An approximate secular equation of Rayleigh waves propagating in an orthotropic elastic half-space coated by a thin orthotropic elastic layer

An approximate secular equation of Rayleigh waves in an elastic half-space coated by a thin weakly inhomogeneous elastic layer

“…in which, from (14), the quantities hγ 0 , hμ 0 and hρ 0 in the expressions ofĀ 1 ,Ā 2 and 2 are given by…”

“…For obtaining the effective boundary conditions, Achenbach and Keshava [5], Tiersten [6] replaced the thin layer with a plate modeled by different theories: Mindlin's plate theory and the plate theory of low-frequency extension and flexure, while Bovik [7] expanded the stresses at the top surface of the layer into Taylor series in its thickness. The Taylor expansion technique was then developed by Rokhlin and Huang [8,9], Niklasson [10], Benveniste [11], Steigmann and Ogden [12], Ting [13], Vinh and Linh [14,15], Vinh and Anh [16,17], Vinh et al [18].…”

“…In [19] Wang et al considered an isotropic half-space covered by a thin electrode layer and the authors obtained an approximate secular equation of first order. In [14] the layer and the half-space were both assumed to be orthotropic and an approximate secular equation of third order was obtained. In [15] the layer and the half-space were both subjected to homogeneous pre-stains and an approximate secular equation of third order was established which is valid for any pre-strain and for a general strain energy function.…”

The frequency equation of Rayleigh waves in a piezoelectric smart material

“…However, due to nonlinearity, it is difficult to get the exact solution of the characteristic equation of Rayleigh waves in anisotropic media [13]. Lately, The propagation of surface Rayleigh waves in a half-space under the effect of pre-stress was examined by many authors such as: [14] and [15]. The piezoelectric materials (are called smart materials) are capable of altering the structure's response through sensing, actuation and control [16] and [17].…”

Rayleigh waves in a layered orthotropic elastic half-space with sliding contact

“…We consider all possible combinations: both the layer and the half-space are compressible (the compressible/compressible case) or incompressible (the incompressible/incompressible case), one is compressible and the other is incompressible (the compressible/incompressible case and the incompressible/compressible case). 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).…”