BACKGROUND OF THE INVENTION
Since 1979, it has been known that one-dimensional sound diffusive surfaces, called reflection phase gratings that scatter sound uniformly, can be formed from a series of divided wells or slats, whose depths or heights respectively, are determined according to a variety of optimal number theory sequences. In August 2016, a reference book was published titled “Acoustic Absorbers and Diffusers: Theory, Design and Application,” by authors Trevor J. Cox and Peter D'Antonio, CRC Press. In the book, it was suggested that a new type of diffuser consisting of a plurality of equally spaced, parallel rectilinear slats of equal cross-sectional width, but of differing heights, determined according to a number theory sequence, specifically a quadratic residue (QR) sequence, might be used to provide high-mid frequency diffusion and low frequency absorption.
FIG. 1 shows a schematic, side view representation of the slatted diffusing-absorbing device, based on a prime 13, QR sequence, disclosed in the above-mentioned book. No design methodology was provided. However, experimental diffusion coefficient data were presented comparing the performance of a simple prime 7, QR sequence, with a few surfaces having slats of equal height, including a regular arrangement and two irregular arrangements, based on optimal binary sequences.
At the base of the slats, a porous absorbing material is also provided, which adds resistance to the slat resonator formed by the channels between the slats. No description was provided to determine the resonant frequencies of the plurality of slat resonators. The necessity to vary the slat heights to improve dispersion is illustrated in FIG. 2.
The graphs in FIG. 2 show the normalized diffusion coefficient for the devices shown. When the device merely consists of a regularly spaced set of slats of uniform height, then at best a coefficient of 0.2 is achieved (Graph line A). Graph line B shows an irregular arrangement based on an optimal aperiodic sequence. Graph line C shows an irregular arrangement based on a periodic, truncated maximum length sequence. Two examples are shown in Graph lines B & C. While arrangements B and C show improved diffusion, at most the normalized diffusion coefficient is 0.5. However, by varying slat heights, based on a prime 7, QR sequence, the maximum diffusion coefficient is increased to almost 0.7 (Graph line D).
After further research, the present invention teaches the theory and design methodology for a practical device that can be utilized in a wide range of architectural spaces, with primes much larger than 7, which offer an aesthetic, symmetrical topology. In addition, the present invention teaches the theory to determine the resonant frequencies of the spaced slats and a number theory sequence to optimize their bandwidth, both of which are not provided by the brief suggestion made in the published book.
SUMMARY OF THE INVENTION
The present invention relates to a combined diffuser-absorber with spaced slats. The present invention includes the following interrelated objects, aspects and features:
(1) In a first embodiment (FIG. 3), the present invention contemplates regularly spaced slats having equal width, but with heights determined by an inverted QR sequence, which converts focusing concave areas into beneficial, diffusing convex areas for improved diffusion, especially in the near field.
(2) The first embodiment also teaches that the inverse sequence provides longer resonator necks, between adjacent slats, which are needed to provide a lower average resonant frequency, not afforded by the non-inverse diffuser design suggested in the published book.
(3) In a second embodiment (FIG. 4), the uniformly spaced, inverted QR slat heights have widths determined by the ground states of a Bernesconi sequence.
(4) In a third embodiment (FIG. 5), the uniformly spaced, inverted QR slat heights have widths determined by the same QR sequence used to determine the heights.
(5) In a fourth embodiment (FIG. 6), the uniformly spaced, inverted QR slat heights have widths determined by a prime 7, primitive root sequence.
(6) In a fifth embodiment (FIG. 11), the uniformly spaced slats have curvilinear forward facing surfaces with their heights based on either a regular or inverted QR sequence, as well as a primitive root or other number theory or optimized sequence, with their widths determined by any of the options mentioned in FIGS. 3-6.
(7) In a sixth embodiment (FIG. 12), each of the uniformly spaced, equal width slats have a different curvilinearly shaped forward facing surface, the multiplicity of slats combining collectively to form an aesthetically pleasing 3-dimensional optimized shape.
(8) In the preferred embodiments of the present invention, the base of the slats emanates forward of an absorbent material, which may be porous or otherwise designed to achieve sound absorbing capabilities. The maximum slat height is designed in accordance with a number theory or optimized sequence formula to provide a desired design frequency, below which the spaced slats provide low frequency absorption. The greater the maximum slat height, the lower the diffusion cutoff frequency.
(9) The low frequency absorption spectrum of each embodiment of the present invention is determined by the spacing between adjacent slats, the width of the slats, the length of the constrained area between adjacent slats and the depth and contents of the rear cavity containing porous absorbing material.
It is a first object of the present invention to provide a combined diffuser-absorber with spaced slats.
It is a further object of the present invention to provide such a device in which forward facing surfaces of adjacent slats may be planar.
It is a further object of the present invention to provide such a device in which forward facing surfaces of adjacent slats may be non-planar.
It is a further object of the present invention for the spaced curvilinear slats to collectively form a 3-dimensional aesthetically pleasing surface
It is a yet further object of the present invention to provide such a device in which the spacing between adjacent slats is the same or different for all adjacent pairs of slats.
