1.1 Membrane for sound absorption

The term oscillating membrane means a thin plate or foil which has a very small bending stiffness and is located at a distance from the fixed wall. The behavior of such a membrane can be compared to the behavior of a body of a certain weight (represented by a membrane) elastically attached to the spring (represented by an air cushion). The space between the membrane and the rear fixed wall is filled with a porous material that dampens the vibrations of air particles in this space and thus the whole system. Typically, the membrane is selected from such a fabric that its flexural stiffness is much smaller than that of an air cushion [1].

Membrane absorbers are used to absorb low frequency sound. In order to increase the sound absorption, the membrane is positioned at a certain distance parallel to the rigid wall, thus creating an air gap between the wall and the membrane. Coates and Kierzkowski [2] in their paper describe the advantages of thin, light membranes that can replace traditional bulky and economically disadvantageous porous absorbers. The work deals with individual parameters such as the size of the air gap; membrane absorber thickness; its density, flexibility, and, in particular, air flow resistance; and its influence on sound absorption coefficient. The study [3] examines in detail the properties of a simple permeable membrane. The effect of membrane parameters such as basis weight and air flow resistance is clarified. The study is based on the theoretical solution presented in [4] for the perpendicular impact of sound waves. The permeable membrane is characterized by basis weight, tension, and air flow resistance Rh, which is a function of the thickness of the membrane. The influence of air flow resistance Rh to the sound absorption coefficient α occurs especially at higher frequencies. For extreme values, sound absorption coefficient α is zero. This is the case with extremely low air flow resistance Rh when all sound energy passes through the membrane. In the case of a very high Rh value, the membrane becomes impermeable, and all the sound energy is reflected. The optimal Rh value varies with the sound frequency and basis weight of the membrane. The influence of the basis weight is evident especially at lower frequencies. For higher sound frequencies, the value of α is almost constant. Thus, the basis weight loses the effect at higher frequencies, and only Rh plays the dominant role.

frequencies higher than 2 kHz. At low frequencies the characteristics are independent on air cavity between both membranes. At high frequencies, they are similar to those of a permeable membrane with an air back cavity and a rigid back wall. The mechanical analogy can be compared to linear electric circuit theory [9]. The electric impedance is defined by the ratio of voltage and current. The acoustic impedance is established analogous to electric impedance as a ratio of sound pressure and acoustic volume velocity. In order to obtain the acoustic impedance of the whole system, the acoustic impedance of the individual elements was first calculated. The relationship was then obtained for calculating the sound absorption coefficient. Two types of glass fiber fabric and a microperforated synthetic membrane were measured to confirm this theory. Measurements took place in both the reverberation room and the impedance tube. The results obtained theoretically are in good agreement with the measured values. A honeycomb structure, or a hexagonal structure, can create a lightweight and stable frame of the acoustic membrane element. Such an absorber studied at work [10] is designed for room acoustics as

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane

DOI: http://dx.doi.org/10.5772/intechopen.82615

In many other studies, various modifications of the oscillating membrane clamped in a circular frame are discussed. Determining the exact solution of oscillations of the circular membrane with inhomogeneous density was studied in works [11–15]. The study [16] focuses on the research of the base frequency of the circular membrane with additional star-shaped distortion originating from the outer edge. It is clear from the results that the base frequency increases with an increasing number of evenly distributed breaches and a length of breach. The article [17] describes the results of the research of the base frequency of a circular membrane that is in contact with water. It is known that the base frequencies of the structures in the water are smaller than in the air, due to the increase in the total kinetic energy of the

A thin circular membrane is a formation that results, for example, from the tension of a thin homogeneous elastic film with a constant basis weight of msq

force Fr, the membrane gains its stiffness. The radially acting tensile force relative to the unit length of the frame circumference is constant in all directions, and then

<sup>ν</sup> <sup>¼</sup> Fr

where Fr (N) is the total tensioning force and R (m) denotes the radius of the membrane (or the radius of the rigid circular support through which the membrane is tensioned). We expect this tension acting in the plane of the membrane to be the same in all places. Apart from circular membranes, other membrane shapes are used

If the membrane deflects from a normal position (e.g., by acoustic pressure), the membrane that originally formed the plane surface is deformed. If the force that causes the deflection ceases to occur, all the membrane points return; their potential energy, which they get by the deflection, changes into kinetic energy of the moving substantial elements, and the membrane vibrates. If the damping is not taken into

) is given by the formula:

account, the membrane will vibrate with free undisturbed vibrations.

in applications, e.g., elliptical, rectangular membranes.

) on a rigid circular frame [18]. By this tension caused by the radially acting

<sup>2</sup>π<sup>R</sup> , (1)

well as for industrial applications.

system due to the presence of water.

