Numerical tools for computational design of acoustic metamaterials

Tesi en modalitat de compendi de publicacionsThe notion of metamaterials as artificially engineered structures designed to obtain specific material properties, typically unachievable in naturally occurring materials, has captured the attention of the scientific and industrial communities. Among the broad range of applications for such kind of materials, in the field of acoustics, the possibility of creating materials capable of efficiently attenuating noise in target frequency ranges is of utmost importance for a lot of industrial areas. In this context, the so-called locally resonant acoustic metamaterials (LRAMs) can play an important role, as their internal topology can be designed to exhibit huge levels of attenuation in specific frequency regions by taking advantage of internal resonance modes. With a proper, optimized topological design, LRAMs can be used, for instance, to build lightweight and thin noise insulation panels that operate in a low-frequency regime, where standard solutions for effectively attenuating the noise sources require dense and thick materials. Given the importance of the topological structure in obtaining the desired properties in acoustic metamaterials, the use of novel numerical techniques can be exploited to cre-ate a set of computational tools aimed at the analysis and design of optimized solutions. These are based on three fundamental pillars: (1) the multiscale homogenization of complex material structures in the microscale to get a set of effective properties capa-ble of describing the material behavior in the macroscale, (2) the model-order reduc-tion techniques, which are used to decrease the computational cost of heavy computa-tions while still maintaining a sufficient degree of accuracy, and (3) the topology optimi-zation methods that can be employed to obtain optimal configurations with a given set of constraints and a target material behavior. This set of computational tools can be applied to design acoustic metamaterials that are both efficient and practical, i.e. they behave according to their design specifications and can be produced easily, for in-stance, making use of novel additive manufacturing techniques.La concepció dels metamaterials com a estructures dissenyades artificialment amb l’objectiu d’obtenir un conjunt de propietats que no són assolibles en materials de manera natural, ha captat l’atenció de les comunitats científiques i industrials. Dins de l’ampli ventall d’aplicacions que se’ls pot donar als metamaterials, si ens centrem en el camp de l’acústica, la possibilitat de crear un material capaç d’atenuar de manera efectiva sorolls en rangs de freqüència concrets és de gran interès en multitud d’indústries. En aquest context, els anomenats “locally resonant acoustic metamaterials” (LRAMs) destaquen per la possibilitat de dissenyar la seva topologia interna per tal que produeixin elevats nivells d’atenuació en regions concretes de l’espectre de freqüències. Amb un disseny topològic òptim, els LRAMs poden servir, per exemple, per a la construcció de panells lleugers aïllants de soroll, que operin en rangs de freqüències baixos, en els quals la solució clàssica requereix de materials d’elevada densitat i espessor. Donada la importància de l’estructura topològica dels metamaterials acústics en l’obtenció de les propietats desitjades, resulta convenient l’ús de mètodes numèrics punters per al desenvolupament d’un conjunt d’eines computacionals que tinguin per objectiu l’anàlisi i el disseny de solucions òptimes. Tals eines es fonamenten en tres pilars: (1) la homogeneïtzació multiescala d’estructures de material complexes a una escala micro que derivi en l’obtenció de propietats efectives que permetin descriure el comportament del material a una escala macro, (2) tècniques de reducció per minimitzar l’esforç computacional mantenint nivells de precisió suficients i (3) mètodes d’optimització topològica emprats per a l’obtenció de configuracions òptimes donat un conjunt de restriccions i unes propietats de material objectiu. Aquestes eines computacionals es poden aplicar al disseny de metamaterials acústics que resultin eficients i pràctics a la vegada, és a dir, que es comportin segons les especificacions de disseny i siguin fàcilment fabricables, per exemple, mitjançant tècniques punteres d’impressió 3D.Postprint (published version

