FIELD OF THE INVENTION

The present invention relates to a sonic crystal noise barrier, and to an element for use in such a barrier. Other aspects of the invention relate to other forms of sound attenuator comprising said elements.

BACKGROUND TO THE INVENTION

Periodically spaced arrays of cylinders, known as sonic crystals, can be used for attenuation of sound. A periodic array of solid cylinders reduces sound selectively according to the distance between the cylinders (called the lattice constant) and their radii. The sound attenuation characteristics of a sonic crystal can be tuned by appropriate selection of lattice constant and cylinder radius. Sonic crystal arrays are visually attractive. One of the major impulses to work on sonic crystals as noise barriers was the discovery that a sculpture (in Madrid) consisting of periodically- arranged arrays of cylinders of same radius but different lengths had interesting sound attenuating properties [R. Martinez - Sala, J. Sancho, J. V .Sanchez, V. Gomez, J. Llinares and F. Meseguer 1995 "Sound attenuation by sculpture", Nature (London) 378, 241 ]. Such sonic crystals have been investigated for use as traffic noise barriers, to replace more traditional solid noise barriers. The particular merits of sonic crystal arrays for traffic noise are the fact that they look more attractive, their performance is less affected by wind and they can be designed with 'deliberate' vacancies i.e. pathways can be made through them thus avoiding the severance caused by conventional noise barriers which have to be airtight.

However, one major drawback for the use of conventional sonic crystals as traffic noise barriers is that the acoustical performance of a rigid cylinder array also depends on the angle between the sound source and the receiver. For traffic barriers the sound sources (vehicles) move along the barrier, with the result that the sound attenuation is not consistent, and the barrier's effectiveness is reduced.

It would be desirable to provide a sonic crystal noise barrier that is less sensitive to the effects of angle between sound source and receiver. Conventional sonic crystals also have a fairly narrow band at which sonic attenuation is greatest; this is a consequence of the cylinder radius and lattice spacing. This may be addressed to some extent by varying these properties of the configuration of an array, but this is unsatisfactory and makes construction more complex. It would therefore also be desirable to provide a sonic crystal noise barrier with identical elements and with a broader band of attenuation frequencies.

Cabrera et al (arXiv:1004.2570v2 [cond-mat.mtrl-sci] 7 Jul 2010, at http://arxiv.org/abs/1004.2570v2) describe a variant sonic crystal noise barrier in which the elements are perforated metal shells filled with rubber crumb. The sound attenuation seen is a consequence of the arrangement of the elements in the array, and the sound absorbing properties of the rubber crumb itself.

SUMMARY OF THE INVENTION

The present inventors have identified that the problems with conventional sonic crystals can be alleviated through use of elements which have their own resonant frequencies; this results in additional attenuation which is largely independent of source-receiver angle. The invention in certain embodiments uses the 'breathing mode' resonance of thin-walled elastic shells placed inside symmetrically-slit hollow cylinders.

According to a first aspect of the present invention, there is provided a constructional element for use in a sound barrier, the element comprising a generally elongate rigid outer shell; a generally tubular elastic inner member disposed within the outer shell and separated from the outer shell by an air gap; the inner member extending lengthwise along at least a portion of the length of the shell; and the outer shell having a plurality of symmetrically disposed openings arranged around the perimeter thereof, such that the air gap is in communication with the exterior of the shell.

The design is novel and advantageous in four respects: (1 ) it incorporates the protection offered by outer cylinders for the relatively delicate thin-walled inner elastic members; (2) it produces multiple angle-independent resonances associated with interaction between the resonances of the inner member and the annulus between the members and the shells; (3) at least one of these resonances will be at frequencies below the first frequency of the peak attenuation that would be achieved with an identical configuration of rigid solid cylinders and (4) since the elastic member resonances are predictable from basic information about diameter and thickness (unlike balloons for which they depend also on tension) it is possible to design the whole system to give a customised acoustical performance. Compared with an array of solid slotted cylinders, or cylinders filled with rubber crumb, for which the only design variables (apart from lattice constant and radius which are common to all sonic crystal cylinder arrays) are the slit or perforation area and the acoustic properties of the filling, the concentric arrangement offers the additional design variables of elastic shell radius and thickness. It is also possible to vary the acoustical performance by varying the width of the openings.

