On the properties of phononic eigenvalue problems

Mokhtari, Amir Ashkan; Lu, Yan; Srivastava, Ankit

doi:10.1016/j.jmps.2019.07.005

Cited by 25 publications

(5 citation statements)

References 39 publications

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“…For complex k components, the solved eigen-modes are the propagating and evanescent waves that constitute the basis solution for the oblique scattering problem. Such problems are rarely studied for metamaterials but are of prime importance for analyzing the scattering dynamics 39,40 . Solving this type of problems in FEM would be nearly impractical, because the real-valued frequency ω can not be easily enforced in the traditional eigenfrequency study for a given complex k components.…”

Section: B Equi-frequency Contoursmentioning

confidence: 99%

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Wang¹,

Amirkhizi²

2023

Preprint

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Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design space spanned by a range of geometric and material parameters. This work aims to develop a generalized reduced order modeling (ROM) approach for determining MM dynamics in low frequency ranges with accuracy and speed, using a limited number of parameters and small matrices. The MM unit cells are treated as assemblies of structural elements and discrete degrees of freedom, whose effective stiffness and inertia are determined by optimizing energy criteria based on continuum results derived from a small number of eigen-study simulations. This proposed approach offers a parameterized and discretized representation of MM systems, which leads to fast and accurate computation of eigen-study results for periodic arrays of repeating unit cells, as well as dynamic responses for finite-sized arrays. The high computational efficiency and physical accuracy of this method will help to streamline the modeling process and aid in design discovery and optimization, especially in combination with scientific machine learning and data-driven techniques.

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Section: B Equi-frequency Contoursmentioning

confidence: 99%

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Wang¹,

Amirkhizi²

2023

Preprint

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“…(46). To address these challenges, several approaches are adopted in literature, including direct computational methods [24,25] as well as dedicated algorithms [37,38]. In the next subsection, we introduce a perturbation method based on the small parameter g , that does not involve very sophisticated algorithms -see technical details in Section 3.4.…”

Section: Pre-deformed Periodic Structurementioning

confidence: 99%

Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals

Berjamin,

De Pascalis

2021

Preprint

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The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design of custom acoustic filters. While nonlinear viscoelastic behaviour is one of the main features of soft solids, it has been rarely incorporated in the study of such phononic media. Here, we study the dynamic response of nonlinear viscoelastic solids within a 'small-on-large' acoustoelasticity framework, that is we consider the propagation of small amplitude waves superimposed on a large static deformation. Incompressible soft solids whose behaviour is described by the Fung-Simo quasi-linear viscoelasticy theory (QLV) are considered. We derive the incremental equations using stress-like memory variables governed by linear evolution equations. Thus, we show that wave dispersion is governed by a strain-dependent generalised Maxwell rheology. Illustrations cover the propagation of plane waves under homogeneous tensile strain in a QLV Mooney-Rivlin solid. The acoustoelasticity theory is then applied to phononic crystals involving a lattice of hollow cylinders, by making use of a dedicated perturbation approach. In particular, results highlight the influence of viscoelastic dissipation on the location of the first band gap. We show that dissipation shifts the band gap frequencies, simultaneously increasing the band gap width. These results are relevant to practical applications of soft viscoelastic solids subject to static pre-stress.

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“…On the way of solving the problem, it was preferred to use an arbitrary oriented acoustic plane wave and change the angle of wave in mathematical models and equations to show the change in relative status between the wave and the two sides of the sphere. The velocity potential function of incident wave field based on the partial wave expansion method [39][40][41] ,…”

Section: Acoustic Field Equationsmentioning

confidence: 99%

Acoustic steering of active spherical carriers

2020

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Following the novel introduced concept of the active carriers, this paper brings forward a technique toward the manipulability of an internally piezo-equipped active spherical carrier subjected to the progressive acoustic plane waves as the handling contactless asset. It is assumed that the piezoelectric part of the active carrier may be actuated as a bi-sectional body (i.e., two continuous hemispherical parts), with prescribed phase difference, and the polar position of the imaginary separating plane may be altered. This issue brings about an asymmetry in the dynamics of the problem which leads to emergence of position/frequency dependent acoustic radiation torque. It is obtained that as the carrier is excited by imposing harmonic voltage with the same amplitude and a π-radians phase difference, the zero-radiation force situation is obtained for a specific amplitude and phase of voltage as a function of frequency. This situation is treated as a criterion to determine the optimal amplitude of operation voltage. It is shown that the net force's direction exerted on the activated carrier may be steered along any desired orientation, assuming the fixed direction of incident wave field. The explained method of excitation and controllability of the spatial position of the divisor plane can possibly be a breakthrough in acoustic handling of active carriers. Noticeably, by this new technique, the single beam acoustic based contact-free methods and their applications in association with the concept of active carriers are now one step forward.

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On the properties of phononic eigenvalue problems

Cited by 25 publications

References 39 publications

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals

Acoustic steering of active spherical carriers

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