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.

has been cited by the following article:

• TITLE: Generalization of Wave Motions and Application to Porous Media

  AUTHORS: Romolo Di Francesco

  KEYWORDS: D’Alambert; Wave Motions; Propagation One/Two/Three-Dimensional; Porous Media

  JOURNAL NAME: Geomaterials, Vol.3 No.3, July 16, 2013

  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.