The precise values selected for these variables (shell and member radius and thickness, opening width, as well as length of element) will vary depending on the use to which the member is to be put. The skilled person is able to select appropriate values depending on the nature of the sound to be attenuated. Similarly, when the elements are used in an array, the lattice constant and arrangement of the elements may be chosen according to the desired properties of the array.

The rigid shell may be made from any suitable material, for example, metal, plastic, or the like. Preferably it is made from PVC.

The shell is preferably cylindrical.

Preferably the perimeter of the shell includes at least two openings, more preferably at least four openings. Preferably the perimeter includes four openings disposed at 90 degree intervals around it. It will be understood that the shell may include multiple sets of four openings; for example, a set of four openings may be disposed around the perimeter of the shell in one location along the length of the shell, with a further set of four openings at a second location along the length of the shell. It is preferred that where multiple sets of openings are present, the openings are aligned with the same orientation across sets.

Preferably the openings are elongate, for example, in the form of slits. The slits may extend along the length of the shell. In preferred embodiments, multiple sets of slits are present; the portions of the shell between the sets of slits serve to increase stability and rigidity of the structure. The length of the slits is not believed to be critical to the operation of the invention, provided that the desired sound attenuating properties are present.

The inner member is preferably formed of an elastomeric material, for example rubber, preferably latex. In preferred embodiments, untreated (non-vulcanised) latex is used. Other suitable elastic materials may be used; for example a synthetic polymer, e.g. polyethylene. We believe that desirable materials have a Young's modulus of between 0.5 - 10 MPa, more preferably 1 - 5 MPa, and most preferably 1 - 2 MPa. The inner member preferably extends along substantially all of the length of the rigid shell; in preferred embodiments the ends of the inner member are fastened or fixed to the ends of the rigid shell.

The inner member is preferably not under tension; or at most is under a slight tension sufficient to hold it in place. It has been found that placing the inner member under a large tension (for example, inflating or partially inflating the inner member) reduces the sound attenuating properties.

The precise dimensions of the rigid shell and the inner member will be selected by the skilled person in accordance with the desired properties of the element. For example, where the member is to be used as part of a traffic noise barrier, the element may be roughly 2 to 3 metres in length, preferably around 3 metres. The outer shell may be around 1 10 mm in outer diameter, and around 5-10 mm thick. The inner member may be around 80 mm in outer diameter, and around 0.5 to 2 mm thick.

Also provided in accordance with the present invention is a sound barrier comprising a plurality of elements as described. The elements are preferably arranged in a regular array. In preferred embodiments the elements have a generally vertical orientation, although in certain embodiments other orientations, for example generally horizontal, may be used. The elements may be of the same length, or may be of differing lengths. The sound barrier may be used as a traffic noise barrier. Alternatively, the sound barrier may comprise part of a ventilation grille, duct cover, or ventilation silencer.

An alternative aspect of the invention provides a constructional element for use in a sound barrier, the element comprising two or more generally parallel elongate elastic beams attached to an elongate rigid backing beam, to form at least one, and preferably multiple, cavities between the elastic beams. In this embodiment, the element provides resonances of the elastic walls formed by the elastic beams as well as the resonances of the open cavities. The rigid beam may comprise plastic, e.g. PVC, or metal, e.g. steel. The elastic beams may comprise rubber or latex; or polyethylene.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will now be described by way of example only and with reference to the accompanying drawings, in which:

Figure 1 shows a cross section of a constructional element in accordance with a first embodiment of the present invention;

Figure 2 shows a side view of the element of Figure 1 ;

Figure 3 shows a cross section of a constructional element in accordance with a second embodiment of the invention;

Figures 4 and 5 show predicted and experimental sound attenuation for a single element and an array of elements in accordance with an embodiment of the present invention. Figure 4 shows insertion loss computed analytically ( ) and measured experimentally ( ) for single scatterer. Distances from scatterer to the source and receiver are 1 .5 m and 0.05m, respectively, (a) The viscoelastic shell made of latex (a ₀ =0.0215 m and h =0.00025 m). (b) Concentric 4-slit rigid cylinder (r ₀ = 0.0275 m, thickness h _r = 0.002 m and d _n = 0.004) and viscoelastic shell made of latex (a ₀ = 0.0215 m and h =0.00025 m). Figure 5 shows insertion loss computed analytically (—

