Non-Monotonic Variation of Acoustic Spectrum with the Mass or Thickness of a Layered Structure

We are examining the behavior of resonance frequencies and their response to variations of material parameters such as thicknesses, masses, and bulk velocities for certain Rayleigh-Lamb acoustic modes in a multilayered structure. The treatment is based on recent explicit analytic solutions that have allowed us to explore the entire parametric space using dimensionless ratios. This exploration has revealed a complex parametric dependence of the phase velocities and their mass loading response. Specifically, for the fundamental flexural modes in a bilayer, we have shown that both quantities change in a strongly non-monotonic way with thickness, density, or bulk velocity ratios. Even in the regime of thin coating, commonly encountered in acoustic sensing applications, we have found important differences from previously known results, e.g., that response to loading may switch its sign multiple times when the velocity of the deposited material is increased. We have also discovered that the fundamental dilatational modes can be highly effective in stabilizing resonant frequencies against even large variations of the thickness or mass of the exposed layer. This property is demonstrated in an explicit form by the derived expression for the mass coefficient of frequency for an arbitrary number of layers.