Effects of corrugation shape on frequency band-gaps for longitudinal wave motion in a periodic elastic layer

The paper concerns determining frequency band-gaps for longitudinal wave motion in a periodic waveguide. The waveguide may be considered either as an elastic layer with variable thickness or as a rod with variable cross section. As a result, widths and locations of all frequency band-gaps are determined by means of the method of varying amplitudes. For the general symmetric corrugation shape, the width of each odd band-gap is controlled only by one harmonic in the corrugation series with its number being equal to the number of the band-gap. Widths of even band-gaps, however, are influenced by all the harmonics involved in the corrugation series, so that the lower frequency band-gaps can emerge. These are band-gaps located below the frequency corresponding to the lowest harmonic in the corrugation series. For the general non-symmetric corrugation shape, the mth band-gap is controlled only by one, the mth, harmonic in the corrugation series. The revealed insights into the mechanism of band-gap formation can be used to predict locations and widths of all frequency band-gaps featured by any corrugation shape. These insights are general and can be valid also for other types of wave motion in periodic structures, e.g., transverse or torsional vibration. (C) 2016 Acoustical Society of America.