Signorini Cylindrical Waves and Shannon Wavelets. (26th June 2012)

• Record Type: Journal Article
• Authors: Cattani, Carlo
• Other Names: Levy Doron Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2012(2012)
• Publication Date: 2012-06-26
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2012/731591
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : Hyperelastic materials based on Signorini's strain energy density are studied by using Shannon wavelets. Cylindrical waves propagating in a nonlinear elastic material from the circular cylindrical cavity along the radius are analyzed in the following by focusing both on the main nonlinear effects and on the method of solution for the corresponding nonlinear differential equation. Cylindrical waves' solution of the resulting equations can be easily represented in terms of this family of wavelets. It will be shown that Hankel functions can be linked with Shannon wavelets, so that wavelets can have some physical meaning being a good approximation of cylindrical waves. The nonlinearity is introduced by Signorini elastic energy density and corresponds to the quadratic nonlinearity relative to displacements. The configuration state of elastic medium is defined through cylindrical coordinates but the deformation is considered as functionally depending only on the radial coordinate. The physical and geometrical nonlinearities arising from the wave propagation are discussed from the point of view of wavelet analysis.