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Generalization of Wave Motions and Application to Porous Media

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DOI: 10.4236/gm.2013.33014    3,693 Downloads   5,500 Views  

ABSTRACT

The examination of wave motions is traditionally based on the differential equation of D’Alambert, the solution of which describes the motion along a single dimension, while its bidimensional extension takes on the concept of plane waves. Considering these elements and/or limits, the research is divided into two parts: in the first are written the differential equations relating on the conditions two/three-dimensional for which the exact solutions are found; in the second the concepts are extended to the analysis of the propagation of wave motions in porous media both artificial and natural. In the end the work is completed by a series of tests, which show the high reliability of the physical-mathematical models proposed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

R. Francesco, "Generalization of Wave Motions and Application to Porous Media," Geomaterials, Vol. 3 No. 3, 2013, pp. 111-119. doi: 10.4236/gm.2013.33014.

References

[1] G. Lanzo and F. Silvestri, “Sismic Local Responce,” Hevelius Edizioni, Benevento, 1999.
[2] D. Lo Presti, “Behaviour of Soils in Dynamic and Ciclic Conditions,” International Center for Mechanical Sciences—CISM, Udine, Italy, 1999.
[3] E. Carrara, A. Rapolla and N. Roberti, “Geophysical Survey for the Study of the Subsoil: Geoelectric and Seismic Methods,” Liguori Editore, Napoli, 1992.
[4] J. D’Alembert, “Research on the Curve Formed by a Rope Set in Vibration,” History of the Royal Academy of Sciences and Belles Letters in Berlin, Vol. 3, 1747, pp. 214-219.
[5] J. D’Alambert, “Addition to the Memory on the Curve Formed by a Rope Set in Vibration,” History of the Royal Academy of Sciences and Belles Letters in Berlin, Vol. 6, 1750, pp. 355-360.
[6] C. B. Boyer, “A History of Mathematics,” John Wiley & Sons, New York, 1968.
[7] L. Landau and E. Lifsits, “Theory of Elasticity,” Editori Riuniti, Roma, 1979.
[8] R. Di Francesco and M. Siena, “The Contribution of Geophysics in Geotechnical Design and Control Work in Progress,” XXIII National Conference of Geotechnical Engineering, Padova, 16-18 May 2007, pp. 211-218.
[9] R. Di Francesco, “Introduction to Soil’s Mechanics—Part I,” Dario Flaccovio Editore, Palermo, 2013.
[10] O. Belluzzi, “Science of Construction—Vol. IV,” Zanichelli Editori, Bologna, 1963.
[11] G. Ondracek, “The Quantitative Microstructure Field Property Correlation of Multiphase and Porous Materials,” Review on Powder Metallurgy and Physical Ceramics, Vol. 3, No. 3-4, 1987, pp. 205-232.
[12] D. N. Boccaccini and A. R. Boccaccini, “Dependence of Ultrasonic Velocity on Porosity and Pore Shape in Seintered Materials,” Journal of Nondestructive Evaluation, Vol. 16, No. 4, 1997, pp. 187-192.
[13] R. Di Francesco, “Introduction to Continum’s Mechanics,” Dario Flaccovio Editore, Palermo, 2012.
[14] K. Aky and P. G. Richards, “Quantitative Seismology: Theory and Methods,” University Science Books, Sausalito, 2002.
[15] A. Zollo and A. Emolo, “Earthquakes and Waves. Methods and Practice of Modern Seismology,” Liguori Editori, Napoli, 2011.
[16] G. Negretti and B. Di Sabatino, “Course of Petrography,” CISU, Rome, 1983.
[17] M. Asmani, C. Kermel, A. Leriche and M. Ourak, “Influence of Porosity on Young’s Module and Poisson’s Ratio in Alumina Ceramics,” Journal of the European Ceramic Society, 2001, Vol. 21, No. 8, pp. 1081-1086.
[18] V. Rzhevsky and G. Novik, “The Physics of Rocks,” Mir Publichers, Moscow, 1971.

  
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