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Harmonic acoustic waves in FG rods with exponential inhomogeneity

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Abstract

Variation of the phase velocity, stress and displacement fields, and specific strain and kinetic energy in functionally graded (FG) rods with longitudinal exponential heterogeneity, are analyzed by a variant of Cauchy formalism, allowing constructing secular dispersion equation and the corresponding closed form solutions. The obtained results on dispersion of harmonic waves in a semi-infinite rod reveal (i) substantial spatial dispersion (at the constant time-frequency) of phase velocity, displacement, and stress, which is caused by the exponential inhomogeneity; and (ii) a non-monotonic spatial dispersion of specific strain and kinetic energy, dependent on the exponents in the exponential terms that specify the considered inhomogeneity.

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  1. Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, Russia

    S. V. Kuznetsov

  2. Bauman Moscow State Technical University, Moscow, Russia

    S. V. Kuznetsov

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Kuznetsov, S.V. Harmonic acoustic waves in FG rods with exponential inhomogeneity. Z. Angew. Math. Phys. 74, 63 (2023). https://doi.org/10.1007/s00033-023-01955-5

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