Damped Phononic Crystals and Acoustic Metamaterials

Hussein, Mahmoud I.; Frazier, Michael J.

doi:10.1007/978-3-642-31232-8_6

Cited by 13 publications

(19 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Hussein [340] and Hussein and Frazier [341] derived dispersion relations for viscously damped phononic materials. The treatment of temporally nonlocal viscoelasticity was also considered [342]. In all studies concerned with free wave propagation, a complex frequency is assumed in the application of Bloch's theorem.…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Hussein

Leamy

Ruzzene

2014

Applied Mechanics Reviews

Self Cite

1,263

633

View full text Add to dashboard Cite

The study of phononic materials and structures is an emerging discipline that lies at the crossroads of vibration and acoustics engineering and condensed matter physics. Broadly speaking, a phononic medium is a material or structural system that usually exhibits some form of periodicity, which can be in the constituent material phases, or the internal geometry, or even the boundary conditions. As such, its overall dynamical characteristics are compactly described by a frequency band structure, in analogy to an electronic band diagram. With roots extended to early studies of periodic systems by Newton and Rayleigh, the field has grown to encompass engineering configurations ranging from trusses and ribbed shells to phononic crystals and metamaterials. While applied research in this area has been abundant in recent years, treatment from a fundamental mechanics perspective, and particularly from the standpoint of dynamical systems, is needed to advance the field in new directions. For example, techniques already developed for the incorporation of damping and nonlinearities have recently been applied to wave propagation in phononic materials and structures. Similarly, numerical and experimental approaches originally developed for the characterization of conventional materials and structures are now being employed toward better understanding and exploitation of phononic systems. This article starts with an overview of historical developments and follows with an in-depth literature and technical review of recent progress in the field with special consideration given to aspects pertaining to the fundamentals of dynamics, vibrations, and acoustics. Finally, an outlook is projected onto the future on the basis of the current trajectories of the field.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Hussein

Leamy

Ruzzene

2014

Applied Mechanics Reviews

Self Cite

1,263

633

View full text Add to dashboard Cite

show abstract

“…In this section, by a state-space transformation of the equations of motion, a standard eigenvalue problem is formulated. 18,28,34 In the case of viscous damping, this transformation adopts the familiar Duncan form. For the viscoelastic description, this formulation is extended by the addition of one or more internal variables.…”

Section: State-space Transformationmentioning

confidence: 99%

“…Although, in this work, the Bloch condition is applied through T, alternative formulations for lumped-parameter 34 and discretized 17,18,36 systems are suitable. One benefit of the formulation is that it brings lumped-parameter and finiteelement (FE) models under the same treatment.…”

Section: A Formulation Of Viscous Wave Propagation Problemmentioning

confidence: 99%

Viscous-to-viscoelastic transition in phononic crystal and metamaterial band structures

Frazier

Hussein

2015

The Journal of the Acoustical Society of America

Self Cite

View full text Add to dashboard Cite

The dispersive behavior of phononic crystals and locally resonant metamaterials is influenced by the type and degree of damping in the unit cell. Dissipation arising from viscoelastic damping is influenced by the past history of motion because the elastic component of the damping mechanism adds a storage capacity. Following a state-space framework, a Bloch eigenvalue problem incorporating general viscoelastic damping based on the Zener model is constructed. In this approach, the conventional Kelvin-Voigt viscous-damping model is recovered as a special case. In a continuous fashion, the influence of the elastic component of the damping mechanism on the band structure of both a phononic crystal and a metamaterial is examined. While viscous damping generally narrows a band gap, the hereditary nature of the viscoelastic conditions reverses this behavior. In the limit of vanishing heredity, the transition between the two regimes is analyzed. The presented theory also allows increases in modal dissipation enhancement (metadamping) to be quantified as the type of damping transitions from viscoelastic to viscous. In conclusion, it is shown that engineering the dissipation allows one to control the dispersion (large versus small band gaps) and, conversely, engineering the dispersion affects the degree of dissipation (high or low metadamping).

show abstract

“…With such applications in mind, it is important to examine the competition between the energy leakage of resonant scatterers and the intrinsic dissipation losses [12,20]. Discrete systems and the mitigation effects of broadband waves at subwavelength scales are examined in [5,30].…”

Section: Introductionmentioning

confidence: 99%

Damping in a row of locally-resonant inclusions: Dynamic homogenization and scattering of transient shear waves

2021

View full text Add to dashboard Cite

The scattering of scalar waves by a periodic row of inclusions is theoretically and numerically investigated. The wavelength in the background medium is assumed to be much larger than the typical sizes of the inclusions. The latter are also much softer than the matrix, yielding localized resonances within the microstructure. Previous works in the inviscid case have concerned: (i) the derivation of effective resonant jump conditions, that are non local in time (Touboul et al., J. Elasticity, 2020); (ii) the introduction of auxiliary fields along the interface, providing a time-domain formulation of the scattering problem (Touboul et al., J. Comput. Phys., 2020). The present contribution extends the analysis to dissipative cases, which allows to be closer from real devices. The effective jump conditions with damping are obtained, both in the frequency domain and in the time domain. An exact plane-wave solution is proposed. A balance of energy is written, and new auxiliary fields are introduced. Practical implementation of the simulation methods is discussed. Then, numerical experiments are proposed to validate the auxiliary-field approach. The effect of dissipation is examined, and the relevance of the homogenized simulations in comparison with full-field simulations of transient waves is assessed. As an application, a numerical experiment of Coherent Perfect Absorption is finally proposed: at critical values of the attenuation parameter and close to the resonant frequencies, the waves impacting the dissipative resonant interface are fully absorbed.

show abstract

Damped Phononic Crystals and Acoustic Metamaterials

Cited by 13 publications

References 22 publications

Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Viscous-to-viscoelastic transition in phononic crystal and metamaterial band structures

Damping in a row of locally-resonant inclusions: Dynamic homogenization and scattering of transient shear waves

Contact Info

Product

Resources

About