Numerical and experimental investigation of stop-bands in finite and infinite periodic one-dimensional structures

Abstract

Adding periodicity to structures leads to wavemode interaction, which generates pass- and stop-bands. The frequencies at which stop-bands occur are related to the periodic nature of the structure. Thus structural periodicity can be shaped in order to design vibro-acoustic filters for reducing vibration and noise transmission. The aim of this paper is to investigate, numerically and experimentally, stop-bands in periodic one-dimensional structures. Two methods for predicting stop-bands are described: the first method applies to infinite periodic structures using a wave approach; the second method deals with the evaluation of a vibration level difference (VLD) in a finite periodic structure embedded within an infinite one-dimensional waveguide. This VLD is defined to predict the performance in terms of noise and vibration insulation of periodic cells embedded in an otherwise uniform structure. Numerical examples are presented, and results are discussed and validated experimentally. Very good agreement between the numerical and experimental models in terms of stop-bands is shown. In particular, the results show that the stop-bands obtained using a wave approach (applied to a single cell of the structure) predict those obtained from the VLD of the corresponding finite periodic structure.

Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial

“…In other words, these frequency ranges are the acoustic band gaps. With the number of unit cells increasing, the transmission gaps tend to be larger and deeper, but few units are sufficient to indicate the frequencies of band gaps [40]. The curves for both the -wave and -wave also show Fano-like interference phenomena [41]; that is, within some specific frequency ranges, highly asymmetrical peaks appeared in the transmission curve.…”

Acoustic transmission properties of pressurised and pre-stressed composite structures

“…Also, as Manconi et al [27] did concerning cylindrical pressure vessels, research might focus on the adaptation of the method on more complex geometries. Another promising aspect of WFEM is the research of the possible effect of pre-stress on band-gaps , since the method has already been used in [23] and [31] on stiffened plates and beams. Wave dispersion graph of periodically pressured beam has been generated (see Fig.23), with the stress exceeding known materials' limits, though, without any useful conclusions yet.…”

“…This way the calculation of the wavenumbers and eigenvectors is achieved with considerably lower cost of time than the previous ones. WFEM has been used in one dimension [22,23] and in two dimensions analyses [24] producing quite satisfying results. Using FE for the structure's modelling has given researchers the ability to broaden the potentials of the method, calculating loss factor [25] with the help of existing theories [26].…”

“…Another use of WFEM is the examination of the potential band gaps in periodic structures. Domadiya et al [23] used WFEM to model two different periodic beams to examine the band gaps and had the results certified with actual experiments. Droz et al [31] proposed a mathematically improved version of the WFEM and calculated the wave propagation and band gaps in a periodically stiffened plate.…”

Using Periodicity to Mitigate Ground Vibration

“…Simple problems can be analysed analytically by means of Floquet analysis, and combining this approach with, for example, the finite-element method, periodic two and three-dimensional structures of complex geometries can be studied regarding their wave propagation properties. Such models have been used, for example, by Manconi and Mace [4] to study curved panels, and by Domadiya et al [5] to study wave propagation in beams with periodically placed masses or changes to the cross section. The combination of Floquet theory and finite-elements has also be used for analysis of railways [6], mainly to allow studying long structures with low computational cost.…”