It is a yet further object of the present invention to provide such a device in which all slats have equal widths in a direction perpendicular to their direction of extension.
It is a still further object of the present invention to provide such a device in which slats may have varying widths or thicknesses in the direction perpendicular to their respective directions of extension.
It is a still further object of the present invention to provide such a device in which the heights of respective slats are determined through calculation of a number theory sequence.
It is a still further object of the present invention to provide such a device in which the heights of respective slats are determined through an Boundary Element optimization calculation.
It is a still further object of the present invention to provide such a device in which the slat spacing, slat width, the lengths of the resonator necks formed from the constrained areas between adjacent pairs of slats, and rear cavity depth containing a porous absorber form a low frequency slat resonator.
It is a still further object of the present invention to provide the theory and methodology to create the diffuser design.
It is a still further object of the present invention to provide the theory and methodology to design and optimize the topology of the curvilinear slats.
It is a still further object of the present invention to provide the theory and methodology to design an optimized 3-dimensional surface topology, which is formed from the collection of spaced, slat slices of such topology.
It is a still further object of the present invention to provide the theory and methodology to create the low frequency slat resonator design.
These and other objects, aspects and features of the present invention will be better understood from the following detailed description of the preferred embodiments when read in conjunction with the appended drawing figures.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a side view schematic representation of a prior art device including a plurality of adjacent, spaced slats, whose heights are deter tined by a QR sequence.
FIG. 2 shows a graph comparing the diffusion coefficient for various diffuser-absorbers as explained earlier.
FIG. 3 shows block heights of a diffuser determined by an inverted QRD sequence.
FIG. 4 shows a diffuser with spaced inverted QRD slat heights with widths determined by the ground states of a Bernesconi sequence.
FIG. 5 shows a diffuser with spaced inverted QRD slats with widths determined by the same QRD sequence used to determine the heights.
FIG. 6 shows a diffuser with spaced inverted QRD slats with widths determined by a Prime 7, primitive root sequence.
FIG. 7 shows a schematic representation of two repeats of a diffuser-absorber with spaced slats based on a Prime 47, QR sequence. Concave dips in the topology are noted.
FIG. 8 shows the same diffuser-absorber of FIG. 7, but with the heights based on the inverse QR sequence. The concave areas are now convex and offer improved diffusion in the near field.
FIG. 9 shows the respective neck lengths formed by a constrained area between adjacent slats.
FIG. 10 shows the slat resonator frequency arising from each neck length between adjacent slats, wherein, as shown, the variable neck lengths provide absorption over a beneficial large bandwidth, with an average resonance at 450 Hz.
FIGS. 11 and 13 show one of two possible spaced, curvilinear slat options, that replace the rectilinear slats with shape optimized slats, suggesting a surface in which any of the rectilinear slats in FIGS. 3-6 are replaced with an optimized curvilinear slat.
FIGS. 12 and 14 suggest an amorphous surface in which each curvilinear slat forms a part of an optimized 3-dimensional surface.
FIG. 15 illustrates the iterative shape optimization software flow diagram.
FIG. 16 shows an example of a 3-dimensional topology which can be sliced into a series of spaced, forward facing curvilinear slats.
FIG. 17 describes the Boundary Element Method (BEM) formula used to predict the scattered pressure (top image), the diffusion coefficient that is used as an optimization metric (middle image), and the intelligent search engine used to navigate error space (bottom image).
SPECIFIC DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 3 shows a diffuser-absorber in which the block heights are determined, not by the QR sequence, but rather to its inverse. To demonstrate why this is significant and an improvement over the prior art, we present a comparison between the two in a practical implementation, which exhibits a symmetrically aesthetic topology, in FIGS. 7 and 8. In FIG. 7, Applicants illustrate a schematic, side view representation which contains 2 repeats of a diffuser-absorber with spaced slats based on a prime 47, QR sequence. Note the concave dips in the topology at 47 and 94 on the abscissa. Also note smaller concave dips at 24, 72 and 120. While the combined surface provides uniform diffusion in the far field, these concave areas can provide focusing when listeners are closer to the surface. To mitigate this problem, the present invention teaches the use of the inverse series, in which the inverse sequence values are equal to the prime, N, minus the QR sequence values, Sn, i.e. N−Sn. In FIG. 8, Applicants illustrate a diffuser-absorber with heights based on the inverse sequence. It can be seen that the prior concave areas are now convex. These convex areas now contribute to the uniform diffusion of the surface and improve the performance.
In the second embodiment (FIG. 4), Applicants illustrate a schematic side view representation of a surface whose heights are based on the inverse QR sequence, but now the widths of the slats are no longer equal, but rather based on the ground states of the Bernasconi model with open boundary conditions (J. Phys. A 29 L473 (1996)). The Bernesconi sequence is an optimal, aperiodic binary sequence of zeros and ones. In this case for N=7, the values are 0, 1, 0, 0, 1, 1, 1 with a repeat for the periodic sequence of 0. The slat widths follow this sequence, such that when the slat is a zero it is of a given base width and when the slat is a one it is twice (or some multiple of) the base zero width. The first slat at 0 on the abscissa is a given width and the second slat at 2-3 on the abscissa is twice the width.
