In this paper, we numerically and experimentally study the waveguiding of Lamb modes in a thin plate with a periodic stubbed surface and propose a frequency-selection method based on the found complete band gaps of Lamb waves in the periodic structure. In the numerical simulations, we employ finite-element method to analyze the waveguiding effect of a line defect created in the periodic plate structure; and on the experimental side, we utilize a pulsed laser to generate broadband elastic-wave energy and a laser interferometer to receive the wave signals inside the line-defect waveguide. In the experiment, well-confined acoustic energy in the acoustic band gaps is observed. Furthermore, a polyline sharply bent waveguide is designed and used for the frequency selection of Lamb waves. Measurements show that acoustic energy with frequencies in the band gaps can be separated out and guided by the bent waveguiding route. The characteristics of deaf bands found in the experiment are discussed as well.
In this paper, the numerical investigation of Lamb wave propagation in two-dimensional phononic crystals composed of an array of stepped resonators on a thin slab is presented. The dispersion relations, power transmission spectra and spectra of resonances are studied using a finite-element method. Because of the simultaneous mechanisms of the local resonances and Bragg scattering, the structures exhibit low-frequency forbidden bands and Bragg band gaps, which can be effectively shifted by changing the resonator geometries as well as the lattice symmetries of the resonator array. As a result, a low-frequency gap within the audible regime can be demonstrated. Furthermore, for a finite phononic crystal slab, the calculated transmission and resonance spectra show an evident resonance nature which can be directly related to the formation of the low-frequency gaps. Based on the spectra of elastic waves through the single-layer stepped resonators, the resonances of the stepped resonators are found to either induce high reflection or intensify the transmission. The effects of different excitation conditions for generating specific slab modes with different polarization states on the acoustic energy transmission and attenuation are also studied. The results show that the polarization states of the incident slab modes influence the spectra of resonances, power transmission and attenuation.
The authors study the propagation of Lamb waves in two-dimensional locally resonant phononic-crystal plates, composed of periodic soft rubber fillers in epoxy host with a finite thickness. Our calculations are based on the efficient plane wave expansion formulation which utilized Mindlin’s plate theory. Calculated results show that the low-frequency gaps of Lamb waves are opened up by the localized resonance mechanism. The resonant frequencies of flexure-dominated plate modes are significantly dependent not only on the radius of circular rubber fillers but also on the plate thickness. The properties of localized resonance are qualitatively analogous to the vibration of a circular thin plate.
Based on Mindlin's plate theory and the plane wave expansion method, a formulation is proposed to study the propagation of Lamb waves in two-dimensional phononic-crystal plates. The method is applied to calculate the frequency band structure of a square array of crystalline gold cylinders in an epoxy matrix with a finite thickness. It is found that complete frequency band gaps for Lamb waves between different pass bands are opened up by tuning thickness of the phononic-crystal plate. The influence of plate thickness on the width of complete frequency band gap is calculated and discussed as well; the existence of frequency stop bands is sensitive to the variation of the thickness of the plate. Finally, we note that the proposed method provides a concise and efficient way in analyzing the frequency band structures of phononic-crystal plates in lower bands.
A Lamb wave resonator utilizing an aluminum nitride (AlN) plate with biconvex edges to enhance the quality factor (Q) is demonstrated. The simulation results based on finite element analysis verify that the use of the biconvex edges, instead of the conventional flat edges, can efficiently confine mechanical energy in the AlN Lamb wave resonator. Specifically, the measured frequency response of a 491.8-MHz AlN Lamb wave resonator with biconvex edges yields a Q of 3280 which represents a 2.6× enhancement in Q over a 517.9-MHz Lamb wave resonator on the same AlN plate but with the suspended flat edges.
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