Abstract
The harmonic acoustic waves in a semi-infinite functionally graded (FG) 1D rod with a longitudinal arbitrary inhomogeneity are analyzed by a combined method based on the modified Cauchy formalism and the exponential matrix method. The closed form dispersion equations for harmonic waves are constructed, yielding the implicit dispersion relations for acoustic waves in FG rods. For longitudinal inhomogeneity of polynomial type the corresponding dispersion relations are constructed explicitly.
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