We study the propagation of shear waves in an anisotropic incompressible medium composed of an elastic bre-reinforced material. We rst derive the general determining equations of such waves when the bres are arbitrarily arranged with respect to the direction of propagation of the waves. Then we examine the standard reinforced model" so as to root the nonlinearity of the dynamic problem directly to the presence of the reinforcing bres, and nally we consider an asymptotic model in terms of the limit of nite and small amplitude of the waves. Clearly, if the bres are arranged along the direction of propagation of the waves the mechanical behaviour of the material will be isotropic. When the bres are tilted an amount of the same order of the amplitude of the wave with respect to this direction, the asymptotic rst order reduced system is characterized by a peculiar mixed second/ third order nonlinearity. This contrasts to what occurs for larger tilting angles where only quadratic nonlinearities must be considered. In the latter case, as we may expect, in the asymptotic limit, we reduce the system to an inviscid classical Burger's equation. Our results are fundamental to the study of the dynamics of bre-reinforced materials and equally when we consider dissipative and/or dispersive effects.

On Shear Motions in Nonlinear Transverse Isotropic Elastodynamics

Ada, Amendola
;
In corso di stampa

Abstract

We study the propagation of shear waves in an anisotropic incompressible medium composed of an elastic bre-reinforced material. We rst derive the general determining equations of such waves when the bres are arbitrarily arranged with respect to the direction of propagation of the waves. Then we examine the standard reinforced model" so as to root the nonlinearity of the dynamic problem directly to the presence of the reinforcing bres, and nally we consider an asymptotic model in terms of the limit of nite and small amplitude of the waves. Clearly, if the bres are arranged along the direction of propagation of the waves the mechanical behaviour of the material will be isotropic. When the bres are tilted an amount of the same order of the amplitude of the wave with respect to this direction, the asymptotic rst order reduced system is characterized by a peculiar mixed second/ third order nonlinearity. This contrasts to what occurs for larger tilting angles where only quadratic nonlinearities must be considered. In the latter case, as we may expect, in the asymptotic limit, we reduce the system to an inviscid classical Burger's equation. Our results are fundamental to the study of the dynamics of bre-reinforced materials and equally when we consider dissipative and/or dispersive effects.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4797709
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