-) and measured experimentally ( ) for square 3x3 array of scatterers with lattice constant L = 0.08 m. Distances from scatterer to the source and receiver are 1 .5 m and 0.05 m, respectively, (a) The viscoelastic shell made of latex (a ₀ = 0.0215 m and h = 0.00025 m). (b) 4-slit rigid cylinder (r ₀ = 0.0275 m, thickness hr = 0.002 m and d _n = 0.004). (c) Concentric 4-slit rigid cylinder (r ₀ = 0.0275 m, thickness hr = 0.002 m and dn = 0.004) and viscoelastic shell made of latex (a ₀ = 0.0215 m and h = 0.00025 m).

Figures 6 and 7 show predicted sound attenuation for a single element and an array of elements in accordance with an alternative embodiment of the present invention. Figure 6 shows insertion loss computed numerically for U-shaped scatterer made of either elastic ( ) or rigid ( ) walls. Distance from scatterer to receiver is 0.05 m.

(a) Polyethylene elastic walls, (b) Steel elastic walls. Figure 7 shows insertion loss computed numerically for 7x3 array of U-shaped scatterers made of either elastic ( -) or rigid ( ) walls. Distance from scatterer to receiver is 0.05 m. (a) Polyethylene elastic walls, (b) Steel elastic walls.

DETAILED DESCRIPTION OF THE DRAWINGS

Referring first of all to Figures 1 and 2, these show a constructional element 10 for use in a sound barrier, in accordance with a first embodiment of the present invention. The element 10 comprises a rigid outer shell 12 made from PVC, which includes a number of groups 14 of four slits 16 arranged at 90 degree intervals around the perimeter of the shell 12. Within the outer shell is located an elastic member 18 in the form of a latex tube. The elastic member is fixed at either end (not shown) to the ends of the outer shell. There is an annular gap 20 formed between the shell 12 and the member 18, which gap is in communication with the slits 16.

In use, a number of elements 10 are arranged into a regular array to form a sound barrier. The radius of the elements 10 and their spacing may be selected by the skilled person to obtain a desired barrier effect.

Figure 3 shows a cross section of an alternative constructional element 1 10, which includes a pair of parallel polyethylene elastic beams 1 18 mounted to a rigid backing beam 1 12, to form a U shaped cavity.

The functioning of each of these constructional elements, and an analysis of their sound attenuating properties, will now be presented.

INTRODUCTION

One of the distinctive features of finite periodic arrays of scatterers is the high attenuation over the selective range of frequency intervals [1 , 2]. This effect is explained by the theory of wave propagation in the infinite periodic structures [3]. In these structures there exist the band gaps where waves do not propagate. It is well- known that the band gaps can be tuned to the selected frequencies by changing the spacing between scatterers that can significantly improve the performance of the periodic structure as the acoustic screens.

There are many different approaches to improving the performance of the periodic structures such as increasing the filling fraction [4], varying the arrangement of the scatterers [5] and replacing scatterers by the resonant elements [6, 7, 8]. Resonating array elements create standing waves that result in the creation of new low frequency band gaps along with the classical Bragg band gaps [9]. In this essay we propose two different resonant elements such as concentric N-slit cylinder and thin elastic shell and U-shaped scatterer with elastic walls, referred to as composites.

Resonant properties of thin elastic structures in air, such as shells and plates, are analysed using Kirchhoff-Love approximations. Using this preliminary result the elastic materials can be chosen so that resonances appear at low frequencies. The elastic shells and plates form a part of the composites, which exhibit additional resonances related to the constructed cavity. When composite elements are arranged in doubly- periodic arrays, these resonances generate band gaps.

The first type of resonators preserves the axisymmetric resonance of the elastic shell although it appears at a lower frequency. Additional resonance due to the annular cavity and the slits is observed at a higher frequency. This resonant behaviour is predicted by a semi-analytical solution of the scattering problem for the proposed concentric composite (array of composites). To solve this problem a multiple scattering technique [2] and approach in modelling gratings [1 1 ] are used. The predictions are then compared with the experimental results.

The second type of the resonating elements is represented by the U-shaped scatterer composed of the elastic plates. The results are obtained with a finite element method (COMSOL Multiphysics 3.4) for single U-shaped resonator as well as for the array of such scatterers.

