Dark acoustic metamaterials as super absorbers for low-frequency sound

Transcription

1 Reeived 5 Jul 11 Aepted 3 Fe 1 Pulished 7 Mr 1 DOI: 1.138/nomms1758 Drk ousti metmterils s super sorers for low-frequeny sound Jun Mei 1, *, Gunong M 1, *, Min Yng 1, Zhiyu Yng 1, Weiji Wen 1 & Ping Sheng 1 The ttenution of low-frequeny sound hs een hllenging tsk euse the intrinsi dissiption of mterils is inherently wek in this regime. Here we present thin-film ousti metmteril, omprising n elsti memrne deorted with symmetri rigid pltelets tht ims to totlly sor low-frequeny irorne sound t seletive resonne frequenies rnging from 1 1, Hz. Our smples n reh lmost unity sorption t frequenies where the relevnt sound wvelength in ir is three orders of mgnitude lrger thn the memrne thikness. At resonnes, the flpping motion of the rigid pltelets leds nturlly to lrge elsti urvture energy density t their perimeter regions. As the flpping motions ouple only minimlly to the rdition modes, the overll energy density in the memrne n e two-to-three orders of mgnitude lrger thn the inident wve energy density t low frequenies, forming in essene n open vity. 1 Deprtment of Physis, Hong Kong University of Siene nd Tehnology, Cler Wter By, Kowloon, Hong Kong, Chin. *These uthors ontriuted eqully to this work. Correspondene nd requests for mterils should e ddressed to P.S. (emil: sheng@ust.hk). 1 Mmilln Pulishers Limited. All rights reserved.

2 nture ommunitions DOI: 1.138/nomms1758 The ttenution of low-frequeny sound hs een hllenging tsk euse the dynmis of dissiptive systems re generlly governed y the rules of liner response, whih ditte the fritionl fores nd fluxes to e oth linerly proportionl to the rtes. It follows tht the dissiptive power is qudrti in rtes, therey ounting for the inherently wek sorption of lowfrequeny sound wves y homogeneous mterils. To enhne the dissiption t low frequenies, it is usully neessry to inrese the energy density inside the relevnt mteril, for exmple, through resonnes. However, in n open system rdition oupling to resonnes is n lterntive tht n e effetive in reduing dissiption. Although the dvent of ousti metmterils hs rodened the relm of possile mteril hrteristis 1, s yet, there re no speifi resonnt strutures trgeting the effiient nd suwvelength sorption of low-frequeny sound. In ontrst, vrious eletromgneti metmterils designed for sorption hve een proposed 54, nd n optil lk hole hs een relized y using metmterils to guide the inident wve into lossy ore 35,36. In this work, we show tht y using thin elsti memrnes deorted with designed ptterns of rigid pltelets, the resulting ousti metmterils n sor 86% of the ousti wves t ~17 Hz, with two lyers soring 99% t the lowest frequeny resonnt mode s well s t higher frequeny modes. The smple is thus oustilly drk, t those frequenies. Finite element simultions of the resonnt mode ptterns nd frequenies re in exellent greement with the experiments. In prtiulr, the mesured displement profiles of the resonnt modes show disontinuities in the slope round the pltelet perimeters, implying signifintly enhned urvture energy is onentrted in these smll volumes, whih re minimlly oupled to the rdition modes. This therey gives rise to strong sorption similr to vity system, even though the system is geometrilly open. This is hrterized y the ft tht t resonnes, the overll energy density in the system n e two-to-three orders of mgnitude lrger thn the inident wve s energy density. Results Smple onstruts nd sorption oeffiient mesurements. We first fous on reltively simple, proof-of-priniple struture, denoted Smple A. In Fig. 1, we show photo of the unit ell used in the experiment, omprising retngulr elsti memrne tht is 31 mm y 15 mm nd. mm thik. The elsti memrne ws fixed y reltively rigid grid, deorted with two semi-irulr iron pltelets with rdius of 6 mm nd thikness of 1 mm. The iron pltelets re purposely mde to e symmetril so s to indue flpping motion, s seen elow. Here the smple lies in the x y plne, with the two pltelets seprted long the x xis. Aousti wves re inident long the z diretion. This simple ell is used to understnd the relevnt mehnism nd to ompre with theoretil preditions. Another type of unit