (coherent) wave field in the composite. The hypotheses of the method reduce the diffraction problem for many inclusions to a diffraction problem for one inclusion and, finally, allow for the derivation of the dispersion equation for the wave vector of the mean wave field in the composite. This dispersion equation serves for all frequencies of the incident field, properties and volume concentrations of inclusions. The long and short wave asymptotics of the solution of the dispersion equation are found in closed analytical forms. Numerical solutions of this equation are constructed in a wide region of frequencies of the incident field that covers long, middle, and short wave regions of propagating waves. The phase velocities and attenuation factors of the mean wave field are calculated for various elastic properties, density, and volume concentrations of the inclusions. Comparisons of the predictions of the method with some experimental data are presented; possible errors of the method are indicated and discussed.

show abstract

Section: Resultsmentioning

confidence: 77%

Section: Solution Of the Dispersion Equation In The Long-wave Regionmentioning

confidence: 99%

Section: Solution Of the Dispersion Equation In The Long-wave Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Propagation of longitudinal elastic waves in composites with a random set of spherical inclusions (effective field approach)

Kanaun

Levin

2007

Arch Appl Mech

View full text Add to dashboard Cite

show abstract

“…The advantage of this method is that it allows approaching the maximum dependence domain of the final and differential equation to the dependence area of the initial differential equation [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

The Method and Software for the Solution of Dynamic Waves Propagation Problem in Elastic Medium

2016

View full text Add to dashboard Cite

This paper describes the numerical method for the solution to the problem of propagation of dynamic waves in elastic media -the bicharacteristics method with the usage of the ideas of the splitting method. The bicharacteristics method is one of the most convenient methods for software creating. In this research paper we have worked on the solution for non-stationary problem of the homogeneous isotropic elastic body dynamics using the bicharacteristics method, based on which the "ProgWave" software was designed. With this software, we have obtained the plots of isolines of normal and tangent tensions, which are very important for the studies of non-stationary dynamic waves propagation in flat elastic bodies, in engineering practice at construction designs calculation, in problems of mechanical engineering, etc.

show abstract

Scattering of anti-plane shear waves by arbitrarily distributed circular cylinders in a functionally graded multiferroic fibrous composite

2017

View full text Add to dashboard Cite

Propagation of shear elastic waves in composites with a random set of spherical inclusions (effective field approach)

Cited by 29 publications

References 31 publications

Propagation of longitudinal elastic waves in composites with a random set of spherical inclusions (effective field approach)

Propagation of longitudinal elastic waves in composites with a random set of spherical inclusions (effective field approach)

The Method and Software for the Solution of Dynamic Waves Propagation Problem in Elastic Medium

Scattering of anti-plane shear waves by arbitrarily distributed circular cylinders in a functionally graded multiferroic fibrous composite

Contact Info

Product

Resources

About