On the impact of damping on the dispersion curves of a locally resonant metamaterial: Modelling and experimental validation

Abstract

Recently, locally resonant metamaterials have come to the fore in noise and vibration control engineering, showing great potential due to their superior noise and vibration attenuation performance in targeted and tunable frequency ranges, referred to as stop bands. Damping has an important influence on the performance of these materials, broadening the frequency range of attenuation at the expense of peak attenuation. As a result, understanding and including the effects of damping is necessary to more accurately predict the attenuation performance of these locally resonant metamaterials. Classically, these often periodic structures are analysed using a unit cell modelling approach to predict wave propagation and thus stop band behaviour, discarding damping. In this work, a unit cell method including damping is used to analyse the complex dispersion curves of a locally resonant metamaterial design. The wave solutions in and around the stop band frequency range are compared to those of the unit cell method discarding damping. The influence on the dispersion curves of damping in resonator and host structure is discussed and the obtained dispersion curves are validated through an experimental dispersion curve measurement based on an Extended Inhomogeneous Wave Correlation method using Scanning Laser Doppler Vibrometry for a metamaterial plate manufactured at a representative scale. Excellent agreement is obtained between the numerically predicted and experimentally retrieved dispersion curves.

Energy Distribution and Exchange Between Spatial Harmonics in Bending Wave Phononic Crystals

“…The use of complex material properties results in a nonzero value of the imaginary wave number, even in pass bands. Moreover, the real part of the wave number no longer remains constant inside a band gap, but shows a smooth transition in accordance with other models [30,31]. This means that there are no discontinuities in the waves' group velocities, as is the case if no material damping is considered.…”

“…The IWC method [28][29][30] delivers the complex dispersion relation based on the knowledge of the FRF along a line. The method compares the measured signal at a chosen frequency, s(x, f 0 ), to a damped traveling wavê o = exp[i(k + ig)x] by calculating the correlation…”

Tacticity in chiral phononic crystals

“…The complex frequency-wave number relations shown in Supplementary Note 4 delivers a straightforward way of investigating the wave attenuation efficiency of metamaterials. The imaginary part of the wave number, calculated by solving a polynomial eigenvalue problem 45,46 , quantifies the amplitude decay per meter traveled by the considered wave. The full model was first reduced to a superelement with only 1740 degrees of freedom, chosen for a set of master nodes along the edges of the disks.…”

K-space analysis of complex large-scale meta-structures using the Inhomogeneous Wave Correlation method

“…For point harmonic excitations, the estimate of the decaying part of the wavenumber can be improved by taking in account the location of the excitation (x 0 , y 0 ) [22]. The spatially decaying plane wave assumes the following expression:w…”

“…For what concerns the stop bands behavior of tuned resonators, Claeys et al [20,21] have demonstrated their potential use to reduce the vibrational response of panels, spatially distributing them over the panel surface. An application of the IWC method on a metamaterial plate with distributed resonators is given by Van Belle et al [22].…”