ell, denoted Smple B, is 159 mm y 15 mm nd omprises 8 identil pltelets deorted symmetrilly s two 4-pltelet rrys (with 15 mm seprtion etween the neighouring pltelets) fing eh other with entrl gp of 3 mm. Smple B is used to ttin ner-unity sorption of the low-frequeny sound t multiple frequenies. The mesured sorption s funtion of frequeny for Smple A is shown in Fig. 1, where it n e seen tht there re 3 sorption peks round 17, 34, nd 813 Hz. But perhps the most surprising is the sorption pek t 17 Hz, t whih more thn 7% of the inident ousti wve energy hs een dissipted. This is very high vlue y suh -µm memrne, given tht the wvelength in ir t suh low frequeny is out m. Below we show this phenomenon to rise diretly from the profiles of the memrne resonnes. Displement w (µm) d Displement w (µm) e Displement w (µm) Position (mm) Position (mm) Position (mm) Asorption , 1, f Asorption Displement w (µm) Figure 1 Asorption oeffiient nd displement profiles of smple A. () Photo of Smple A. The sle r is 3 mm. () The mesured sorption oeffiient (red urve) nd the positions of the sorption pek frequenies predited y finite-element simultions (lue rrows). There re three sorption peks loted t 17, 34 nd 813 Hz. (), (d), (e) The ross-setionl profiles of z-displement, w, long the x xis of the unit ell for eh of the three resonnes. The mesured z-displement profiles y lser virometer (red squres) nd the finite-element simultion results (lue urves) round 17, 34 nd 813 Hz re shown in (), (d) nd (e), respetively. The stright setions ( 7. 5 mm x mm) of the profile indite the positions of the pltelets, whih my e regrded s rigid. (f) Red irles denote the experimentlly mesured sorption oeffiient nd the mgnitude of the memrne displement w t 17 Hz when the distne etween the memrne nd the luminum refletor ws vried from 7 to 4 mm with 7 mm steps. The lue solid urve is guide to the eye. The dshed line denotes the sorption level when the luminum refletor is removed, tht is, when the distne etween the memrne nd the luminum refletor tends to infinity. 1 Mmilln Pulishers Limited. All rights reserved.

3 nture ommunitions DOI: 1.138/nomms1758 ARTICLE In Fig. 1 we lso indite the lulted sorption pek frequenies y lue rrows. The Young s modulus nd Poisson s rtio for the ruer memrne re P nd 8, respetively, whih hd een mesured experimentlly y Dmping Tehnologies (Methods). The imginry prt of the Young s modulus is tken to e in the form Im(E) ωχ, where ω is the ngulr frequeny nd χ = P s is otined y fitting to the sorption (Methods). Mny eigenmodes re found in the simultions. Out of these, we selet the ones tht re left right symmetri, euse the ntisymmetri ones would not ouple to the normlly inident plne wve. The resulting sorption pek frequenies re loted t 19, 346 nd 71 Hz, respetively (indited y the lue rrows in Fig. 1). They re seen to gree very well with the oserved pek frequenies. Out-of-plne displement profiles mesurement. In Fig. 1 e, we show the ross-setionl profile of the z-displement w long the x xis, within the unit ell for the three sorption pek frequenies. Red squres denote the experimentl mesured dt y lser virometer, wheres the lue urves re the finite-element simultion results. Exellent greement is seen. But the most prominent feture of the profiles is tht lthough the z-displement w is ontinuous t the perimeters of the pltelets (whose positions re indited y the stright setions of the urves where the urvture is zero), there exists shrp disontinuity in the first-order sptil derivtive of w norml to the perimeter. For the low-frequeny resonne, this disontinuity is used y the flpping motion of the two semiirulr pltelets tht is symmetri with respet to the x xis, wheres, for the 71 Hz resonne, it is used y the lrge virtion of the entrl memrne region, with the two pltelets ting s nhors. The intermedite frequeny mode is lso flpping mode, ut with the two ends of eh wing in opposite phse. Tuning the smple impedne. In Fig. 1f, we show the results of further tuning the impedne of the memrne y pling n luminum refletor t vrious ner-field distnes ehind the memrne. Here the sorption t 17 Hz is plotted s funtion of the mesured mximum norml displement of the memrne, for n inident wve with