Non-principal Rayleigh waves in deformed transversely isotropic incompressible non-linearly elastic solids

Rayleigh waves in nonlinear elasticity

“…In passing, we note that our formulation particularized for transversely isotropic materials and isotropic materials coincides with the ones given in [62] and [84], respectively. In particular, for instance, the matrices N 1 , N 2 and K in (3.21) particularized for isotropic materials coincide, respectively, with the matrices N 1 , N 2 and N 3 + XI, where X = ρc 2 , given by (2.9) and (2.10) in [84].…”

“…In chapter three, we extend the analysis presented in chapter 2 [62] dealing with Rayleigh waves for materials reinforced with one family of fibers to obtain the explicit and implicit secular equations of non-principal Rayleigh waves propagating in imcompressible materials reinforced with two families of fibers in the framework of nonlinear elasticity [63].…”

“…Equation (3.25) is called the implicit secular equation (see also [84] and [62]) because the expressions for the ω I , ω II , ω III in terms of X are unkown.…”

“…In this chapter we extend the analysis presented in chapter 2 [62] dealing with Rayleigh waves for materials reinforced with one family of fibers to materials reinforced with two families of fibers in the framework of nonlinear elasticity. This is motivated by several factors.…”

“…For transversely isotropic materials the explicit secular equation was given in [62] while the implicit one was given in [65]. We build upon these results and use the polarization vector method to get the secular equation in explicit form.…”