Waves in a gradient-elastic medium with surface energy

Yerofeyev, V.I.; Sheshenina, O.A.

doi:10.1016/j.jappmathmech.2005.01.006

Cited by 13 publications

(5 citation statements)

References 4 publications

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“…Vardoulakis and Georgiadis (1997), Georgiadis et al (2000), Georgiadis and Velgaki (2003) and Georgiadis et al (2004) in their study of surface waves in a gradient elastic half-space were able to (a) observe that, while stability and uniqueness are satisfied for Àg 2 in the gradient elastic model, acceptable (i.e., consistent with atomic-lattice theory) dispersion curves are obtained only for +g 2 ; and (b) propose the inclusion of micro-inertia (through the coefficient h with length dimensions) in the model with Àg 2 , which results in acceptable dispersion curves for high frequencies. These findings were restated by Askes and Aifantis (2006) giving results for the one-dimensional case and by Yerofeyev and Sheshenina (2005) giving results for body and surface waves. To be sure, inclusion of micro-inertia in the gradient elastic model with Àg 2 has been first proposed by Mindlin (1964) and in homogenized composite materials by Wang and Sun (2002).…”

Section: Introductionmentioning

confidence: 99%

Wave dispersion in gradient elastic solids and structures: A unified treatment

Papargyri-Beskou

Polyzos

Beskos

2009

International Journal of Solids and Structures

164

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a b s t r a c tAnalytical wave propagation studies in gradient elastic solids and structures are presented. These solids and structures involve an infinite space, a simple axial bar, a Bernoulli-Euler flexural beam and a Kirchhoff flexural plate. In all cases wave dispersion is observed as a result of introducing microstructural effects into the classical elastic material behavior through a simple gradient elasticity theory involving both micro-elastic and micro-inertia characteristics. It is observed that the micro-elastic characteristics are not enough for resulting in realistic dispersion curves and that the micro-inertia characteristics are needed in addition for that purpose for all the cases of solids and structures considered here. It is further observed that there exist similarities between the shear and rotary inertia corrections in the governing equations of motion for bars, beams and plates and the additions of micro-elastic (gradient elastic) and micro-inertia terms in the classical elastic material behavior in order to have wave dispersion in the above structures.

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Section: Introductionmentioning

confidence: 99%

Wave dispersion in gradient elastic solids and structures: A unified treatment

Papargyri-Beskou

Polyzos

Beskos

2009

International Journal of Solids and Structures

164

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“…It is well known that within the classic linear elasticity, anti-plane surface waves in an elastic half-space do not exist [24]. For extended models of continua, such waves may exist, see Eremeyev et al [25] for the surface elasticity, and Vardoulakis and Georgiadis [26], Yerofeyev and Sheshenina [27], and Gourgiotis and Georgiadis [28] for the strain-gradient elasticity. Dynamics within the special case of the strain-gradient elasticity motivated by beam lattices were analysed in Giorgio et al [29,30].…”

Section: Introductionmentioning

confidence: 99%

Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses

Eremeyev¹,

Rosi

Naı̈li

2018

Mathematics and Mechanics of Solids

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Here we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model are more localised near the free surface. For the strain-gradient elasticity model there is a range of wavenumbers where the amplitude of displacements decays very slowly.

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“…The surface effects are incorporated into the constitutive relation of bulk material by the direct postulation of a specific function of strain energy density, for example, Vardoulakis and Georgiadis (1997), Exadaktylos (1999), Tsepoura et al (2002), Georgiadis et al (2000), Yerofeyev and Sheshenina (2005) and others. Recently, the propagation of different types of elastic waves in a gradient-elastic medium with surface energy is studied (Vardoulakis and Georgiadis, 1997;Georgiadis et al, 2000;Yerofeyev and Sheshenina, 2005). The dispersion characteristics of longitudinal and shear body waves, Rayleigh surface waves and antiplane shear surface waves, antiplane shear waves in a layer, and torsional surface waves are analysed.…”

Section: Introductionmentioning

confidence: 99%

Reflection and transmission of elastic waves at the interface between two gradient-elastic solids with surface energy

Wei

Tang³

2015

European Journal of Mechanics - A/Solids

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a b s t r a c tThe reflection and transmission of an incident plane wave at an interface between two gradient elastic solids with surface energy are studied. First, some functions of strain energy density with the surface effects taken into consideration are postulated and the surface effects of gradient elastic solid are incorporated into the constitutive relations. Then, the nontraditional interface conditions by requiring the auxiliary monopolar tractions and the auxiliary dipolar tractions continuous across the interface are used to determine the reflection and transmission coefficients. Some numerical results of the reflection and transmission coefficient in terms of energy flux ratio are given for different microstructure parameters and surface parameters. The microstructure effects and the surface energy effects on the reflection and transmission waves are discussed based on the numerical results. It is found that the microstructure effects result in the appearance of two surface waves and the surface energy effects have apparent different influence on the body waves in gradient elastic solids and the surface waves at the interface. However, this phenomenon becomes pronounced only when the incident wavelength is close to the characteristic length of microstructure.

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Waves in a gradient-elastic medium with surface energy

Cited by 13 publications

References 4 publications

Wave dispersion in gradient elastic solids and structures: A unified treatment

Wave dispersion in gradient elastic solids and structures: A unified treatment

Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses

Reflection and transmission of elastic waves at the interface between two gradient-elastic solids with surface energy

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