ABSTRACT
Functionally Graded Material concepts, manufacturing techniques, and modeling were briefly introduced in Section 3.3. In this chapter, spectral analysis is used to study the wave behavior in 1D and 2D FGM waveguides. Compared to the wave propagation in anisotropic media, the waves in inhomogeneous media have different characteristics. Typically, the wave motion in the direction of inhomogeneity is characterized by reduction in the amplitude of the wave while it is propagating (see [39], [360]). Waves of this type are called inhomogeneous waves. Homogeneous plane waves have the form
f = Φ(ω) exp[i(kxx+ kyy + kzz − ωt)] = Φ(ω) exp[i(k · r− ωt)] , where Φ(ω) is the wave amplitude (real) and k is the wave vector (real). This form describes the wave propagation phenomena in homogeneous, linear and non-dissipative solids. Inhomogeneous waves are described by the above form with complex Φ and k (see [54]).
