Spatial Dispersion of Acoustic Waves in Functionally Graded Rods

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Harmonic acoustic waves in a semi-infinite functional-gradient (FG) one-dimensional rod with arbitrary longitudinal inhomogeneity are analyzed by a combined method based on the modified Cauchy formalism and the method of exponential matrices. Closed dispersion equations for harmonic waves are constructed, from the solution of which implicit dispersion relations for acoustic waves in FG rods are obtained. For longitudinal heterogeneity of polynomial type, the corresponding dispersion relations are constructed explicitly.

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作者简介

A. Karakozova

National Research Moscow State University of Civil Engineering

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Email: karioca@mail.ru
俄罗斯联邦, Moscow, 129337

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2. Fig. 1. 1D FG is a rod; n shows the direction of the wave normal and x shows the direction of the coordinate axis along the direction of wave propagation.

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3. Fig. 2. Variations of magnitudes and specific energies with distance for a linear binomial with time-harmonic excitation of 2 Hz and increasing phase velocity; (a) magnitudes; (b) specific energies.

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4. Fig. 3. Changes in modules and specific energies with distance for a linear binomial with time-harmonic excitation of 2 Hz and decreasing phase velocity; (a) magnitudes; (b) specific energies.

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