pressure modultion mplitude of.3 P. Eh symol (open irle) indites distne of seprtion etween the memrne nd the refletor, vrying from 7 to 4 mm in steps of 7 mm eh. It is seen tht dding n ir ushion n enhne the sorption, up to 86% t seprtion of 4 mm. Tht is roughly % of the wvelength. However, moving the refletor further will eventully redue the sorption to the vlue without the refletor, s indited y the dshed line. Asorption frequeny tunility. The hrters of the memrne eigenmodes ditte the mnner under whih their resonne frequenies re tunle: while for the flpping mode the frequeny is shown to derese when the pltelet mss is inresed, the memrne virtion mode frequeny n e inresed or deresed y vrying the distne of seprtion etween the two semiirulr pltelets. More speifilly, in Fig.,, we show the tunility of the sorption peks t 17 Hz nd 813 Hz, respetively. The messge is essentilly tht the low-frequeny pek vries s 1/ M, where M denotes the mss of single pltelet (wheres the high-frequeny pek is only minimlly ffeted y vrying M), nd the highfrequeny pek vries s 1/L, with L eing the seprtion etween the two pltelets (wheres the low-frequeny pek is only minimlly ffeted y vrying L). It is seen tht the mesured dt (red irles) gree very well with the simultion results (lue tringles). Elsti energy density vi finite-element simultions. To understnd the strong sorption, it is useful to onsider the ending wve (or flexurl wve) of thin solid elsti memrne Energy density enhnement ftor , 1,1 1, , , 4 stisfying the ihrmoni eqution 37 : w ( rh / D) w w =, where 3 D = Eh / 1( 1 n ) is the flexurl rigidity nd h is the thikness of the memrne, with ρ, E, nd v eing the mss density, Young s modulus, nd Poisson s rtio, respetively. The orresponding elsti urvture energy per unit re is given y 37,38 1/sqrt(M) (g 1/ ) 1/L (mm 1 ) Figure Asorption frequeny tunility nd the EDEF. () The flpping mode frequeny plotted s funtion of eh pltelet s mss M. The red irles denote the experimentl dt nd lue tringles the simultion results. It n e seen tht the low-frequeny sorption pek (17 Hz) in Fig. 1 vries s the inverse of the squre root of M. The lue solid line is to guide the eye. () The memrne virtion mode frequeny (813 Hz in Fig. 1) s funtion of the seprtion L etween the two pltelets. The red irles denote the experimentl dt nd lue tringles the simultion results. It n e seen tht the high-frequeny sorption pek (813 Hz) in Fig. 1 vries s the inverse of the seprtion L. The lue solid line is to guide the eye. () The EDEF for Smple A, plotted s funtion of frequeny. The mximum vlues of EDEF our t the sme frequenies s the sorption peks. The reltively smller vlues of EDEF t higher frequenies re noted to e ompensted y the ω dependene of the sorption oeffiient (see eqution ()). 1 W = + w w + w w w D n + ( 1 n) x y x y x y. As Ω is funtion of the seond-order sptil derivtives of w, when the first-order derivtive of w is disontinuous ross the edge oundry, it is esy to infer tht the rel energy density Ω should hve very lrge vlue within the perimeter region (divergent in the (1) 1 Mmilln Pulishers Limited. All rights reserved.

4 nture ommunitions DOI: 1.138/nomms1758 limit of thin shell). Moreover, s the seond derivtive is qudrti, the integrted vlue of the totl potentil energy must lso e very lrge. In the limit of smll h, the virtionl modes of our system my e regrded s wek-form solution of the shell model, in the sense tht, lthough the ihrmoni eqution is not stisfied t the perimeter of the pltelets (euse the higher order derivtives do not exist), esides this set of points with mesure zero, the solution is still minimizer of the relevnt Lgrngin. The predited lrge vlue of Ω within the perimeter region is esily verified s shown in Fig. 3, where we plot the elsti potentil energy density U otined from the COMSOL simultions (Fig. 3, where the olour is ssigned ording to logrithmi sle, se 1) nd displement w (Fig. 3) distriution within the x-y plne (tht is, the mid-plne of the memrne) round three sorption pek frequenies: 19, 346, nd 71 Hz (from top to ottom). The energy density in the perimeter region is seen to e lrger thn tht in other regions y 3 orders of mgnitude. There re lso highenergy density