In the third embodiment (FIG. 5), the widths are based on the same QR sequence used to determine the heights, which is 7, 6, 3, 5, 5, 3, 6 and a repeat 7. Thus, the slat at 0-6 on the abscissa is 7 times the width of a base width slat, the slat at 8-13 is 6 times the base width, etc.
In the fourth embodiment (FIG. 6), the slat widths are determined by a Prime 7, primitive root sequence, whose values are 3, 2, 6, 4, 5, 1 and repeats 3 and 2. Therefore, the first slat has a width of 3 (0-2 on the abscissa), the second slat has a width of 2 (4-5), etc.
The science behind the present invention in its numerous embodiments is as follows. The slat heights can be determined by any number theory sequence, shape optimization or random selection. In the embodiments presented thus far, the heights are determined by a QR sequence:
Sn=n2 modulo N, where Sn is the sequence value of the nth slat, modulo indicates the least non-negative remainder and N is a prime, for example, 7. The relative sequence heights can be seen in the embodiments of FIGS. 3-6, with the sequence values shown on the ordinate. The diffusion design frequency, f0, is given by:
f
0
=cS
max/(2Nhmax)
where c is the speed of sound (13560 in/sec), Smax is the maximum sequence value, N is a prime and hmax is the maximum slat height. It can be seen, that as the slats get longer the diffusion extends to lower frequency. In practice, effective diffusion occurs roughly an octave or two below this design frequency. With hmax=4″, Smax=42 and N=47, f0=1515 Hz.
The upper frequency is given by:
fmax=c/2w, where c is the speed of sound and w is the slat width. Therefore, a 1″ wide slat should scatter up to 6,780 Hz, and in practice roughly a half octave above that. This describes the design of the diffusion portion of the surface.
Concerning the slat resonator design, typically slat resonators are formed from equally spaced, equal height and width slats. The absorption design frequency, f0, is given by:
f
0
=c/2pi*sqrt(p/(t′d)
where c is the speed of sound, pi=3.14159, sqrt is the square root and p is the fractional open area, t′ is the length of the resonator neck formed by the spacing between adjacent slats+0.8*s (which is a rough approximation of the radiation impedance of the resonator neck opening) and d is the depth of the absorbing rear cavity. p=s/(s+w), where s is the slat spacing and w is the width of the slats.
In the present invention, t′ is no longer constant, but rather is determined by the length of the constrained area between each adjacent pair of slats. This can be given by:
t′
m
=h
max
/N*(if(Sn>Sn+1) then Sn+1 else Sn)+0.8*s
where m is the index of the resonator neck between slat n and slat n+1.
As an example, for the N=47 QR diffuser in FIG. 7 with hmax=4″, s=0.5″, w=1″, p=0.33 and a cavity depth d=4″, the lengths of the resonator necks are shown in FIG. 9 and the slat resonator frequencies are plotted in FIG. 10. The average resonance is 450 Hz, with a bandwidth of 386 Hz. This is 63% lower than it would be for the non-inverse QR sequence. The bandwidth can be extended by slanting the depth of the rear cavity, which introduces a range in values of d.
In FIGS. 11-12, Applicants show two additional embodiments which replace the previously described embodiments utilizing rectilinear slats with forward-facing, shape optimized, curvilinear slats. FIG. 11 describes a surface in which any of the rectilinear slats in FIGS. 3-6 are replaced with an optimized curvilinear slat. FIG. 12 describes an optimized, 3-dimensional surface topology formed by spaced, curvilinear slats, which comprise it. FIGS. 13 and 14 show renderings of two possible 3D shapes.
In FIG. 15, Applicants show an iterative software flow chart used to obtain a desired optimized curvilinear slat or surface. We start with a given motif described by Fourier series shape coefficients. The angular scattering is calculated using a boundary element program, whose formula is shown in the upper image of FIG. 17. The polar response or the diffusion coefficient, shown in the middle image of FIG. 17 at each frequency is compared with the desired values. If the agreement is acceptable, the program ends. If not acceptable, a downhill simples or genetic algorithm, shown in the bottom image of FIG. 17 is used to suggest the next possible shape to evaluate. This iteration proceeds until a satisfactory shape is produced.
FIG. 16 illustrates an example of a 3-dimensional topography which can be sliced into a series of spaced, forward facing curvilinear slats.
Accordingly, an invention has been disclosed in terms of preferred embodiments that fulfill each and every one of the objects of the invention as set forth hereinabove, and provide new and useful combined diffuser-absorber with well-dividing slats of great novelty and utility.
Of course, various changes, modifications and alterations in the teachings of the present invention may be contemplated by those skilled in the art without departing from the intended spirit and scope thereof.
As such, it is intended that the present invention only be limited by the terms of the appended claims.
Patent Application
20190244596
