Focusing flexural lamb waves by designing elastic metamaterials bonded on a plate

In this paper, a method to focus flexural Lamb waves to a local area by mounting elastic metamaterials (EMMs) on the surface of the plate is proposed. The EMM consists of silicon rubber and lead connected in series bonded vertically on an aluminum plate. A simplified effective mass-"spring"- mass model is used to study the EMM plate. The frequency-dependent effective mass density of the EMM plate is determined with the aid of the numerically based effective medium method. By making use of the low locally resonant frequency of the EMM plate, the EMM plate is carefully designed with different dimensions to attain high effective mass densities. The effective mass density can be assumed to dominate the change of wave velocity and propagation direction in the EMM plate. An effective mass density profile is then employed along the transverse direction of wave propagation to achieve focusing. Finally, numerical simulation with finite element method (FEM) is utilized to investigate the focusing phenomenon of the A₀ mode Lamb waves at 30 kHz and the out-of-plane displacement response beyond the EMM region. Numerical simulation results have shown that focusing the low frequency A₀ mode Lamb waves using EMMs is feasible. The focusing may have potential applications in structural health monitoring by manipulating Lamb waves through controlling and focusing Lamb waves to any arbitrary location of the plate with amplified displacement and yet largely retained five-peaked toneburst waveform.