regions t the upper nd lower edges of the unit ell, where the memrne is lmped. In our simultions, the integrted energy density U within the perimeter region ounts for 98% (19 Hz), 87% (346 Hz), nd 8% (71 Hz) of the totl elsti energy in the whole system. As the lol dissiption is proportionl to the produt of energy density with dissiption oeffiient, the lrge multiplying effet implied y the huge energy density n men very sustntil sorption for the system s whole. This ft is lso refleted in the strin distriution round the three sorption pek frequenies, s shown in Fig. 3. It is found tht the strin in the perimeter region, on the order of , is muh lrger thn tht in the other prts of the memrne y t lest 1 orders of mgnitude. Energy density enhnement ftor. In ordne with our metmteril eing highly sorptive, our smple my e hrterized y n effetive prmeter the energy density enhnement ftor (EDEF) defined to e the rtio of the verge energy inside the smple to the energy density of the inident wve. As disussed previously, the physil mehnism of suh high sorption is the flpping motion of the metlli pltelets, ttendnt with very high elsti urvture energy density within the perimeter region of the pltelets. A plot of the lulted EDEF for Smple A s funtion of frequeny, rnging from 1 1, t resonnes, is shown in Fig.. It is seen tht the vlue of EDEF rnges from 1 1, t resonnes. For sorption, the reltively smller vlues of EDEF t higher frequenies re ompensted y the ω dependene of the sorption oeffiient (see eqution () elow). Thus, our smples my e regrded s n open vity, onept tht is further elorted in the Disussion. Ahieving ner-unity sorption. As the high urvture energy density is mostly onfined in the perimeter regions of the pltelets nd the edges of the unit ell, we my ttin etter sorption y further tweking the unit ell struture. Compred with Smple A, the unit ell of Smple B hs more pltelets nd longer edges (Fig. 4), while its eigenmodes mostly remin unhnged in hrter due to the similr lyout (see Supplementry Fig. S1 for experimentl dt in fvour of this onlusion). Therefore, Smple B should e similr to Smple A ut should disply etter sorption performne. As shown in Fig. 4, tht is indeed the se. In our mesurements, we hve two lyers of Smple B, nd tune the impedne of the system y pling n luminum refletor 8 mm ehind the seond lyer. The distne etween the first nd seond lyers ws lso 8 mm. It n e seen tht there re mny sorption peks round 164, 376, 511, 645, 87, nd 96 Hz. The sorption peks t 164 Hz nd 645 Hz re seen to e ~99%. By using COMSOL, we hve lso lulted the sorption pek frequenies for single lyer of Smple B. They re loted round 17, 31, 546, 771, Figure 3 Elsti energy density distriution within Smple A. () The lulted distriutions of the elsti potentil energy density within the x y plne. () The lulted norml displement w within the x y plne. () The lulted distriution of the tre of the strin tensor e = exx + eyy + ezz within the x y plne. In (), (), nd (), the three rows, from top to ottom, re for the three sorption pek frequenies of 19 Hz, 346 Hz, nd 71 Hz, respetively. In () nd (), the olour rs indite the reltive mgnitudes of the quntities in question, with the numers shown to e the logrithms of the mgnitudes, se 1. In (), the olour r sle is liner. As these modes re symmetri with respet to the x oordinte, we plot only the left hlf for etter resolution. The stright dshed lue lines indite the mirroring plnes. The sle r is 1 mm. 1 Mmilln Pulishers Limited. All rights reserved.

5 nture ommunitions DOI: 1.138/nomms1758 ARTICLE nd 969 Hz, respetively. These re indited y lue rrows in Fig. 4. Resonly good greement with the experimentl vlues is seen, with no djustle prmeters. Asorption lultion. In ordne with the Poynting s theorem for elsti wves 39, the dissipted power within the memrne n e lulted s Q w / E UdV, = ( ) where U is the elsti energy density in the smple. Asorption is defined s Q/(PS), where P = p /(ρ) denotes the Poynting s vetor for the inident ousti wve nd S is memrne s re, with p, ρ nd eing the pressure mplitude, mss density nd sound veloity of ir, respetively. With the previously given prmeter vlues, the sorption t the three resonnt frequenies of