BACKGROUND

[0001] Honeycomb sandwich panel has long been preferred for its good mechanical properties.

Disclosed is a honeycomb panel that can achieve 90% sound absorption from 600 Hz to 1000 Hz with a thickness that can be less than 30 mm by doing minor modifications on commercialized honeycomb sandwich panel. The panel is made up of periodically and horizontally arranged honeycomb “supercells” which comprises different types of honeycomb unit cells. Each unit cell acts as a Helmholtz resonator (HR) with hexagonal prism-shaped cavity and cylindrical neck. The absorption performance of designed honeycomb panel is designed both with surface impedance theory and the complex frequency plane theory and has been validated by numerical simulations.

[0002] Absorption of sound especially at low frequencies has drawn great interest for its wide range of applications in rooms acoustics, noise control, automobile, and aerospace industries, etc. However, conventional methods of sound absorption are far from satisfactory. Porous or fibrous materials are traditionally used as sound absorbing coatings, but they usually have thickness comparable to the wavelength of sound, resulting in bulky structures. In the past few years, there is growing popularity of resonator-based acoustic absorbers because they are able to achieve near total absorption at deep sub-wavelength thickness. The main disadvantage of such absorbers is that they have a very narrow bandwidth confined at the vicinity of resonant frequency, so their ability to absorb broadband noise is limited.

[0003] Honeycomb sandwich panel is known for its ability to yield minimum weight while keeping mechanical strength unimpaired and has been widely used in constructing lightweight yet strong structures. The honeycomb sandwich panel is composed of two layers of high-modulus laminate facesheets and a honeycomb core in between. Despite being light and strong, honeycomb sandwich panels have rather poor acoustics performances because their hollow structure does not contribute much to sound insulation. One existing solution that enables a honeycomb panel to reduce noise is to perforate one of the face-sheets (drill tiny holes of the same size) to introduce a Helmholtz- resonator-type sound absorption. The sound absorption arises due to the interplay between the resonance of the honeycomb hollow cell and the thermos-viscous losses in the perforation. This design, however, is suboptimal, as it also suffers from a narrow operating frequency band. By drilling tiny holes of different sizes on one of the two facesheets, as described below, a honeycomb sandwich panel can be turned into a plurality of broadband sound absorbers.

[0004] One application for such a panel is in the aerospace industry. The progress of aerospace industry has been hampered by the aircraft engine noise. Excessive engine noise results in expensive landing fees at airports, reduces fleet flexibility, and also creates poor cabin comfort levels. Currently there is no effective way to reduce this noise without significant weight penalty, which is adverse to fuel-efficiency.

[0005] The technology, a new class of honeycomb composite material, significantly reduces noise (e.g., of commercial aircrafts) without penalty to the structural weight. This will address a long standing noise issue in the aerospace and other industries, such as to reduce residential noise and noise in ships and trains.

BRIEF DESCRIPTION OF DRAWINGS

[0006] Example features and implementations are disclosed in the accompanying drawings.

However, the present disclosure is not limited to the precise arrangements and instmmentalities shown.

[0007] FIG. la is a perspective view of a sound absorption panel in accordance with one implementation.

[0008] FIG. lb is a perspective view of a unit cell of the sound absorption panel of FIG. la with the bottom face-sheet excluded.

[0009] FIG. 2 is a top view of the honeycomb core of the sound absorption panel of FIG. 1, showing unit cells and supercells.

[0010] FIG. 3 is a graph displaying the individual absorption spectrum of each unit cell and overall absorption performance of a supercell according to one implementation.

[0011] FIG. 4 is a graph displaying the zeros of the supercell of FIG. 3 on the complex frequency plane.

[0012] FIG. 5 is a graph displaying the overall absorption performance of a supercell according to another implementation.

[0013] FIG. 6a is a side view of a unit cell in accordance with one implementation. [0014] FIG. 6b is a perspective view of a unit cell in accordance with one implementation.

[0015] FIG. 7 is a graph displaying the absorption spectrums by analytical model and numerical simulation of a supercell in accordance with one implementation.

DETAILED DESCRIPTION

[0016] The following is a description of various implementations of a sound absorption panel.

