On Rayleigh waves in incompressible orthotropic elastic solids

Abstract

In this paper the secular equation for the Rayleigh wave speed in an incompressible orthotropic elastic solid is obtained in a form that does not admit spurious solutions. It is then shown that inequalities on the material constants that ensure positive definiteness of the strain-energy function guarantee existence and uniqueness of the Rayleigh wave speed. Finally, an explicit formula for the Rayleigh wave speed is obtained.

Some new considerations concerning the Rayleigh‐wave velocity in auxetic materials

“…These experimental results confirm the potential of using high-end laminate composites with sinclastic curvature [22] and high NPR effect using special stacking sequences [23]. In this work, the theoretical approach of Ogden and Vinh is used for incompressible anisotropic solids [15], and applied to 3D crossply laminates as per Clarke et al [20] exhibiting throughthe-thickness NPR behaviour. The dependence of the Rayleigh velocity versus the cross-ply angles of the prepreg and the stress -strain coefficients obtained with the Classical Laminate Theory (CLT) is investigated, highlighting trends specific to auxetic thick laminate configurations.…”

“…Ogden and Pham Chi Vinh [15,16] found exact formulas for the phase velocity of Rayleigh waves in incompressible and compressible orthotropic materials, which were partly obtained by generalizing Malischewsky's exact formula [9].…”

“…Following [15], we consider a plane motion in the (x 2 , x 3 ) plane with displacement components 1 2 3 ( , , ) u u u such that The variable t is time. For an incompressible material [32]:…”

Untitled

“…The value η 0 corresponds to the Rayleigh wave propagating in the incompressible transversely isotropic elastic solids (without pre-stresses) and, according to [Ogden and Vinh 2004], η 0 is given by…”

Rayleigh waves in nonlinear elasticity

“…They are also convenient tools to solve the inverse problem that deals with measured values of the wave speed and their agreement with material parameters as well as other practical applications. Such expressions have been given by Vinh & Ogden [49], Malischewsky [50] for isotropic solids, Ogden & Vinh [51], Vinh & Ogden [52; 53] for orthotropic solids and Vinh [54; 55] for pre-stressed media, among others. These investigations deal with harmonic surface waves travelling along the traction-free flat surface of half-spaces.…”