Smple A (in order of inresing frequeny) is lulted to e 6, 9 nd 43%, respetively. It is noted tht the lulted vlues reprodue the reltive pttern of the three sorption peks, lthough they re smller thn the experimentl vlues y ~1 %. This disrepny is ttriuted to the imperfetion in the symmetry of the smple, wherey multitude of symmetri virtionl eigenfuntions n e exited y the normlly inident plne wve. Together with the width of these modes, they n effetively ontriute to level of kground sorption not ounted for in the simultions. In ft, the exittion of symmetri virtionl mode ws experimentlly oserved, shown in Supplementry Fig. S1. Differene with the refletive metmteril. To ontrst with our previous memrne-type metmterils tht exhiit ner-totl refletion t n nti-resonne frequeny,3, here we desrie riefly the mehnism of suh refletive metmterils s well s present their mesured sorption performne. Strong refletion of sound n our t frequeny in-etween two neighouring resonnt (eigenmode) frequenies. Tht is, while t the resonnt eigenmode frequeny the exittion of the eigenmodes n led to trnsmission peks, t the nti-resonne frequeny the out-of-phse hyridiztion of two nery eigenmodes leds to ner-totl deoupling of the memrne struture from the rdition modes. This turns out to lso oinide with divergent resonne-like ehviour of the dynmi mss density. Nertotl refletion of the ousti wve is therey the onsequene t the nti-resonne frequeny. Beuse the struture is ompletely deoupled from the ousti wve t the nti-resonne frequeny, Asorption.. () , 1, Figure 4 Asorption oeffiient of smple B. () Photo of Smple B. The sle r is 3 mm. () The red urve indites the experimentlly mesured sorption oeffiient for two lyers of Smple B with n luminum refletor pled 8 mm ehind the seond lyer. The distne etween the first nd seond lyers is lso 8 mm. The sorption peks re loted t 164, 376, 511, 645, 87 nd 96 Hz. Blue rrows indite the positions of the sorption pek frequenies predited y finite-element simultions. Good greement is seen. the sorption is nturlly very low s shown in Fig. 5 ner 45 Hz ( shrp trnsmission dip n e seen t this frequeny in the logrithmi sle). But, even t the resonnt frequenies, we note tht the sorption oeffiient for this type of metmteril is still low, rely rehing 45% t the reltively high frequeny of 913 Hz, not even lose to wht we hve hieved with the drk ousti metmterils. This is ttriuted to the reltively strong oupling to the rdition modes used y the piston-like motion of memrne tht n led to high trnsmission (8 t 51 Hz, 3 t 913 Hz). Even for five-lyer smple 3, the verged sorption oeffiient is mere., with mximum vlue not surpssing 5, s shown in Fig. 5. And, we must emphsize tht esides the lrge numer of memrne lyers, this smple ws lso sndwihed y two soft Trnsmission, refletion, sorption Figure 5 Differene etween the refletive nd sorptive metmterils. () Mesured trnsmission T (green dshed urve), refletion R (lue dot-dshed urve) nd sorption A = 1 R T (red solid urve) for one-lyer smple of refletive metmteril (see ref. for detils) omprising irulr elsti memrne fixed y rigid grid nd with one irulr disk tthed to the entre. It is seen tht t the nti-resonne frequeny of 45 Hz, where the memrne is nerly totlly refletive ( shrp dip in trnsmission, t tht frequeny, is visile in the logrithmi sle), the sorption is very low. Even t the resonne frequenies, the two peks of sorption re just over 4%, muh smller thn tht of Smple A, shown in (). () The orresponding experimentl dt for five-lyer smple of refletive metmteril (see ref. 3 for detils) sndwihed y two soft pnels with holes (for the purpose of enhning the sorption), with eh lyer omprising mtrix of squre elsti memrnes fixed y rigid grid, nd deorted with multiple irulr disks with different weights (for the purpose of induing multiple resonnes nd hene effeting nerly rod-nd refletive funtionlity etween 1 nd 1, Hz). The overll sorption is seen to e smll s ompred with tht of Smple A, shown in (). () The orresponding experimentl dt for the one-lyer Smple A, without k refletor. The overll sorption is high (round 4%). In prtiulr, t the resonne frequeny of 17 Hz, the pek sorption n reh 7%. 1 Mmilln Pulishers Limited. All rights reserved.

