N2 - 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. L1 - http://journals.pan.pl/Content/101391/PDF/14_paper.pdf L2 - http://journals.pan.pl/Content/101391 PY - 2015 IS - No 2 EP - 281 DO - 10.1515/aoa-2015-0030 KW - surface Love waves KW - group velocity KW - phase velocity KW - functionally graded materials KW - profiles of elastic constants KW - direct Sturm-Liouville problem A1 - Kiełczyński, Piotr A1 - Szalewski, Marek A1 - Balcerzak, Andrzej A1 - Wieja, Krzysztof PB - Polish Academy of Sciences, Institute of Fundamental Technological Research, Committee on Acoustics VL - vol. 40 DA - 2015[2015.01.01 AD - 2015.12.31 AD] T1 - Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials SP - 273 UR - http://journals.pan.pl/dlibra/publication/edition/101391 T2 - Archives of Acoustics