Abstract
This paper presents a theoretical study of the propagation behaviour of
surface Love waves in nonhomogeneous functionally graded elastic
materials, which is a vital problem in acoustics. The elastic properties
(shear modulus) of a semi-infinite elastic half-space vary monotonically
with the depth (distance from the surface of the material). Two Love wave
waveguide structures are analyzed: 1) a nonhomogeneous elastic surface
layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite
nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that
describes the propagation of Love waves in nonhomogeneous elastic
functionally graded materials is formulated and solved 1) analytically in
the case of the step profile, exponential profile and 1cosh2 type profile,
and 2) numerically in the case of the power type profiles (i.e. linear and
quadratic), by using two numerical methods: i.e. a) Finite Difference
Method, and b) Haskell-Thompson Transfer Matrix Method.
The dispersion curves of phase and group velocity of surface Love waves in
inhomogeneous elastic graded materials are evaluated. The integral formula
for the group velocity of Love waves in nonhomogeneous elastic graded
materials has been established. The results obtained in this paper can
give a deeper insight into the nature of Love waves propagation in elastic
nonhomogeneous functionally graded materials.
Go to article