6 nture ommunitions DOI: 1.138/nomms1758 pnels with holes, with the purpose of enhning the sorption. Therefore, even with these efforts, this pnel s sorption performne is still wy elow our drk ousti metmterils. To ontrst with the refletion pnels, in Fig. 5 we show the trnsmittne nd refletne dt (together with the sorption) of our Smple A. It is seen tht with this single-lyer smple the sorption n lredy exeed tht of the five-lyer smple y signifint mount. Suh lrge differene is due to the ft tht the high energy density regions in our super-sorptive ousti metmteril ouple minimlly with the rdition modes, therey ehving s n open vity. Asorption under olique inidene. As mentioned erlier, there re mny eigenmodes in the system tht re deoupled from the normlly inident wve owing to its left right symmetry. To explore the onsequene when suh symmetry is roken, we hve lso rried out mesurements on Smple B under olique inidene. The mesured dt nd simultion results, disussed nd presented in Supplementry Figs S S4 nd the Supplementry Disussion, indite qulittive similrity up to 6, t whih ngle the frequeny rnges of Hz nd 1, 1, Hz exhiit pronouned inrese in sorption. Thus, the overll performne of the drk ousti metmterils does not deteriorte under rod rnge of inident ngles ut my even improve within ertin frequeny regimes. Disussion In onventionl open system, high energy density is eqully likely to e rdited, vi trnsmitted nd refleted wves, s to e sored. We wish to point out tht in the present se, the smll volumes in whih the elsti energy is onentrted my e regrded s n open vity in whih the lterl onfinement in the plne of the memrne is supplemented y the onfinement in the norml diretion, owing to the ft tht the reltive motion etween the pltelets nd the memrne ontriutes only minimlly to the verge norml displement of the memrne. Hene, from the dispersion reltion k + k = k ( / ) p l for the wves in ir, where k (k ) denotes the omponent of the wve vetor eing prllel (perpendiulr) to the memrne plne nd λ is the wvelength in ir, it n e seen tht the reltive motions etween the pltelets nd the memrne must e on sle smller thn the smple size d λ. Therefore, these motions n only ouple to the evnesent wves s the relevnt k k. Only the verge norml displement of the memrne, orresponding to the piston-like motion, would hve k omponents tht re peked t zero nd hene n rdite. But the high energy density regions (espeilly those ssoited with the flpping modes), owing to their smll lterl dimensions, ontriute minimlly to the verge omponent of the norml displement. We hve demonstrted tht the effet of very lrge urvture energy density t the perimeter of the pltelets, in onjuntion with its onfinement effet, n e prtiulrly effetive for suwvelength low-frequeny ousti sorption. As the memrne system hs lso een shown to e effetive in totlly refleting low-frequeny sound,3, together they n onstitute system of lowfrequeny sound mnipultion with rod potentil pplitions. In prtiulr, lowering the in noise in irliners nd ships, tuning the ousti qulity of musi hlls, nd environmentl noise tement long highwys nd rilwys re some promising exmples. Methods Young s modulus nd Poisson s rtio of the memrne. In the experiments, the memrne is mde of silione ruer Silsti The Young s modulus nd the Poisson s rtio of the memrne were mesured y Dmping Tehnologies. The mesurement ws performed in the ASTM E-756 sndwih em onfigurtion, where the dynmi mehnil properties of the memrne were otined from the mesured differene etween the steel se em (without memrne) properties nd the properties of the ssemled sndwih em test rtile (with the memrne sndwihed in the ore of the em). In the mesurement, the Young s modulus (P) , Figure 6 Young s modulus of the thin-film memrne. Red irles denote the mesured Young s modulus E t severl frequenies. Blue dshed urves denote the verge vlue, P, within the relevnt frequeny rnge. sher modulus (µ) dt of the memrne t severl disrete frequenies ould e otined. The Poisson rtio (ν) of the memrne ws found to e round 8. Therefore, ording to the reltion etween different elsti prmeters, E = m( 1+ n), we otin the Young s modulus (E) t