A remarkable generalization of the Zabolotskaya equation. (October 2018)

• Record Type: Journal Article
• Authors: Pucci, Edvige; Saccomandi, Giuseppe
• Is Part Of: Mechanics research communications. Volume 93(2018)
• Page Start: 128
• Page End: 131
• Publication Date: 2018-10
• Subjects: Zabolotskaya equation -- Multiple scales -- Generalized neo-Hookean materials -- Linearly degenerate hyperbolic system; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2017.06.016
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: An asymptotic equation for nonlinear wave propagation is obtained. The equation is a generalization of the Z-equation. The mathematical structure is investigate and we find that waves of permanent form are possible solution. Abstract: In the framework of the theory of isotropic incompressible nonlinear elasticity we derive an asymptotic system of equations using a multiple scales expansion and considering waves of finite but small amplitude composed by an anti-plane shear superposed to a general plane motion. The system of equations generalizes the classical Zabolotskaya equation. Moreover, we show that the hyperbolic system, we derive, has a mathematical structure similar to the systems determining the propagation of transverse waves in nonlinear elasticity.