Numerical tools for computational design of acoustic metamaterials

The notion of metamaterials as artificially engineered structures designed to obtain specific material properties, typically unachievable in naturally occurring materials, has captured the attention of the scientific and industrial communities. Among the broad range of applications for such kind of materials, in the field of acoustics, the possibility of creating materials capable of efficiently attenuating noise in target frequency ranges is of utmost importance for a lot of industrial areas. In this context, the so-called locally resonant acoustic metamaterials (LRAMs) can play an important role, as their internal topology can be designed to exhibit huge levels of attenuation in specific frequency regions by taking advantage of internal resonance modes. With a proper, optimized topological design, LRAMs can be used, for instance, to build lightweight and thin noise insulation panels that operate in a low-frequency regime, where standard solutions for effectively attenuating the noise sources require dense and thick materials. Given the importance of the topological structure in obtaining the desired properties in acoustic metamaterials, the use of novel numerical techniques can be exploited to cre-ate a set of computational tools aimed at the analysis and design of optimized solutions. These are based on three fundamental pillars: (1) the multiscale homogenization of complex material structures in the microscale to get a set of effective properties capa-ble of describing the material behavior in the macroscale, (2) the model-order reduc-tion techniques, which are used to decrease the computational cost of heavy computa-tions while still maintaining a sufficient degree of accuracy, and (3) the topology optimi-zation methods that can be employed to obtain optimal configurations with a given set of constraints and a target material behavior. This set of computational tools can be applied to design acoustic metamaterials that are both efficient and practical, i.e. they behave according to their design specifications and can be produced easily, for in-stance, making use of novel additive manufacturing techniques.La concepció dels metamaterials com a estructures dissenyades artificialment amb l’objectiu d’obtenir un conjunt de propietats que no són assolibles en materials de manera natural, ha captat l’atenció de les comunitats científiques i industrials. Dins de l’ampli ventall d’aplicacions que se’ls pot donar als metamaterials, si ens centrem en el camp de l’acústica, la possibilitat de crear un material capaç d’atenuar de manera efectiva sorolls en rangs de freqüència concrets és de gran interès en multitud d’indústries. En aquest context, els anomenats “locally resonant acoustic metamaterials” (LRAMs) destaquen per la possibilitat de dissenyar la seva topologia interna per tal que produeixin elevats nivells d’atenuació en regions concretes de l’espectre de freqüències. Amb un disseny topològic òptim, els LRAMs poden servir, per exemple, per a la construcció de panells lleugers aïllants de soroll, que operin en rangs de freqüències baixos, en els quals la solució clàssica requereix de materials d’elevada densitat i espessor. Donada la importància de l’estructura topològica dels metamaterials acústics en l’obtenció de les propietats desitjades, resulta convenient l’ús de mètodes numèrics punters per al desenvolupament d’un conjunt d’eines computacionals que tinguin per objectiu l’anàlisi i el disseny de solucions òptimes. Tals eines es fonamenten en tres pilars: (1) la homogeneïtzació multiescala d’estructures de material complexes a una escala micro que derivi en l’obtenció de propietats efectives que permetin descriure el comportament del material a una escala macro, (2) tècniques de reducció per minimitzar l’esforç computacional mantenint nivells de precisió suficients i (3) mètodes d’optimització topològica emprats per a l’obtenció de configuracions òptimes donat un conjunt de restriccions i unes propietats de material objectiu. Aquestes eines computacionals es poden aplicar al disseny de metamaterials acústics que resultin eficients i pràctics a la vegada, és a dir, que es comportin segons les especificacions de disseny i siguin fàcilment fabricables, per exemple, mitjançant tècniques punteres d’impressió 3D

A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling

A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuations and their gradients are then accounted for in a saddle-point formulation of that variational principle in terms of Lagrange functionals. A physical interpretation of the involved Lagrange multipliers can then be readily obtained. The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuation.Peer ReviewedPostprint (author's final draft

Experimental and numerical assessment of local resonance phenomena in 3D-printed acoustic metamaterials

The so called Locally Resonant Acoustic Metamaterials (LRAM) are a new kind of artificially engineered materials capable of attenuating acoustic waves. As the name suggests, this phenomenon occurs in the vicinity of internal frequencies of the material structure, and can give rise to acoustic bandgaps. One possible way to achieve this is by considering periodic arrangements of a certain topology (unit cell), smaller in size than the characteristic wavelength. In this context, a computational model based on a homogenization framework has been developed from which one can obtain the aforementioned resonance frequencies for a given LRAM unit cell design in the sub-wavelength regime, which is suitable for low-frequency applications. Aiming at validating both the proposed numerical model and the local resonance phenomena responsible for the attenuation capabilities of such materials, a 3D-printed prototype consisting of a plate with a well selected LRAM unit cell design has been built and its acoustic response to normal incident waves in the range between 500 and 2000 Hz has been tested in an impedance tube. The results demonstrate the attenuating capabilities of the proposed design in the targeted frequency range for normal incident sound pressure waves and also establish the proposed formulation as the fundamental base for the computational design of 3D-printed LRAM-based structures.Peer ReviewedPostprint (author's final draft