CONCENTRIC N-SLIT CYLINDER AND ELASTIC SHELL

Auxiliary problem. Single scatterer

Consider the two-dimensional problem of acoustic wave scattering by a single N-slit rigid cylindrical shell of thickness h _r ard of external radius r ₀ in air (p= 1 .25kg/m ³ and c = 344m/s). The sound is generated by the cylindrical point source placed at the origin of the Cartesian (x,y)/Polar (r, Θ) coordinate system. The width of consecutive slits in Oxy plane is denoted as d _n , n = 1 ..Λ/ and they are infinitely long in the direction of the cylinder main axis Oz, see Figure 1 . It is also assumed that the thickness of the rigid cylinder is much smaller than its radius jr _a «1 .

The N-slit cylinder is concentrically arranged with thin elastic shell of external radius a _a and half thickness h. The physical parameters of the shell are given by density p _s , the compressional ο and shear c¾ wave speeds. The wave field outside of the composite is described by an acoustic potential p(r) that is the solution of the Helmholtz equation p+ ^p ^ Q, (!)

and subject to the Somerfeld's radiation conditions

-· skp ·-·-·-· o I r ^" - ·· - ) , r ··- {2} where r =SQRT(x ² + ), k = ω/c is the ratio between angular frequency and sound speed of the acoustic environment and Laplacian Δ is given by either

The scattering problem formulated only for the elastic shell surrounded by the acoustic environment (i.e. air) can be analysed by using Kirchh off- Love approximations. Provided that thickness of the shell is much smaller than its mid-radius R =(a ₀ +ai)/2 (i.e. hlR«A ) we can derive simple analytical form of the solution in the outer acoustic environment that satisfies equation (1 ) and continuity conditions imposed on the surface of the shell. This solution is given by [8]

where

Using this solution we can find insertion loss at the point of observation in the following form

Figure 4(a) illustrates results obtained for the single shell made of latex with E = Ε(ω) and v = 0.4997 [8].We must note that to introduce viscosity the general form of Young's modulus is dependent o in the following form

where Young's modulus E related to the equilibrium state is always set to 1 .75 MPa and the dynamic moduli E _j and relaxation times τ are taken from [10]. In this plot the axisymmetric resonance of the elastic shell (i.e. n = 0) is observed at around 1300 Hz. This resonance is followed by the resonance of the index n = 1 which is found at around 800 Hz.

For scattering by the concentric N-slit rigid cylinder and elastic shell the solution of the elastic shell has to be coupled with the solutions found inside the slits and outside/inside of the rigid cylinder. In doing so we first derive boundary conditions imposed on the surface of N-slit cylinder in the following form [1 1 ]

where p ₀ and are the solutions of equation (1 ) at r = r _a , η and f (Θ) is the piecewise function setting the boundary conditions at the slit faces. In this paper we consider the case of four symmetrically distributed identical slits (i.e. N =4 and φ„ =φ) that corresponds to

The inner product . .. .. . „ , . transforms boundary conditions (8) into the following algebraic system of equations in A _m , m e Z, variables

where 5 _m, „ is Kronecker delta, vector Q = Q(cosa, sina) is the radius vector to the centre of the protector and

with C _n defining the concentric elastic shell as

C„ = ll, (13)

C _n = elastic shell. (14) To find a numerical solution, the infinite system of equations (10) is truncated at m = -30..30 that gives results accurate to three significant figures. Knowing the coefficients A _n the insertion loss (6) can be found through the outer solution written as

Figure 4(b) shows the insertion loss derived for the concentrically arranged thin elastic shell and 4-slit rigid cylinder. The resonant behaviour of the concentric elastic shell (related to the axisymmetric resonance) is observed around 1000 Hz. By comparing this result with those in Figure 4(a) it is seen that this resonance is shifted towards lower frequency by approximately 300 Hz. This shift is explained by the coupling of two resonators that are elastic shell and 4-slit cylinder. In Figure 4(b) we can also identify resonances above 2000 Hz that are related to the Helmholtz resonator and the annular cavity formed by surfaces of concentric elements.