[0017] Certain terminology is used herein for convenience only and is not to be taken as a limitation on the present invention. In the drawings, the same reference numbers are employed for designating the same elements throughout the several figures. A number of examples are provided, nevertheless, it will be understood that various modifications can be made without departing from the spirit and scope of the disclosure herein. As used in the specification, and in the appended claims, the singular forms“a,”“an,”“the” include plural referents unless the context clearly dictates otherwise. The term“comprising” and variations thereof as used herein is used synonymously with the term “including” and variations thereof and are open, non-limiting terms. Although the terms“comprising” and“including” have been used herein to describe various implementations, the terms“consisting essentially of’ and“consisting of’ can be used in place of“comprising” and“including” to provide for more specific implementations and are also disclosed.

[0018] Consider the honeycomb core as a periodic arrangement of numerous identical hexagonal prisms. As shown in FIG. 1, if circular holes are drilled in the facesheet above every hexagonal prism, an array of Helmholtz resonators (HRs) are created where the honeycomb core serves as the cavities and the holes in the top facesheet serve as necks. Since Helmholtz resonators are commonly used as building blocks of sub-wavelength sound absorbers, this structure is expected to be able to absorb low frequency sound with minimum thickness. Moreover, broadband absorption is available by taking advantage of the coupling effect of HRs with different geometries and resonant frequencies.

[0019] FIG. la shows an implementation of a sound absorption panel 100. The panel 100 has a plurality of chambers 120, a facesheet 140, and a backplate 160. In FIG. 1, the chambers 120 are hexagonal in shape and are arranged in a honeycomb pattern, but in some implementations the chambers can be any shape and arranged in any desired pattern. One end of each of the chambers 120 is sealed by the backplate 160, leaving an opening 122 with an edge 124 at the opposite end of each of the chambers 120.

[0020] The facesheet 140 has a plurality of holes or apertures 142 extending through both sides of the facesheet 140. While the apertures 142 in FIG. 1 are round, any shape aperture can be used. In FIG. la, the aperture sizes vary to correspond to a desired frequency-band absorption, as discussed below. However, in some implementations, the volume of the cavity, as seen in FIG. lb, can be varied to achieve the same effect. Furthermore, in some implementations, both the aperture sizes and chamber volumes can be varied simultaneously to provide even better control of the frequency absorption.

[0021] The facesheet 140 is disposed over the openings 122 of each of the chambers 120 such that it seals the openings 122 along the edge 124. One aperture 142 in the facesheet 140 is aligned with one chamber opening 122, allowing the chamber 120 to be in fluid communication with the environment through the aperture 142. While in FIG. 1 the apertures 142 are centered on the openings 122 in each of the chambers 120, in some implementations, the apertures are off-center from the chamber openings.

[0022] Each chamber 120 and aperture 142 represents one unit cell 180 of the panel 100. By varying the aperture size and/or the chamber volume, a supercell 190 of unit cells 180 can be designed to correspond to a range of frequency absorption. FIG. 2 shows one implementation where a supercell 190 has 9 unit cells 180. The supercell 190 pattern is repeated throughout the panel 100 such that the same sound frequency absorption range is achieved throughout the entire panel 100. The absorption frequency ranges can be calculated and selected based on a desired application, as described below.

[0023] While the implementation shown in FIG. la has a backplate 160, in some implementations, no backplate is included.

[0024] In the implementation shown in FIG. 6b, the unit cells 280 are similar to the unit cells 180 of FIG. 1, discussed above, but only consist of cylindrical chambers 220 having an opening end 222. Thus, no facesheets are utilized. The opening ends 222 of each of the chambers contain an aperture 242. Multiple chambers 220 having varying aperture sizes and/or chamber volumes are combined in a similar way as above to form supercells, which can be repeated across a panel.

