Dispersion and non-reciprocal elastic wave propagation in a membrane coupled with a uniform flow

In this paper, we carry out an analytical study to investigate the dispersive and non-reciprocal properties of harmonic elastic wave propagation in a membrane on an elastic foundation. One side of the membrane is in contact with a uniform inviscid and incompressible flow. The analysis shows that the frequency spectrum and the dispersion curve are not symmetric, therefore breaking the principle of reciprocity. We show that the dynamics of the wave propagation of the system depends on the dimensionless phase velocity of the membrane and the dimensionless stiffness of the elastic foundation. The system possesses one region where the phase velocity of the propagating waves in opposite directions is different, and another where the waves travel only in one direction (directional band gap). There also exist regions in which only evanescent and spatially growing waves are excited.In this paper, we carry out an analytical study to investigate the dispersive and non-reciprocal properties of harmonic elastic wave propagation in a membrane on an elastic foundation. One side of the membrane is in contact with a uniform inviscid and incompressible flow. The analysis shows that the frequency spectrum and the dispersion curve are not symmetric, therefore breaking the principle of reciprocity. We show that the dynamics of the wave propagation of the system depends on the dimensionless phase velocity of the membrane and the dimensionless stiffness of the elastic foundation. The system possesses one region where the phase velocity of the propagating waves in opposite directions is different, and another where the waves travel only in one direction (directional band gap). There also exist regions in which only evanescent and spatially growing waves are excited.

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