Existence of backward propagating acoustic waves in supported layers

Conditions for the existence of acoustic waveguide modes with the direction of the group velocity opposite to that of the phase velocity in supported layers are investigated. We begin with a study of a clamped-free layer and show that the occurrence of the negative slope in the dispersion of the second and higher order modes leading to backward propagation is a commonly encountered phenomenon related to accidental degeneracies between longitudinal and transverse thickness resonances. For a layer on an elastic substrate, the negative dispersion slope exists only when the transverse velocity of the layer is very small compared to that of the substrate, which makes backward propagation a rarely occurring phenomenon in real structures. Finally, we explain how mode-crossing in certain bi-layer structures results in the negative slope in the dispersion of the fundamental mode.

Research highlights
► Backward propagation (negative group velocity) is encountered in supported layers.
► Origin of backward propagation is in accidental degeneracies at zero wavenumber.
► Backward propagation occurs for 2nd and higher order modes.
► Layer must be much softer than the substrate.
► Bi-layer structures yield backward propagation of the fundamental mode.