[0025] In order to better illustrate the sound-absorbing honeycomb panel, start from the case where plane incident wave along z-axis p,„ normally impinges on the assumed sound absorbing panel. The sound absorbing system could be fully characterized by its normalized surface impedance (NSI) z _s = pKfi _oCo v). Here p and v stand for sound pressure and particle velocity along the z-axis on the air- absorber boundary, and _Zo = p ₀ c ₀ ~ 413.3 Pa-s/m is the characteristic acoustic impedance of air. The absorption coefficient can be calculated by a = 4Re(z _s )/[(l+Re(z _s )) ² +Im(z _s ) ² ], where Re denotes the real part and Im denotes the imaginary part. For the perforated honeycomb panel, although the NSI is not the same everywhere, the NSI of the proposed structure can be derived by only taking one repetitive segment into account due to the periodic nature of honeycomb arrangement. And since the wavelength of sound wave at an HRs’ working frequency is much longer than the geometric size of a single resonator, a panel surface with orifices can be treated as a homogenous surface with equivalent NSI under the long wavelength assumption. We note that the NSI of a single HR can be calculated by existing theories (e.g., Kim, S., et al "A theoretical model to predict the low-frequency sound absorption of a Helmholtz resonator array." J. Acoust. Soc. Am. 119(4) 1933-1936 (2006)) and the NSI of the repetitive segment can be derived thereof, as shown below. This analytical method is validated by a Finite Element Method where the whole panel is modeled with periodic boundary conditions.

[0026] In the design of honeycomb panel, every 9 nearby honeycomb unit cells form a cluster together. These clusters are called honeycomb“supercells”. The honeycomb panel can be seen as periodically arranged“supercells” across the infinite plane as seen in FIG. 2. By drilling holes on the facesheet, each of the 9 unit cells inside a supercell has a HR as its functional part. The resonant frequencies of these HRs differ from each other because orifice radii (areas) are different. The absorption performance of each unit cell can be determined by the NSI method with 5 parameters: orifice radius a ,· (z=l,2,3,...,9), facesheet thickness/neck length /„, hexagon length a, cavity depth l _c , and surface area S,,, . It should be noted that the existing model for analyzing HRs applies to cylindrical cavities rather than honeycomb cavities, and the equivalent cavity radius a _c can be calculated approximately by

[0027] since it indicates that the honeycomb cavity has the same volume as a cylindrical cavity. The honeycomb wall thickness t can be also taken into consideration in calculating S,,, . Here,

[0028] By carefully tuning the 9 orifice radii, desired absorption can be achieved.

[0029] For a honeycomb supercell composed of 9 unit cells, the unit cells are placed in parallel connection with each other. Consequently, the NSI of the supercell z _s could be derived as

[0030] where _Zi denotes NSI of isolated unit cells. FIG. 2 shows the above view of honeycomb supercells. The numbers indicate different unit cell configurations (different neck radii). The parameters are as follows: ai=l.lmm; a2=l.lmm; a ₃ = l.2mm; a ₄ =l.3mm; a ₅ =l.4mm; a ₆ =l.55mm; a ₇ =l.7mm; a ₈ =l.9mm; a ₉ =2.05mm; l _n =3.2mm; a=9.525mm; t=0.2mm; and l _c =25mm.

[0031] It can be seen in FIG. 3 that the proposed honeycomb panel shows good absorption performance of over 90% throughout frequency band 600Hz-l000Hz. Moreover, the thickness is less than 30mm (/„+/ _c =25mm+3.2mm=28.2mm, plus an arbitrary thickness of the other side of facesheet).

[0032] A numerical simulation based on Finite Element Method was implemented solving the linearized Navier-Stokes equation, the continuity equation, and the energy equation for the neck area, in order to take the viscos-thermal losses into account. The cavities are model by solving the Helmholtz equation. Hard boundary conditions are applied on the facesheet and walls of honeycomb core since the impedance mismatch between honeycomb material and air is large. The periodic arrangement of supercells is simulated by using Floquet boundary conditions, and plane wave radiation boundary condition is applied to model the normal incident wave. The background medium is air with its density p ₀ = 1.21 kg/m ³ , speed of sound r -343.2 m/s, and dynamic viscosity m=1.8c10 ⁵ kg/(nrs). The simulation result shows good agreement with the analytical result, except for dips around 770Hz and 900Hz. This is possibly due to the mutual radiation impedance between unit cells, which is not taken into consideration in the analytical model.

