Spiral Lamb Waveguide for Spatial Filtration of Frequencies in a Confined Space

Abstract

Objective of this paper is to present a predictive design of a mechanical filter which is capable of filtering frequencies along a waveguide. A mathematical design procedure is described to filter Lamb wave frequencies in a confined space. Complementary to the existing idea of wave guiding in a plate within an absolute band gap created by a 2D array of phononic crystals, the proposed acoustic metamaterial has a capability of wave guiding using a single but continuous array of crystals in a confined space. Further through fabrication, experiments and numerical modeling, sequential filtration of a frequency band is demonstrated. A conceptual design of a selective pass band filter (i.e., a mechanical pass band filter) is achieved by enhancing the phenomenon of steering, guiding and confinement of the Lamb waves inside a proposed waveguide, fabricated by spirally arranging a number of cylindrical quartz crystals, bonded on an aluminum plate. Experimentally Lamb waves were excited by a PZT transducer inside the spiral waveguide using a wideband chirp signal and the out-of-plane wave motion was recorded using a one dimensional scanning laser Doppler vibrometer (SLDV). The propagation within the waveguide was evaluated in time, frequency and wave number domains. By analyzing the equi-frequency contours and the transmission spectra inside the waveguide, the study demonstrate that the frequency based Lamb wave sensing and spectral separation of different frequencies are mechanically enhanced. Frequency based sensing capabilities of the waveguide depends on the geometrical location of the wave front inside the waveguide, which is a function of spatially varying radius and phase rotation due to the spiral geometry.