Array of scatterers

We next consider finite periodic array of N scatterers. Using a multiple scattering technique [2] the infinite system of equations in A ^p _m , p = 1 ..N , m <≡ Z, variables is derived as

™ _™ i it

where A ^p _m are the unknown coefficient of the solution of equation (1 ) given by

vector Q _m = Q _m (cosoc _m , sina _m ) is the radius vector to the centre of m-th scatterer, Q _mp = Q _mp (cos _mp , sinoc _mp ) are the coordinates of p-th scatterer with respect to m-th scatterer, C r _m (r, Θ), ^" Q _m (r, Θ)) are the polar coordinates with origin at the centre of m-th scatterer and factors F _m and P _m are given by equations (1 1 ) and (12), respectively.

Figure 5 illustrates the performance of the finite square array made of the resonant elements. The Bragg band gap is observed around 2100 Hz. Below this frequency the elastic shell resonances are identified by the maxima of the insertion loss in Figure 5(a) and (c). As seen in Figure 5(a) the strongest effect is achieved for the axisymmetric resonance around 1300 Hz for the array of elastic shells. In Figure 5(c), plotted for the array of concentric 4-slit cylinders and elastic shells, the insertion loss maximum is shifted to 1000 Hz. This effect is related to the shift of the axisymmetric resonance described in the previous section. Figure 5(b) demonstrates the acoustic effects predicted with (16) and observed experimentally for the array of 4-slit rigid cylinders. One can see positive insertion loss peak around the Helmholtz resonance 1500 Hz followed by Bragg band gaps at 2100 and 4200 Hz and cavity resonance around 4900 Hz.

U-SHAPED RESONATORS

Auxiliary problem. Single scatterer

In this section we consider scattering by a single U-shaped resonator surrounded by air. The resonator is formed by two parallel elastic beams attached to the rigid backing, see Figure 3. This scatterer may support the resonances of the elastic beam (see Table 1 ) as well as the resonances of the open cavity. In the low-frequency range (wavelength λ is much bigger than width of the cavity d) and provided that R is much bigger than d the first cavity resonance can be approximated by [12]

Mateds!

01

Steel 690 4324 12109

The results are obtained by using finite element method implemented in COMSOLMultiphysics 3.4. In the numerical model the outer acoustic environment is surrounded by the perfectly matched layer (PML). It is also assumed that sound is generated by the incident plane wave that is taken as exp(-ikx). These assumptions allow us to narrow down the active domain in Comsol model to array-receiver distance and, as a result, to reduce the computational time.

Figure 6 illustrates insertion loss computed for the elastic and rigid U-shaped scatterers In Figure 6(a) elastic beams are made of polyethylene. It can be seen that the second resonance of the elastic beam at f ~ 850 Hz is followed by the first cavity resonance. This resonance is slightly shifted towards higher frequencies compared to that of the rigid cavity whose first resonance is approximated by equation (18). The observed effect of coupling of resonances is analogous to that of the concentrically arranged 4- slit cylinder and elastic shell. The performance of the steel resonator shown in Figure 6(b) has little difference with that of the rigid scatterer. Nevertheless one can observe the appearance of first resonance of the steel beam at f~ 690 Hz. Array of scatterers

The resonators whose performance is analysed in the previous section can now be used in constructing the finite array. The distance between the centres of the scatterers in the array is 0.08 m and the scatterers are arranged in a finite square lattice. As before the incident plane wave propagates parallel to Ox axis.

In Figure 7 the performance of the finite array is analysed. Figure 7(a) illustrates the existence of the band gap around f ~ 850 Hz related to the resonance of the elastic beam made of polyethylene. The second positive insertion loss peak around f ~ 1 150 Hz is generated by the first cavity resonance. Due to the low filling fraction (approximately 9%) the first Bragg band gap does not contribute to the positive performance of the array. The insertion loss of the array of steel resonators shown in Figure 7(b) is similar to that of the rigid resonator array. As can be seen the structural vibration excited in the steel beam is weak so that it does not contribute into the scatterered wave field in the acoustic medium.

CONCLUSION

The use of the resonating elements in Sonic Crystals results in effective sound attenuation in the low-frequency range while still preserving the existence of the Bragg band gaps. The composite scatterer made of resonators supports resonances characterised by both structural and air born vibrations. The coupling between these vibrations results in shift of the resonances corresponding to each element of the composite, the effect that is observed in the mass-spring system with multiple degree of freedom.

REFERENCES

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