[0033] The absorption spectrum of each individual unit cell is also shown in FIG. 3. It is clear that the individual unit cells produce much smaller sound absorption. The stark difference between absorption spectra of the supercell and unit cells demonstrates that the honeycomb panel relies on a strong coupling effect between different unit cells rather than merely“adding up” narrow-band absorbers.

[0034] The complex frequency plane provides an alternative view towards designing and understanding the honeycomb panel. By substituting w,=w,+/ ^' w, in the wave number k, the sound reflection coefficient (r) of proposed honeycomb panel is plotted on a complex frequency plane in negative logarithmic scale -log(lrl). Maximum absorption occurs at the brightest points, called“zeros” ( IH~0 and a~ 1 ), while near-total reflection occurs at the“poles” (\r\~ 1 and a~0). The reflection coefficient of an arbitrary system r is determined by r=(z _s -l)/(z _s +l), here the NSI z _s is related to the complex wave number kc=0)c/c _o . If all dissipation factors are neglected and the system is considered to be lossless, , becomes purely imaginary (real part r _s =0, _Zs =j _s ). In this lossless case, the coordinates of zeros and poles are complex conjugates. The zeros have a positive imaginary part and the poles have a negative imaginary part, and they are distributed symmetrically about the real-frequency axis.

[0035] Since the absorption coefficient is a=l-lrl ² , perfect absorption (a=l) should always occur at zeros. However, an imaginary frequency has no realistic physical meaning, so perfect absorption cannot be observed even if there is a zero on the complex frequency plane, unless it falls on the real frequency axis. As loss is introduced, the zeros and poles shift down along the imaginary frequency axis simultaneously. The higher loss in the system, the more distance zeros and poles move away from their original locations in the lossless case. Since the zeros are always located above the real frequency axis in the lossless case, perfect absorption can be obtained when it finally falls on the real frequency axis. Judging from the zeros’ relative locations with respect to the real frequency axis, it can be determined whether a system is inadequately damped (zeros above real frequency axis) or over damped (zeros below real frequency axis).

[0036] FIG. 4 shows that the 8 zeros of the proposed honeycomb are all located near the real frequency axis, compared with zeros of individual unit cells (marked by asterisks) which are located far above the real frequency axis. The locations of zeros indicate that these unit cells are inadequately damped themselves, so high absorption coefficient is not expected at any real frequency range. For the supercell, high absorption coefficient is achievable because the system is critically damped. The dash- dotted line in the complex frequency map denotes high sound absorption (>90%) inside the contour, and the intersections of the contour and the real frequency axis give the 90% absorption bandwidth. In this way, strong coupling between different unit cells is validated.

[0037] By altering the parameters of the honeycomb panel, optimal sound absorption can be obtained for other desired frequency ranges. In particular, the number of unit cells in one supercell can be increased for more zeros in the system and wider bandwidth. The complex frequency map offers a tool to observe and quantify the damping effect in the honeycomb panel so the parameters can be adjusted accordingly to achieve better absorption performance.

[0038] In summary, this specific honeycomb panel can achieve 90% broadband sound absorption between 600 Hz and 1000 Hz with a thickness of around 30 mm. A complex frequency plane is used to illustrate strong coupling between unit cells. The honeycomb panel has unique features and advantages such as having a small thickness compared to the wavelength of sound, broadband absorption, light weight, and excellent mechanical properties.

[0039] A sound absorbing system could be characterized by its normalized surface impedance

(NSI) Zs- Here, it is shown how to derive z, for a single Helmholtz resonator (HR) unit cell and calculate the absorption coefficient of the system. As shown in FIG. 6a, the plane incident wave along z-direction impinges on a surface backed by a HR with cylindrical cavity and cylindrical neck. The surface together with the HR form a unit cell here. For the unit cell, the wavelength of sound at working frequency is much larger than the geometric size of the unit cell, so the pressure reflection coefficient of the system could be derived by r = (z _s -l)/(z _s +l) and the absorption coefficient a = l-lrl ² , where z _s denotes the NSI of the unit cell.