Computational design of locally resonant acoustic metamaterials

The so-called Locally Resonant Acoustic Metamaterials (LRAM) are considered for the design of specifically engineered devices capable of stopping waves from propagating in certain frequency regions (bandgaps), this making them applicable for acoustic insulation purposes. This fact has inspired the design of a new kind of lightweight acoustic insulation panels with the ability to attenuate noise sources in the low frequency range (below 5000 Hz) without requiring thick pieces of very dense materials. A design procedure based on different computational mechanics tools, namely, (1) a multiscale homogenization framework, (2) model order reduction strategies and (3) topological optimization procedures, is proposed. It aims at attenuating sound waves through the panel for a target set of resonance frequencies as well as maximizing the associated bandgaps. The resulting design’s performance is later studied by introducing viscoelastic properties in the coating phase, in order to both analyse their effects on the overall design and account for more realistic behaviour. The study displays the emerging field of Computational Material Design (CMD) as a computational mechanics area with enormous potential for the design of metamaterial-based industrial acoustic parts.Peer ReviewedPostprint (author's final draft

Coiled phononic crystal with periodic rotational locking: subwavelength bragg band gaps

Phononic crystals (PnC) are spatially periodic materials with band gaps that form by Bragg scattering of elastic waves. Within the frequency range of a band gap, wave propagation is not admitted. A long-standing limitation of this class of materials is that the wavelength for band-gap formation must be on the order of the unit-cell size. This restricts the presence of band gaps to relatively high frequencies for a given lattice spacing. Locally resonant metamaterials, on the other hand, enable the opening of low-frequency, subwavelength band gaps through resonance hybridization. However, their band gaps are characteristically narrow and require large or massive local resonators to form. Here, we break both limitations using beam-based PnCs by (1) locking the rotation degree of freedom at the edges of the primitive unit cell, and (2) coiling the PnC by applying full beam-axis rotations at the locked locations. These respective kinematic and geometric transformations convert a conventional beam PnC from its extended form with a nominal lattice constant to an extremely compact coiled configuration with a greatly reduced lattice constant. With the periodic rotational locking, the band gaps remain intact and are still large, and in fact increase noticeably in size. With the subsequent coiling, the band gaps remain based on Bragg scattering and are quantitatively conserved except now appearing at lower frequencies as dictated by the ratio of the extended-to-coiled lattice constants. This ratio defines a coiling factor, which is a measure of the reduction in the PnC unit-cell length in the direction of wave transmission while maintaining the band structure of its original extended form except for the favorable changes induced by the periodic rotational locking. A coiling factor of ß lowers, by construction, the location of the normalized central frequency of any given band gap by a factor of ß . The only limitation is the need for lateral space to accommodate the coiling of the beam segments. The vibration behavior of a finite version of the coiled structure is experimentally tested demonstrating a matching band-gap response, despite the reduction in length, to that obtained by finite-element analysis of the extended rotationally locked version. This concept creates effectively subwavelength Bragg band gaps. It clears the path for PnCs to serve in applications that are orders-of-magnitude smaller in scale than are currently possible, while featuring band gaps that are significantly larger than those generated by locally resonant metamaterials.This research is funded by the Air Force Office of Scientific Research under grant number 20RXCOR058.Peer ReviewedPostprint (author's final draft

