Vibration attenuation and bandgap characteristics in plates with periodic cavities

Abstract

Plates with periodic cavities show excellent vibration attenuation characteristics. This behavior can be attributed to the presence of frequency bandgaps on account of interference between the incident wave and the reflected wave from the cavities. The present work investigates the vibration attenuation/bandgap characteristics of plates with varying shapes of periodic cavities, such as square, circular, vertical rectangle, and horizontal rectangle, through experiments and simulation. Vibration responses of different periodic plates have been studied by carrying out frequency sweep on a vibration shaker. The investigation has been restricted to flexural vibrations of the plates, which are the predominant mode of vibration in many practical vibration scenarios. The frequency bandgaps, observed through the experiment, have been compared with the numerical simulation by harmonic analysis and by carrying out dispersion analysis on a unit cell of the periodic structure using Floquet–Bloch theory. Dispersion curves of the periodic plates yielded bandgaps, which were observed to be in agreement with the bandgaps from the experiment. The effect of variation in the aspect ratio of the cavities, that is length-to-width ratio, on the bandgaps has also been examined. It has been demonstrated that by suitable selection of the shape/size of the periodic cavity, desired vibration attenuation bandgaps can be realized for a 2-dimensional structure.

Investigations on the band-gap characteristics of one-dimensional flexural periodic structures with varying geometries

“…However, these cannot be considered as band-gaps and can be attributed to partial interference of incident and reflected waves at the boundaries of finite structure. Similarly, minor attenuation zones, observed for the uniform structure, could also be attributed to interference between the incident wave and the reflected waves from the boundaries of the structure, see Das et al (2020).…”

“…Nouh et al (2016) estimated the propagation constants by obtaining the mass/stiffness matrices of a periodic cell from the finite element method (FEM). Effect of the geometry of periodicity for a flexural 2-D periodic structure was studied by Das et al (2020) through experiments, dispersion analysis and FEM. It was brought out that since the band-gap characteristics of a flexural periodic structure were dependent upon the cavity-geometry, the band-gaps could be tailored by suitable alteration of the periodic cavities.…”

Experimental and numerical investigation on effects of viscoelastic rubber and local resonator mass on broadband vibration attenuation in acoustic-metamaterial plates

“…The wave filtering behavior is affected by geometrical discontinuities and material of the individual substructure or unit cells (Nouh et al, 2015). Consequently, wave propagation through periodic cells is allowed only for a specific frequency range while completely blocked for other frequencies (Das et al, 2021).Wave propagation in periodic lattices containing locally resonant metamaterials was studied for their vibration suppression applications (Nouh et al, 2016;Pai, 2010;Pai et al, 2014), and applications including energy harvesting (Chen et al, 2014;Gonella et al, 2009). Contrary to Bragg scattering phononic crystal (Deymier, 2013), where band-gap is dependent on the periodic constant, for locally resonant phononic structures, the mechanism is independent of the periodic constant (Huang and Sun, 2010;Liu et al, 2000).…”

“…The present investigation focuses on using an optimized cavity shape to maximize Bragg scattering based on previous research by the Das et al (2021). Local resonant structures, based on locally resonant phononic crystals with membrane-based viscoelastic damping material, are then introduced in the optimized cavity.…”

Elastic wave attenuation in a metaplate with periodic hollow shapes for vibration suppression

“…For example, Movchan et al created circular holes in plates to form band gaps Movchan et al (2007). Other studies investigated the relationships between the shapes of the holes and the band gap frequencies for holes of various shapes Liu et al (2009); Wang et al (2011); Huang et al (2018); Das et al (2021). However, these MPs with periodic holes generally have band gaps in the high-frequency range.…”