[0040] The NSI of unit cell is determined by 5 parameters, and 4 of them are HR parameters: neck radius a , neck length cavity radius a _c , and cavity depth l _c . (See FIG. 6b.) The remaining parameter is the cross-sectional area of unit cell S _ue . Also, z _s = z.pk/ , where ZHR denotes normalized acoustic impedance of a single HR and s = na ² IS _Uc denotes the porosity of unit cell. The normalized acoustic impedance of HR can also be written in complex form as ZHR = r _HR +j m, where

[0041] Here, d _n = V(2v/cw) is the viscous boundary layer thickness, v is the kinematical viscosity of air ( v ~ l5xl0 ⁶ m ² /s). g is the Poisson constant of air. S _t = S(2K// _oCp0j) ~ 0.25x10 ^_2 /V(/) is the thermal boundary layer thickness where K is the heat conduction coefficient, and C _p is the specific heat per unit mass at constant pressure. G = l _n +l _C orri +l _C orr2 is the neck length taking two end corrections into account. The two end corrections are

(6)

(7)

[0042] Perfect absorption can be achieved with a single HR unit cell if the impedance match condition is fulfilled at a certain frequency. For example, four parameters of Helmholtz resonators are set to be

[0043] The surface area of unit cell S _ue = p a _uc ² = p·(14.5 mm) ² .

[0044] Absorption spectra by the analytical model and numerical simulation are shown in FIG.

7. It can be seen in the graph that the absorption coefficient a reaches 1 at a resonant frequency around 800Hz.

[0045] While it is possible to achieve different ranges of resonant frequency in a Helmholtz resonator by changing the size of the hole, it is also possible to achieve the same results by varying the volume of the cavity. In addition, the smaller the neck radius is, the lower the resonant frequency of the Helmholtz resonator. Therefore, it is natural to think that in order to achieve low frequency sound absorption, small holes need to be applied. However, the forgoing theory only applies to the case of relatively large holes (hole radius approximately > 1 mm). In order to calculate sound absorption of small holes, let perforate constant K = a V( r _a( oIh ), where a denotes the radius of the hole and h the dynamic viscosity of air. When 1 < K < 10, the NSI of a micro-perforated panel (MPP) unit cell could be derived by

[0046] Here s is the perforate ratio, l is the cavity depth, and the facesheet thickness is t = lf _S .

By substituting the new formula to calculating the NSI of a unit cell _¾ a honeycomb panel can be designed based on the MPP theory.

[0047] A MPP-based honeycomb design made up of 9 unit cells is presented here. We vary both the hole size and cavity volume. Hole radii and cavity depth have been calculated to cover a specified range: an=0.35mm, ln=l0mm; ai ₂ =0.35mm, li ₂ =10mm; ai ₃ =0.45mm, li ₃ =10mm; a _2i =0.35mm, l _2i =5mm; a ₂₂ =0.40mm, l ₂₂ =5mm; a ₂₃ =0.50mm, l ₂₃ =5mm; a _3i =0.40mm, l _3i =3mm; a ₃₂ =0.45mm, l ₃₂ =3mm; and a ₃₃ =0.50mm, l ₃₃ =3mm. Here, facesheet thickness t = 0.50mm and cavity length a _c = 5mm. FIG. 5 shows the analytically predicted results. Sound absorption has been achieved for over 90% for a frequency range of 400 Hz- 1000 Hz.

[0048] A number of implementations of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other implementations are within the scope of the following claims.

[0049] Disclosed are materials, systems, devices, methods, compositions, and components that can be used for, can be used in conjunction with, can be used in preparation for, or are products of the disclosed methods, systems, and devices. These and other components are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these components are disclosed that while specific reference of each various individual and collective combinations and permutations of these components may not be explicitly disclosed, each is specifically contemplated and described herein. For example, if a device is disclosed and discussed each and every combination and permutation of the device, and the modifications that are possible are specifically contemplated unless specifically indicated to the contrary. Likewise, any subset or combination of these is also specifically contemplated and disclosed. This concept applies to all aspects of this disclosure including, but not limited to, steps in methods using the disclosed systems or devices. Thus, if there are a variety of additional steps that can be performed, it is understood that each of these additional steps can be performed with any specific method steps or combination of method steps of the disclosed methods, and that each such combination or subset of combinations is specifically contemplated and should be considered disclosed.