1. Field
The present disclosure relates to novel sound attenuating structures in which locally resonant sonic materials (LRSM) act as membrane-type acoustic metamaterials (MAMs). The MAMs are able to provide a shield or sound barrier against one or more particular frequency ranges as a sound attenuation panel. More particularly, the disclosure relates to active control or adjustment of such panels by electromagnetic, electrostatic or other means.
2. Background
Sound attenuation panels are described in U.S. Pat. No. 7,395,898, which discloses a rigid frame divided into a plurality of individual cells, a sheet of a flexible material, and a plurality of weights. Each weight is fixed to the sheet of flexible material such that each cell is provided with a respective weight and the frequency of the sound attenuated can be controlled by suitable selecting the mass of the weight. The flexible material may be any suitable soft material such as an elastomeric material like rubber, or another soft material such as nylon. The flexible material is ideally impermeable to air and without any perforations or holes; otherwise the sound attenuation effect is significantly reduced. The rigid frame may be made of a material such as aluminum or plastic. The function of the frame is for support and therefore the material chosen for the frame is not critical provided it is sufficiently rigid and preferably lightweight.
In the above configuration, a single panel may attenuate only a relatively narrow band of frequencies. A number of panels may be stacked together to form a composite structure so that each panel is formed with different weights and thus the resultant panel attenuates a different range of frequencies in order to increase the attenuation bandwidth.
It would be desirable if the individual cells could be adjusted in order to adjust the range of frequencies attenuated by the individual cells, and consequentially the range of frequencies of the panel could be adjusted.
An acoustically transparent planar, rigid frame and sheet of a flexible material fixed to the rigid frame, is divided into individual cells configured for attenuating sound. Each cell has a weight fixed to the membrane. The planar geometry of each said individual cell, the flexibility of said flexible material and the weights establish a base resonant frequency of said sound attenuation. One or more of the cells having an electromagnetic or electrostatic response unit configured to modify the resonant frequency of the cell.
Overview
The sound attenuation structure of
With the addition of either specially designed electrodes or an electrically conducting wire coil, the working frequency of the sound attenuation structures can be tuned by either the electric voltage across the electrodes (
The electrodes shown in
By employing a metal-coated central platelet and a fishnet electrode which is transparent to acoustic waves, the present disclosure shows that the membrane-type acoustic metamaterials (MAMs) can be easily tuned by applying an external voltage. With static electric field the MAM's eigenfrequencies are tunable up to 70 Hz. The phase of the reflected or the transmitted wave can thereby be tuned when the sound wave frequency falls within the tunable range. The MAM's vibration can be significantly suppressed or enhanced by using phase-matched AC voltage. Functionalities, such phase modulation and controllable acoustic switch with on/off ratios up to 21.3 dB, are demonstrated.
The development of acoustic metamaterials has significantly enhanced design capabilities in sound wave manipulation. Acoustic metamaterials' unusual constitutive effective parameters, usually not found in nature, have led to numerous remarkable phenomena such as acoustic cloaking, acoustic focusing and imaging beyond diffraction limit, nonreciprocal transmission, and super absorption. To date, most metamaterials are passive, with minimum adjustment capability once fabricated. As a result, such metamaterials cannot adapt to real-life scenarios that are likely to change constantly as a function of time. One promising way to mitigate these problems is to incorporate active designs. According to the present disclosure, acoustic properties of membrane-type metamaterials (MAMs) can be controlled by external voltage to achieve a number of functionalities, such as phase modulation and acoustic wave switch.
The structures, comprising decorated membrane resonators (DMRs), have been studied previously. It is known that the low frequency transmission and reflection characteristics of a DMR are mainly determined by its first two eigenmodes. Transmission peaks at these resonant frequencies, and total reflection occurs at the anti-resonance frequency between the resonant frequencies. To demonstrate the actively controllable functionality, an analysis of the first eigenmode is used.
The basic structure of the sound attenuation structure in existing MAMs comprises a two dimensional array of structural units, each unit or cell consisting of a rigid boundary, an elastic membrane fixed on the boundary, and a weight attached to the center of the membrane. Each cell has an inherent resonant frequency which can be modified by an electromagnetic or electrostatic response unit or electromagnetic transducer.
In one configuration, the MAMs provide a sound attenuation panel comprising a substantially acoustically transparent planar, rigid frame divided into a plurality of individual cells, generally provided as two-dimensional cells. Each cell comprises a sheet of elastic material fixed on the cell frame, and one platelet attached to the sheet. The flexible materials can be either impermeable, such as rubber or plastic sheet, or permeable to air, such as open weave elastic fabric such as used in athletic apparel. The sheet can also be made in multiple layers. A pair of electrodes is placed near the platelet, one electrode above the platelet and one electrode below the platelet. The materials type of the platelet is either dielectric or metallic. A plurality of the panels may be stacked together.