Numerical tools for computational design of acoustic metamaterials

The notion of metamaterials as artificially engineered structures designed to obtain specific material properties, typically unachievable in naturally occurring materials, has captured the attention of the scientific and industrial communities. Among the broad range of applications for such kind of materials, in the field of acoustics, the possibility of creating materials capable of efficiently attenuating noise in target frequency ranges is of utmost importance for a lot of industrial areas. In this context, the so-called locally resonant acoustic metamaterials (LRAMs) can play an important role, as their internal topology can be designed to exhibit huge levels of attenuation in specific frequency regions by taking advantage of internal resonance modes. With a proper, optimized topological design, LRAMs can be used, for instance, to build lightweight and thin noise insulation panels that operate in a low-frequency regime, where standard solutions for effectively attenuating the noise sources require dense and thick materials. Given the importance of the topological structure in obtaining the desired properties in acoustic metamaterials, the use of novel numerical techniques can be exploited to cre-ate a set of computational tools aimed at the analysis and design of optimized solutions. These are based on three fundamental pillars: (1) the multiscale homogenization of complex material structures in the microscale to get a set of effective properties capa-ble of describing the material behavior in the macroscale, (2) the model-order reduc-tion techniques, which are used to decrease the computational cost of heavy computa-tions while still maintaining a sufficient degree of accuracy, and (3) the topology optimi-zation methods that can be employed to obtain optimal configurations with a given set of constraints and a target material behavior. This set of computational tools can be applied to design acoustic metamaterials that are both efficient and practical, i.e. they behave according to their design specifications and can be produced easily, for in-stance, making use of novel additive manufacturing techniques.La concepció dels metamaterials com a estructures dissenyades artificialment amb l’objectiu d’obtenir un conjunt de propietats que no són assolibles en materials de manera natural, ha captat l’atenció de les comunitats científiques i industrials. Dins de l’ampli ventall d’aplicacions que se’ls pot donar als metamaterials, si ens centrem en el camp de l’acústica, la possibilitat de crear un material capaç d’atenuar de manera efectiva sorolls en rangs de freqüència concrets és de gran interès en multitud d’indústries. En aquest context, els anomenats “locally resonant acoustic metamaterials” (LRAMs) destaquen per la possibilitat de dissenyar la seva topologia interna per tal que produeixin elevats nivells d’atenuació en regions concretes de l’espectre de freqüències. Amb un disseny topològic òptim, els LRAMs poden servir, per exemple, per a la construcció de panells lleugers aïllants de soroll, que operin en rangs de freqüències baixos, en els quals la solució clàssica requereix de materials d’elevada densitat i espessor. Donada la importància de l’estructura topològica dels metamaterials acústics en l’obtenció de les propietats desitjades, resulta convenient l’ús de mètodes numèrics punters per al desenvolupament d’un conjunt d’eines computacionals que tinguin per objectiu l’anàlisi i el disseny de solucions òptimes. Tals eines es fonamenten en tres pilars: (1) la homogeneïtzació multiescala d’estructures de material complexes a una escala micro que derivi en l’obtenció de propietats efectives que permetin descriure el comportament del material a una escala macro, (2) tècniques de reducció per minimitzar l’esforç computacional mantenint nivells de precisió suficients i (3) mètodes d’optimització topològica emprats per a l’obtenció de configuracions òptimes donat un conjunt de restriccions i unes propietats de material objectiu. Aquestes eines computacionals es poden aplicar al disseny de metamaterials acústics que resultin eficients i pràctics a la vegada, és a dir, que es comportin segons les especificacions de disseny i siguin fàcilment fabricables, per exemple, mitjançant tècniques punteres d’impressió 3D

Estudi de la resolució numèrica de les equacions de conservació de massa, moment i energia, orientat a diversos problemes d'enginyeria: energia solar concentrada.

Consolidar i ampliar els coneixements en termodinàmica, transferència de calor, dinàmica de fluids computacional, aerodinàmica, etc. en genral i eficiència energètica en particular.Desenvolupar un treball d'aplicació al disseny en àmbits propis de la enginyeria en general i la optimizació energètica en particular.Aprofitant els grans avenços tecnològics dels darrers anys en eines computacional, en aquest treball es pretén desenvolupar un codi en C++ per a dur a terme càlculs CFD senzills de manera que serveixi d’introducció al camp de la dinàmica de fluids computacional.Malgrat, com s’ha dit, el present treball tingui un caràcter introductori la idea és que assenti les bases per a futurs projectes més elaborats que es centrin, més en concret, en l’àmbit d’aplicació escollit, que és la tecnologia CSP

Estudi de la resolució numèrica de les equacions de conservació de massa, moment i energia, orientat a diversos problemes d'enginyeria: energia solar concentrada.

Consolidar i ampliar els coneixements en termodinàmica, transferència de calor, dinàmica de fluids computacional, aerodinàmica, etc. en genral i eficiència energètica en particular.Desenvolupar un treball d'aplicació al disseny en àmbits propis de la enginyeria en general i la optimizació energètica en particular.Aprofitant els grans avenços tecnològics dels darrers anys en eines computacional, en aquest treball es pretén desenvolupar un codi en C++ per a dur a terme càlculs CFD senzills de manera que serveixi d’introducció al camp de la dinàmica de fluids computacional.Malgrat, com s’ha dit, el present treball tingui un caràcter introductori la idea és que assenti les bases per a futurs projectes més elaborats que es centrin, més en concret, en l’àmbit d’aplicació escollit, que és la tecnologia CSP