those disrete frequenies, shown s red irles in Fig. 6. For our mteril, the mesured E vries from P to P within the relevnt frequeny rnge. We hve hosen to use frequeny-independent vlue of the Young s modulus E = P (shown s the dshed line in Fig. 6) so s to simplify the model. Experimentl set-up. Mesurements of the sorption oeffiients shown in Figs 1,f; 4 nd 5 were onduted in modified impedne tue pprtus 4 omprising two Brüel & Kjær Type-46 impedne tues with the smple sndwihed in etween. The front tue hs loud speker t one end to generte plne wve. Two sensors were instlled in the front tue to sense the inident nd refleted wves, therey otining oth the refletion mplitude nd phse. The third sensor in the k tue (whih is terminted with n nehoi sponge) senses the trnsmitted wve, to otin the trnsmission mplitude nd phse. The nehoi sponge hs length of 5 m, suffiient to ensure omplete sorption of the trnsmitted wve ehind the third sensor. The signls from the three sensors re suffiient to resolve the trnsmitted nd refleted wve mplitudes, in onjuntion with their phses. The sorption oeffiient ws evluted s A = 1 R T, with R nd T eing the mesured refletion nd trnsmission oeffiients, respetively. The sorption mesurements were lirted to e urte y using mterils of known dissiption. For the olique inidene, wedges with designted ngles re mhined out of luminum to introdue ngles etween the xis of the impedne tue nd the smple. An luminum plte is fixed ehind the smple to eliminte trnsmission. Therefore, the sensor on the trnsmission side is not needed for olique mesurement of sorption. A photo of the set-up is shown in Supplementry Fig. S. The ross-setionl profiles of the z-diretion displement shown in Fig. 1 e were otined y using the lser virometer (Type No. Grphte AT5-5) to sn the Smple A long the x xis, within the unit ell round the three sorption pek frequenies. Theory nd simultions. The numeril simultion results shown in Figs 1 e,, 3 nd 4 were prepred using COMSOL MULTIPHYSICS, finite-element nlysis nd solver softwre pkge. In the simultions, the edges of the retngulr mem- initil initil rne re fixed. An initil stress in the memrne, s x = s y =. 1 5 P ws used in the lultion s the tunle prmeter to fit the dt. The mss density, Young s modulus nd Poisson s rtio for the ruer memrne re 98 kg m 3, P, nd 8, respetively. The mss density, Young s modulus nd Poisson s rtio for the iron pltelets re 7,87 kg m 3, 1 11 P, nd.3, respetively. Stndrd vlues for ir, tht is, ρ = 1.9 kg m 3, mient pressure of 1 tm, nd speed of sound in ir of = 34 m s 1, were used. Rdition oundry onditions were used t the input nd output plnes of the ir domins in the simultions. Referenes 1. Liu, Z. et l. Lolly resonnt soni mterils. Siene 89, ().. Yng, Z., Mei, J., Yng, M., Chn, N. & Sheng, P. Memrne-type ousti metmteril with negtive dynmi mss. Phys. Rev. Lett. 11, 431 (8). (3) 1 Mmilln Pulishers Limited. All rights reserved.

7 nture ommunitions DOI: 1.138/nomms1758 ARTICLE 3. Yng, Z., Di, H., Chn, N., M, G. & Sheng, P. Aousti metmteril pnels for sound ttenution in the 5 1 Hz regime. Appl. Phys. Lett. 96, 4196 (1). 4. Liu, Z., Chn, C. & Sheng, P. Anlyti model of phononi rystls with lol resonnes. Phys. Rev. B 71, 1413 (5). 5. Mei, J., Liu, Z., Wen, W. & Sheng, P. Effetive mss density of fluid-solid omposites. Phys. Rev. Lett. 96, 431 (6). 6. Mei, J., Liu, Z., Wen, W. & Sheng, P. Effetive dynmi mss density of omposites. Phys. Rev. B 76, 1345 (7). 7. Li, J., Fok, L., Yin, X., Brtl, G. & Zhng, X. Experimentl demonstrtion of n ousti mgnifying hyperlens. Nture Mter. 8, (9). 8. Pendry, J. & Li, J. An ousti metfluid: relizing rodnd ousti lok. New J. Phys. 1, 1153 (8). 9. Li, J. & Chn, C. Doule-negtive ousti metmteril. Phys. Rev. E 7, 556 (4). 1. Fng, N. et l. Ultrsoni metmterils with negtive modulus. Nture Mter. 5, 4556 (6). 11. Zhng, S., Yin, L. & Fng, N. Fousing ultrsound with n ousti metmteril network. Phys. Rev. Lett. 1, (9). 1. Milton, G. W. New metmterils with mrosopi ehvior outside tht of ontinuum elstodynmis. New J. Phys. 9, 359 (7). 13. Milton, G. W. & Willis, J. R. On modifitions of Newton s seond lw nd liner ontinuum elstodynmis. Pro. R. So. A 463, (7). 