“…[20], the exact expressions of displacements in Ref. [21] and the incompressible limit method [20]. It is shown from Figs.…”
Section: An Approximate Formulas For the Rayleigh Wave H/v Ratiomentioning
confidence: 96%
“…Note that the Rayleigh wave H/V ratio χ depends on the dimensionless Rayleigh wave velocity x that is a solution of the secular equation (3.14) in [19] and it depends also on 5 dimensionless parameters mentioned above. [20], the exact expressions of displacements in Ref. [21] and the incompressible limit method [20].…”
Section: An Approximate Formulas For the Rayleigh Wave H/v Ratiomentioning
This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the Rayleigh wave H/V ratio.Keywords: Rayleigh waves, the Rayleigh wave H/V ratio, incompressible orthotropic elastic half-space, thin incompressible orthotropic elastic layer, approximate formula for the Rayleigh wave H/V ratio.
“…[20], the exact expressions of displacements in Ref. [21] and the incompressible limit method [20]. It is shown from Figs.…”
Section: An Approximate Formulas For the Rayleigh Wave H/v Ratiomentioning
confidence: 96%
“…Note that the Rayleigh wave H/V ratio χ depends on the dimensionless Rayleigh wave velocity x that is a solution of the secular equation (3.14) in [19] and it depends also on 5 dimensionless parameters mentioned above. [20], the exact expressions of displacements in Ref. [21] and the incompressible limit method [20].…”
Section: An Approximate Formulas For the Rayleigh Wave H/v Ratiomentioning
This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the Rayleigh wave H/V ratio.Keywords: Rayleigh waves, the Rayleigh wave H/V ratio, incompressible orthotropic elastic half-space, thin incompressible orthotropic elastic layer, approximate formula for the Rayleigh wave H/V ratio.
“…However, in practical applications it is possible that: the half-space is compressible and the layer is incompressible (Frostig, 2016), the half-space is incompressible and the layer is compressible (Kelly and Konstatinidis, 2011), the half-space and the layer are both incompressible (Genzer and Groenewold, 2006; Annaidha et al., 2012). The explicit secular equations for these three cases therefore need be found and they have been derived recently by Vinh et al. (2016b) using the incompressible limit method.…”
Section: Introductionmentioning
confidence: 99%
“…For the compressible/compressible case (the compressible case), the explicit secular equation is derived by employing the effective boundary condition method (Achenbach and Keshawa, 1967; Tiersten, 1969; Bovik, 1996, Steigmann and Ogden, 2007; Vinh and Linh, 2012, 2013; Vinh and Anh, 2014a, 2014b, 2015, 2016). For the three (incompressible) remaining cases, the explicit secular equations are deduced directly from the secular equation for the compressible case by using the incompressible limit approach (Vinh et al., 2016b). Note that the incompressible limit method used in this paper is more convenient than the one introduced by Destrade et al.…”
The presented paper is concerned with the propagation of Rayleigh waves in an orthotropic elastic half-space overlaid by an orthotropic elastic layer of arbitrary thickness. The layer and the half-space may be compressible or incompressible and they are in sliding contact with each other. The main aim of the paper is to derive explicit exact secular equations of the wave for four possible combinations: both the layer and the half-space are compressible or incompressible, one is compressible and the other is incompressible. When the layer and the half-space are both compressible, the explicit secular equation is derived by using the effective boundary condition method. For the three remaining cases, the explicit secular equations are deduced directly from this secular equation by using the incompressible limit technique. Based on the obtained secular equations, the effect of incompressibility and the sliding contact on the Raleigh wave propagation is considered through some numerical examples. It is shown that the incompressibility (of half-spaces and coating layers) and the sliding contact strongly affects the Raleigh wave velocity.
“…Несмотря на это, электроупругие волны плоской деформации (электроакустические волны Рэлея) в пьезоэлектрических кристаллах сравнительно мало исследованы [13÷15] и др. Наряду с этим, ещё бурно исследуются особенности локализации волн Рэлея в трёхмерных задачах упругости [16,17], явления, связанные с анизотропией материала [18,19], или с неоднородностью структуры [20,21 ].…”
Մեխանիկա 71, №1, 2018 Механика УДК 593.3 ЭЛЕКТРОУПРУГИЕ ВОЛНЫ РЭЛЕЯ В ВОЛНОВОДЕ С ЭЛЕКТРИ-ЧЕСКИ ЗАКРЫТЫМИ ИЛИ ОТКРЫТЫМИ ПОВЕРХНОСТЯМИ Аветисян А.С., Мкртчян С.А. Ключевые слова: электроакустическая волна, пьезоэлектрическое полупространство, краевая задача, высокочастотная акустическая волна, электрически прозрачная поверхность, электрически экранированная поверхность, дисперсионное уравнение, частотная зависимость. Ավետիսյան Ա.Ս., Մկրտչյան Ս.Հ. Ռելեյի էլեկտրաառաձգական ալիքները էլեկտրականապես բաց կամ փակ մակերևույթներով ալիքատարում Բանալի բառեր: էլեկտրաառաձգական ալիք, պյեզոէլեկտրական կիսատարածություն, եզրային խնդիր, բարձր հաճախակային էլեկտրաձայնային ալիքր, էլեկտրաթափանցիկ մակերևույթ, էլեկտրափակ մակերևույթ, դիսպերսիոն հավասարում, հաճախականային կախվածություն: Հետազոտվում են պյեզոէլեկտրական կիսատարածությունում հարթ դեֆորմացիայի էլեկտրաառաձգական ալիքի տարածման օրինաչափությունները: Ցույց է տրվում՝ էլեկտռաառաձգականության եզրային խնդրի քանի տարբերակ կարելի է ձևակերպել հեքսագոնալ համաչափության 6 2 m դասի պյեզոբյուրեղից կիսատարածությունում: Մեխանիկական բեռից ազատ պեզո-կիսատարածության մակերևույթին տարբեր էլեկտրական եզրային պայմանների դեպքում, քննարկված է հարթ դեֆորմացիայի բարձր հաճախության էլեկտրաձայնային ալիքի տարածման խնդիրը: Որոշ էլեկտրական մակերևութային պայմանների դեպքում ցույց է տրված հարթ դեֆորմացիայի ալիքի տեղայնացման նոր հնարավորությունը: Հարթ դեֆորմացիայի ալիքն ուղեկցող էլեկտրական դաշտի տատանումների առկայությունը բերում է Ռելեյի էլեկտրաառաձգական ալիքի տեղայնացման բնութագրիչների քանակական և որակական փոփոխությունների: Avetisyan A.S., Mkrtchyan S.H. The electro elastic Rayleigh waves in the waveguide with an electrically closed or open surfaces Keywords: Electro-acoustic waves; piezoelectric half-space; boundary value problem; high frequency acoustic waves; electrically transparent surface; electrically screened surface; dispersion equation; frequency dependence.The patterns of propagation of electro-acoustic waves of plane strain in a piezoelectric half-space is examined. In paper is shows how many possible variants of the boundary value problem of electro-elasticity can be formulated in a piezoelectric half-space of piezoelectric crystal class 6 2 m of the hexagonal symmetry. The problem of propagation of high frequency acoustic waves of plane strain (electro-acoustic Rayleigh waves) at different electric boundary conditions for mechanically free surface of a piezoelectric half-space is discussed. The possibility of a new localization of wave's plane strain, under certain electrical conditions at a surface is shown. The presence of a concomitant fluctuations of electric field, the waves of plane strain giving to the results in both quantitative and qualitative changes of the characteristics of a localization of electro-acoustic Rayleigh waves.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.