Strategic Damping Placement in Viscoelastic Bandgap Structures: Dissecting the Metadamping Phenomenon in Multiresonator Metamaterials

Abstract

Energy dissipation in polymeric composite metamaterials requires special mathematical models owing to the viscoelastic nature of their constituents, namely, the polymeric matrix, bonding agent, and local resonators. Unlike traditional composites, polymeric metamaterials are a class of hybrid composites which can distinctly be tailored for damping to achieve superior noise, vibration, and harshness (NVH) properties with no trade-offs in strength and while maintaining a high stiffness to mass ratio. The objective of this paper is to investigate viscoelastic metadamping in one-dimensional (1D) multi-bandgap polymeric composite metamaterials by combining the linear hereditary theory of viscoelasticity with the Floquet-Bloch theory of wave propagation in infinite elastic media. Important distinctions between metamaterial and phononic unit cell models are explained based on the free wave approach with wavenumber-eliminated damping-frequency band structures. The developed model enables viscoelastic metadamping to be investigated by varying two independent relaxation parameters describing the viscoelasticity level in the host structure and the integrated resonators. The dispersion mechanics within high damping regimes as well as the effects of boundary conditions on the damped response are discussed in detail. Finally, the results are generalized for composite metamaterials with multiple resonators.

Complex dispersion analysis of topologically protected interface states in two-dimensional viscoelastic phononic crystals

“…The Kelvin-Voigt model has been widely used for theoretical and numerical studies of the viscoelastic effect on the dispersion relations of the solid PnCs and metamaterials [25,30,[32][33][34]. It should be pointed out that, in addition to the Kelvin-Voigt model, different models have been used to investigate the viscoelastic effect on the band-gaps of PnCs, such as the generalized Maxwell model [33,41], the Rayleigh model [26] and the exponential damping model [42]. Herein, the material parameters of the epoxy matrix are used as follows: the mass density ρ = 1180 kg m −3 , the bulk modulus B = 4.615 GPa and the shear modulus G = 1.314 GPa.…”

Multiple resonances, fragmented propagation and homogenized attenuation of the beam model coupled with bi-periodic resonators

“…Numerical results show that these innovative measures can effectively increase the bandwidth of the band gaps. At the same time, it was found that multiple band gaps for flexural waves were obtained in beams coupled with lateral local resonators with a four-link-mechanism [22], multiple resonators [23,24] constructed by a vertical spring connecting with two oblique springs [7], a distributed array of nonlinear spring-mass resonators [25], interconnected local resonators [13], two-stage high-static-low-dynamic stiffness oscillators [26] and disordered local resonators [19], composite sandwich beam with pyramidal truss cores [27] and metamaterial beams with a series of local resonators [16,28,29]. Another subject of study in this field is to obtain lower frequency band gaps.…”

Theoretical band-gap bounds and coupling sensitivity for a periodic medium with branching resonators

“…A Email addresses: mary.bastawrous@colorado.edu (Mary V. Bastawrous ), mih@colorado.edu (Mahmoud I. Hussein ) simple mass-in-mass lumped-parameter model for 1D wave propagation has emerged as a canonical model for branched acoustic or elastic metamaterials [28], and more complex models have appeared examining the effects of damping [29][30][31] and nonlinearity [13,32]. Numerous applications have been proposed that utilize local resonances stemming from various types of branched substructures including, for example, sound isolation [33], elastic waveguiding [22,34], topological insulation [35,36], and nanoscale phonon manipulation for thermal conductivity reduction [37,38].…”