14. Lu, M. H. et l. Negtive irefrtion of ousti wves in soni rystl. Nture Mter. 6, (7). 15. Feng, L. et l. Aousti kwrd-wve negtive refrtions in the seond nd of soni rystl. Phys. Rev. Lett. 96, 1431 (6). 16. Lee, S. H., Prk, C. M., Seo, Y. M., Wng, Z. G. & Kim, C. K. Composite ousti medium with simultneously negtive density nd modulus. Phys. Rev. Lett. 14, 5431 (1). 17. Guenneu, S., Movhn, A., Petursson, G. & Rmkrishn, S. A. Aousti metmterils for sound fousing nd onfinement. New J. Phys. 9, 399 (7). 18. Ding, Y., Liu, Z., Qiu, C. & Shi, J. Metmteril with simultneously negtive ulk modulus nd mss density. Phys. Rev. Lett. 99, 9394 (7). 19. Wu, Y., Li, Y. & Zhng, Z. Q. Effetive medium theory for elsti metmterils in two dimensions. Phys. Rev. B 76, 5313 (7).. Li, Y., Wu, Y., Sheng, P. & Zhng, Z. Q. Hyrid elsti solids. Nture Mter. 1, 64 (11). 1. Hu, X., Chn, C. T. & Zi, J. Two-dimensionl soni rystls with Helmholtz resontors. Phys. Rev. E 71, 5561 (5).. Yo, S., Zhou, X. & Hu, G. Experimentl study on negtive effetive mss in 1D mss spring system. New J. Phys. 1, 43 (8). 3. Cheng, Y., Xu, J. Y. & Liu, X. J. One-dimensionl strutured ultrsoni metmterils with simultneously negtive dynmi density nd modulus. Phys. Rev. B 77, (8). 4. Zhu, X., Ling, B., Kn, W., Zou, X. & Cheng, J. Aousti loking y superlnes with single-negtive mterils. Phys. Rev. Lett. 16, 1431 (11). 5. To, H. et l. A metmteril sorer for the terhertz regime: design, frition nd hrteriztion. Opt. Express 16, (8). 6. Lndy, N., Sjuyige, S., Mok, J., Smith, D. & Pdill, W. Perfet metmteril sorer. Phys. Rev. Lett. 1, 74 (8). 7. Avitzour, Y., Urzhumov, Y. A. & Shvets, G. Wide-ngle infrred sorer sed on negtive-index plsmoni metmteril. Phys. Rev. B 79, (9). 8. Diem, M., Koshny, T. & Soukoulis, C. M. Wide-ngle perfet sorer/ therml emitter in the terhertz regime. Phys. Rev. B 79, 3311 (9). 9. Hu, C., Zho, Z., Chen, X. & Luo, X. Relizing ner-perfet sorption t visile frequenies. Opt. Express 17, (9). 3. Hu, C., Liu, L., Zho, Z., Chen, X. & Luo, X. Mixed plsmons oupling for expnding the ndwidth of ner-perfet sorption t visile frequenies. Opt. Express 17, (9). 31. Liu, X., Strr, T., Strr, A. F. & Pdill, W. J. Infrred sptil nd frequeny seletive metmteril with ner-unity sorne. Phys. Rev. Lett. 14, 743 (1). 3. Hu, C. G., Li, X., Feng, Q., Chen, X. N. & Luo, X. G. Investigtion on the role of the dieletri loss in metmteril sorer. Opt. Express 18, (1). 33. Liu, N., Mesh, M., Weiss, T., Hentshel, M. & Giessen, H. Infrred perfet sorer nd its pplition s plsmoni sensor. Nno Lett. 1, 3448 (1). 34. Liu, X. et l. Tming the Blkody with infrred metmterils s seletive therml emitters. Phys. Rev. Lett. 17, 4591 (11). 35. Nrimnov, E. E. & Kildishev, A. V. Optil lk hole: rodnd omnidiretionl light sorer. Appl. Phys. Lett. 95, 4116 (9). 36. Cheng, Q., Cui, T. J., Jing, W. X. & Ci, B. G. An omnidiretionl eletromgneti sorer mde of metmterils. New J. Phys. 1, 636 (1). 37. Ventsel, E & Kruthmmer, T. Thin Pltes nd Shells: Theory, Anlysis, nd Applitions (Mrel Dekker, 1). 38. Lndu, L. D. & Lifshitz, E. M. Theory of Elstiity, 3rd edn. (Pergmon, 1986). 39. Auld, B. A. Aousti Fields nd Wves in Solids (John Wiley & Sons, 1973). 4. Ho, K. M., Yng, Z., Zhng, X. & Sheng, P. Mesurements of sound trnsmission through pnels of lolly resonnt mterils etween impedne tues. Appl. Aoust. 66, (5). Aknowledgements This work is supported y Hong Kong RGC grnt HKUST 647, HKUST 66611, nd HKUST/CRF/11G. Author ontriutions P.S. initited nd designed the reserh; Z.Y., G.M., nd W.W. designed nd rried out the experiments; J.M. nd P.S. provided the theory frmework; J.M., G.M., Z.Y., M.Y. nd P.S. nlysed dt, nd J.M., G.M., P.S. wrote the mnusript. Additionl informtion Supplementry Informtion ompnies this pper t ntureommunitions Competing finnil interests: The uthors delre no ompeting finnil interests. Reprints nd permission informtion is ville online t reprintsndpermissions/ How to ite this rtile: Mei, J. et l. Drk ousti metmterils s super sorers for low-frequeny sound. Nt. Commun. 3:756 doi: 1.138/nomms1758 (1). 1 Mmilln Pulishers Limited. All rights reserved.