Spiral Lamb Waveguide for Spatial Filtration of Frequencies in a Confined Space A. Shelke 1 & S. Banerjee 2 & T. Zhenhua 2 & L. Yu 2 Received: 2 October 2014 /Accepted: 25 March 2015 # Society for Experimental Mechanics 2015 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 pro- cedure is described to filter Lamb wave frequencies in a con- fined space. Complementary to the existing idea of wave guid- ing 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 fabrica- tion, experiments and numerical modeling, sequential filtra- tion 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 pro- posed waveguide, fabricated by spirally arranging a number of cylindrical quartz crystals, bonded on an aluminum plate. Experimentally Lamb waves were excited by a PZT transduc- er 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, fre- quency 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 fre- quencies are mechanically enhanced. Frequency based sensing capabilities of the waveguide depends on the geomet- rical location of the wave front inside the waveguide, which is a function of spatially varying radius and phase rotation due to the spiral geometry. Keywords Acoustic metamaterial . Dispersion . Bandgap . Equi-frequency surfaces . Lamb wave . Phononics . Spiral waveguide Introduction Phononic crystals are the subset of acoustic metamaterial hav- ing heterogeneous structure with periodic repetition of unit cells in one, two or three dimensions [ 1 ]. Acoustic metamaterial are artificially fabricated materials capable of waveguiding, control and manipulation of sound waves. They are judicially arranged or embedded in a host matrix or placed on a host structure. Few of the interesting characteris- tics exhibited by the phononic crystals and acoustic metama- terials are the formation of absolute acoustic band gap, posi- tive and negative refraction of the propagating wave and pos- sibility of guiding, trapping, collimation and methodical con- trol of the acoustic waves [2–4]. Acoustic metamaterials with locally resonant elements are used to realize interesting phe- nomena at selected frequency such as negative refraction and wave guiding and steering [5]. Phononic crystals exhibits ab- solute band gaps due to destructive interferences and local resonances, resulted from the apparent contrast in the elastic modulus and the mass densities of the host and constituent matrices [6, 7]. It is shown by creating artificial defect in the crystals, the acoustic waves are guided through a waveguide [8]. Such phenomenon occurs when a guided wave mode exists within an absolute band gap in the phononic crystals. * S. Banerjee banerjes@cec.sc.edu 1 Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, India 2 Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA Experimental Mechanics DOI 10.1007/s11340-015-0018-0