The cells may each be provided with a platelet. In such a configuration of one electrode above the platelet and one electrode below the platelet, resonant frequency of the sound attenuation structure is defined by the planar geometry of each individual cell, the flexibility of the flexible material and the platelet, and the electric voltage difference between the electrodes.
In an alternative configuration, front and back sides of the same membrane are provided with conductive electrodes. In a specific non-limiting example, one side of the membrane is coated with a thin conductive film, such as a gold film. The opposite side of the same membrane from the conductive film has a mesh grid in contact with the membrane. The distance between the front and back electrodes is then determined by the thickness of the membrane, and can be maintained precisely, with the back electrodes provided as two concentric rings.
In another configuration, the platelet is made of permanent magnetic materials and an electric conducting wire coil is placed on the boundary of the structural unit.
In another configuration, each cell is provided with a platelet, and a wire coil is fixed on the boundary. The resonant frequency of the sound attenuation structure is defined by the planar geometry of each individual cell, the flexibility of the flexible material and platelet, and the electric current through the coil.
In order to modify the resonant response of the MAMs, at least a plurality of the cells have an electromagnetic or electrostatic response units capable of modifying the resonant frequency of the cell.
The arrangement allows active sound wave manipulations, including detection, processing, and emission of sound waves in close correlation in phase and amplitude with the incoming sound waves.
Working Principle
z
0
=F(z0)/k (1)
For a small displacement from the balance position, the net force is:
So the effective force constant is:
The first eigenmode frequency of the membrane-weight structure is given approximately by:
where m is the mass of the weight.
The central weight in disk shape is polarized by the electric field to form an electric dipole p=A·E(z), where A is a constant depending on the disk dimension and material property. The force on an electric dipole is:
So the electric field force is:
Put into Eq. 3, we have
The first term in Eq. 7 is always positive so its contribution is to lower the eigenfrequency. The second term can be positive or negative, so it can increase or decrease the eigenfrequency. The cross section of a particular pair of electrodes with cylindrical symmetry is shown in
is large but
is near zero, as the electric field there is nearly linearly dependent on position z. The other is at the bottom of the cone (marked as position 442) where
is non-zero but
is 0.
For an eigenfrequency of 100 Hz with weight mass m=1.0 g, the force constant due to the membrane is:
k=m(2πf)2≈4 N/m. (8)
For a disk shaped weight, its dipole moment due to an electric field of 1.0 V/m is about 1.5×10−8 A·s·m.
If the weight is placed at position-1 where the position dependence of the field is nearly linear, then
so only the first term in Eq. 7 contributes:
The magnitude of the effective force constant due to the electric field is smaller but comparable to that of the membrane, so the working voltage should be set around 1 volt. The change of electric force is opposite of the membrane so the effective force constant is reduced by the electric field. Therefore, the applied field will reduce the eigenfrequency.
At position-2,
so there is no initial force due to the field. The second term in Eq. 7 provides an effective force constant:
As the field force is proportional to square of the voltage, applying 7 volts to the electrodes will produce k2=−1.6 N/m, so the working voltage should be set around 7 V. The change of electric force is opposite of the membrane so the effective force constant is reduced by the electric field.
In this case the central platelet is a permanent magnet with dipole moment M, and the magnetic field by the coil is:
where a is the radius of the coil carrying electric current I.
The magnetic field force is
which is zero at z=0, i.e., when the membrane is placed in the plane of the coil:
For a=1 cm, I=1.0 A, and a typical 1.0 g magnet disk M=0.02 A·m2, so:
k
M≈−0.6 N/m, (11)
which is in the suitable range for eigenfrequency tuning.
The effect of a DC voltage U across the fishnet electrode and the central disk-shaped mass on the membrane is first analyzed. The fishnet electrode and the central disk-shaped mass on the membrane serve as the two electrodes of a parallel plate capacitor. When excited by incident acoustic wave, the vibration of the membrane introduces a small harmonic variation in the distance between the electrodes. Assuming that the mesh does not deform, the electric force exerted on the disk is:
where S is the effective area of the disk electrode,
∈≈1 represents the dielectric constant of air,
U is the amplitude of the applied voltage, and
d is the separation between the mesh and the disk at zero voltage.
The electric force can be clearly divided into two parts: a constant attractive force F0, and a force that is linearly proportional to the disks normal displacement Δz, with effective force constant
where K0 comes from the membrane's pre-stress.