(kg m�<sup>2</sup>

23

the tension ν (N m�<sup>1</sup>

1.2 Resonance frequency of membrane

1.2.1 Resonance frequency of circular membrane

In the study [5, 6], the complete form of the analytical solution of the membrane sound absorption coefficient was described. A membrane of infinite dimensions lying in a plane parallel to the fixed wall at a certain distance is envisaged. The membrane characterized by the basis weight and the tension is vibrating by the impact of the plane wave below a given angle of incidence. Both side surfaces of the membrane, the source and back sides, as well as the wall surface, are described by a specific acoustic admittance. The sound absorption coefficient expresses the amount of energy absorbed, including energy losses of different types, which may be caused by different mechanisms at different locations in the system. The frequency of the α maxima, which is caused by the resonance of the system, decreases with the growth of the basis weight. The highest peak of α is recorded in a sample basis weight of 2 kg m<sup>2</sup> . With the increasing acoustic admittance of the back side of the membrane, sound absorption coefficient increases in frequency range up to 2 kHz; above this frequency, no effect of surface admittance on the back side, α is constant. Therefore, it can be argued that the sound absorption at higher frequencies is affected mainly by the acoustic admittance of the surface of the source side of the membrane.

A double resonant element, an acoustic element composed of two membranes separated by an air gap, was investigated in studies [7, 8]. Four types of two-layered resonant elements were measured, differing in basis weights [7]. The first membrane positioned in the direction of the incident sound wave always had a substantially smaller (approx. 10x) basis weight over the second membrane. The experimental results were in good agreement with the theoretical model. Furthermore, the influence of the thickness of the air gap, the weight of the two membranes, and their air flow resistance Rh were investigated. The study [8] also monitors the effect of airflow resistance of the first membrane on the acoustic behavior system. In this case, however, the first membrane positioned in the direction of the incident sound waves was permeable, characterized by an air flow resistance Rh.

The permeability of the membrane with optimal air flow resistance improves the absorption properties in the high sound frequency band. At low frequencies, the sound absorption coefficient increases with increasing mass of the first permeable membrane, while it decreases with increasing mass of the second solid membrane. Any effect of membrane mass on sound absorption coefficient is not found at

### Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane DOI: http://dx.doi.org/10.5772/intechopen.82615

frequencies higher than 2 kHz. At low frequencies the characteristics are independent on air cavity between both membranes. At high frequencies, they are similar to those of a permeable membrane with an air back cavity and a rigid back wall.

The mechanical analogy can be compared to linear electric circuit theory [9]. The electric impedance is defined by the ratio of voltage and current. The acoustic impedance is established analogous to electric impedance as a ratio of sound pressure and acoustic volume velocity. In order to obtain the acoustic impedance of the whole system, the acoustic impedance of the individual elements was first calculated. The relationship was then obtained for calculating the sound absorption coefficient. Two types of glass fiber fabric and a microperforated synthetic membrane were measured to confirm this theory. Measurements took place in both the reverberation room and the impedance tube. The results obtained theoretically are in good agreement with the measured values. A honeycomb structure, or a hexagonal structure, can create a lightweight and stable frame of the acoustic membrane element. Such an absorber studied at work [10] is designed for room acoustics as well as for industrial applications.

In many other studies, various modifications of the oscillating membrane clamped in a circular frame are discussed. Determining the exact solution of oscillations of the circular membrane with inhomogeneous density was studied in works [11–15]. The study [16] focuses on the research of the base frequency of the circular membrane with additional star-shaped distortion originating from the outer edge. It is clear from the results that the base frequency increases with an increasing number of evenly distributed breaches and a length of breach. The article [17] describes the results of the research of the base frequency of a circular membrane that is in contact with water. It is known that the base frequencies of the structures in the water are smaller than in the air, due to the increase in the total kinetic energy of the system due to the presence of water.

### 1.2 Resonance frequency of membrane

#### 1.2.1 Resonance frequency of circular membrane

A thin circular membrane is a formation that results, for example, from the tension of a thin homogeneous elastic film with a constant basis weight of msq (kg m�<sup>2</sup> ) on a rigid circular frame [18]. By this tension caused by the radially acting force Fr, the membrane gains its stiffness. The radially acting tensile force relative to the unit length of the frame circumference is constant in all directions, and then the tension ν (N m�<sup>1</sup> ) is given by the formula:

$$\nu = \frac{F\_r}{2\pi R},\tag{1}$$

where Fr (N) is the total tensioning force and R (m) denotes the radius of the membrane (or the radius of the rigid circular support through which the membrane is tensioned). We expect this tension acting in the plane of the membrane to be the same in all places. Apart from circular membranes, other membrane shapes are used in applications, e.g., elliptical, rectangular membranes.