This can be estimated as:
K
0
m(2πf0)2≈425 (N/m) (14)
It is then clear that the eigenfrequency will decrease as a result of the additional
A modified impedance-tube method was used to obtain the transmission spectra, as shown in
Resonant transmission of the DMR is accompanied by a 180° phase change. With tunable eigenfrequencies, the DMR can function as an active phase modulator. As shown in
The ability to tune the resonance frequency with static electric field allows us to construct a simple acoustic switch.
The resonance frequencies of the two cells are originally set to be the same so that a single transmission peak appears at 166 Hz. After a voltage is applied in cell 2, its resonance frequency is lowered. As stated before, its transmission field shall have a nearly 180° phase change across the new resonance frequency. Hence within the frequency region between the current resonance frequencies of the two cells, the transmitted fields through these two passageways are essentially out of phase, causing destructive interference. A transmission dip appeared at 156 Hz where the transmitted intensities from the two units are nearly equal. The transmission contrast over zero voltage is 21.3 dB (0.7/0.06).
AC voltage with angular frequency ω is then applied between the electrodes. The electric force on the disk can be expressed as:
Here A and w are the amplitude and the frequency of the AC voltage, respectively, and θ is the initial phase. It is noted that the out-of-plane displacement of the membrane leads to a negligible
In addition, the harmonic force is sensitive to the relative phase 2θ between the AC voltage and the incident sound wave. Its effect is seen for the first eigenmode, in which the central disk vibrates with the membrane in unison. The electric force can either enhance or suppress the vibration of the disk. By changing 2θ from 0 to π, the role of the harmonic electric force can be continuously altered from gain to loss.
In order to obtain large sound transmission loss, optimum amplitude of the voltage should be identified so as to totally counteract the sound pressure, as well as keep the phase condition 2θ=π. To investigate the dependence of the amplitude and the phase condition separately, the amplitude and the initial phase of the AC voltage is identified, in order to satisfy the two conditions to obtain highest sound transmission loss (STL) of 52 dB as compared to zero voltage. Then the amplitude of the AC voltage is tuned while keeping the phase to its optimum value. Referring to
Since the vibration profile is quite similar around the resonant frequency within a wide range, the above method is applicable in the adjacent frequency region. STL level exceeding 40 dB could be achieved in the nearby ±40 Hz range. Gain effect can also be demonstrated once the initial phase of the voltage was set so that the electric force becomes in-phase with the sound pressure.
As can be seen, with the assistance of an externally applied electric voltage, active control of the membrane-type acoustic metamaterials can be achieved. DC voltage can be used to modulate the resonance frequency and tune the phase, serving as an active phase modulator in a phase array that could manipulate sound waves at will. AC voltage provides an extra vibration source that can act as an acoustic switch, and can thereby serve as a good candidate to be used at specific surroundings within certain frequency ranges.
Electrodes with Minimized Gap Distances
In order to reduce the operation voltage in the structure in an electric field arrangement, the gap distance between the two electrodes must be further reduced; however, smaller gap distances are difficult to maintain.
In the configuration of
When no voltage is applied between mesh electrode 914 and the ring electrodes 923 and 924, the whole membrane 911 can vibrate which gives rise to resonance of DMR 901 in accordance with the flexibility of membrane 911, the area of membrane 911 and the weight of platelet 921. When a voltage is applied between outer ring electrode 924 and mesh electrode 914, the resultant electrostatic force will hold this part of membrane 911 firmly to the mesh 914 to turn it immobile. The effective membrane size of DMR 901 is reduced to only the part within the inner edge of outer ring 924, and the resonant frequency of DMR 901 is increased significantly. When a voltage is applied between inner ring electrode 923 and mesh electrode 914, this part of membrane 911 is also fixed so the resonant frequency of DMR 901 is further increased. By coating membrane 911 with a series of concentric ring electrodes, the effective size of the membrane can be adjusted by the applied voltage between the individual rings and the mesh electrode, thereby controlling the resonant frequency of DMR 901 over a large frequency range. The mesh 914 may be provided with an empty central opening with diameter equal to that of the inner diameter of the smaller metal ring on the membrane 923.
Field-Driven Sound Sources
For the cases when there is an initial force due to external field on the platelet, such as in the case when the platelet is placed in 441 in the electric field (
The sound attenuation is achieved by causing the central active element to vibrate in the opposite phase as the sound waves in the empty channels, therefore canceling their contribution. This results in the whole device acting to provide sound attenuation, with empty channels providing air flow.
It will be understood that many additional changes in the details, materials, steps and arrangement of parts, which have been herein described and illustrated to explain the nature of the subject matter, may be made by those skilled in the art within the principle and scope of the invention as expressed in the appended claims.
Filing Document | Filing Date | Country | Kind |
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PCT/CN2014/086939 | 9/19/2014 | WO | 00 |
Number | Date | Country | |
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61960478 | Sep 2013 | US |