If the membrane deflects from a normal position (e.g., by acoustic pressure), the membrane that originally formed the plane surface is deformed. If the force that causes the deflection ceases to occur, all the membrane points return; their potential energy, which they get by the deflection, changes into kinetic energy of the moving substantial elements, and the membrane vibrates. If the damping is not taken into account, the membrane will vibrate with free undisturbed vibrations.

light membranes that can replace traditional bulky and economically disadvantageous porous absorbers. The work deals with individual parameters such as the size of the air gap; membrane absorber thickness; its density, flexibility, and, in particular, air flow resistance; and its influence on sound absorption coefficient. The study [3] examines in detail the properties of a simple permeable membrane. The effect of membrane parameters such as basis weight and air flow resistance is clarified. The study is based on the theoretical solution presented in [4] for the perpendicular impact of sound waves. The permeable membrane is characterized by basis weight, tension, and air flow resistance Rh, which is a function of the thickness of the membrane. The influence of air flow resistance Rh to the sound absorption coefficient α occurs especially at higher frequencies. For extreme values, sound absorption coefficient α is zero. This is the case with extremely low air flow resistance Rh when all sound energy passes through the membrane. In the case of a very high Rh value, the membrane becomes impermeable, and all the sound energy is reflected. The optimal Rh value varies with the sound frequency and basis weight of the membrane. The influence of the basis weight is evident especially at lower frequencies. For higher sound frequencies, the value of α is almost constant. Thus, the basis weight loses the effect at higher frequencies, and only Rh plays the domi-

In the study [5, 6], the complete form of the analytical solution of the membrane sound absorption coefficient was described. A membrane of infinite dimensions lying in a plane parallel to the fixed wall at a certain distance is envisaged. The membrane characterized by the basis weight and the tension is vibrating by the impact of the plane wave below a given angle of incidence. Both side surfaces of the membrane, the source and back sides, as well as the wall surface, are described by a specific acoustic admittance. The sound absorption coefficient expresses the amount of energy absorbed, including energy losses of different types, which may be caused by different mechanisms at different locations in the system. The frequency of the α maxima, which is caused by the resonance of the system, decreases with the growth of the basis weight. The highest peak of α is recorded in a sample

of the membrane, sound absorption coefficient increases in frequency range up to 2 kHz; above this frequency, no effect of surface admittance on the back side, α is constant. Therefore, it can be argued that the sound absorption at higher frequencies is affected mainly by the acoustic admittance of the surface of the source side of

A double resonant element, an acoustic element composed of two membranes separated by an air gap, was investigated in studies [7, 8]. Four types of two-layered resonant elements were measured, differing in basis weights [7]. The first membrane positioned in the direction of the incident sound wave always had a substan-

experimental results were in good agreement with the theoretical model. Furthermore, the influence of the thickness of the air gap, the weight of the two membranes, and their air flow resistance Rh were investigated. The study [8] also monitors the effect of airflow resistance of the first membrane on the acoustic behavior system. In this case, however, the first membrane positioned in the direction of the incident sound waves was permeable, characterized by an air flow

The permeability of the membrane with optimal air flow resistance improves the absorption properties in the high sound frequency band. At low frequencies, the sound absorption coefficient increases with increasing mass of the first permeable membrane, while it decreases with increasing mass of the second solid membrane. Any effect of membrane mass on sound absorption coefficient is not found at

tially smaller (approx. 10x) basis weight over the second membrane. The

. With the increasing acoustic admittance of the back side

nant role.

Acoustics of Materials

basis weight of 2 kg m<sup>2</sup>

the membrane.

resistance Rh.

22

If the assumption of axially symmetrical vibrations is fulfilled, then the following relation (2) applies, from which it is possible to determine the base membrane frequencies f0,i (Hz) using the constant of the vid a0,i (equal to 2.4048 for f0,1, 5.5201 for f0,2, 8.6537 for f0,3, 11.97915 for f0,4):

$$f\_{0,i} = \frac{1}{2\pi R} a\_{0,i} C\_{\text{M\nu}} \tag{2}$$

For the rectangular membrane, its resonant frequency fm,n (Hz) according to the

where m and n are vids in each axis and a and b (m) are the dimensions of the

The nodal lines of the circle in the simplest case of symmetry are concentric circles, the node lines of the rectangle pointing in the simplest case in the direction of the membrane stresses (perpendicular to the sides of the shape) and dividing the rectangle into the same parts in either direction or in both directions. In a more complex case, the node line is guided along the diagonal rectangle. The constant tension of the membrane ν was achieved by observing the constant conditions during the electrospinning of nanofibrous membrane to the grid support. The optical method according to study [19] determined the base resonant frequency of the circular membrane f0,i. Assuming a constant value ν and thus CM, then the relation Eq. (9) can be modified by assigning the relation Eq. (2) as follows:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m a � �<sup>2</sup>

� �<sup>2</sup> <sup>r</sup>

þ n b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m a � �<sup>2</sup> <sup>þ</sup> <sup>n</sup> b

� �<sup>2</sup> <sup>q</sup>

a0,i

The acoustic element is based on a rigid frame in the form of a perforated plate or a flexible frame in the form of linear shapes or grids, the back side of which covers a thin carrier layer with a nanofibrous membrane which is covered with frames to some extent against mechanical damage. The frame also has a visual function. The element arrangement based on a perforated panel with a nanofibrous layer wherein the area of the nanofibrous membrane is determined by the size and shape of the perforation which, in general, does not necessarily have to be repeated throughout its shape and size, and the element thus consists of many different sheets that allow vibration of the membrane resulting in the unique properties of each vibrating area. The properties of the cavity resonator also enter the system, where the thickness of the plate and its distance from the reflecting surface (wall/ ceiling application) are also important in addition to the size and spacing of the

The frequency of the perforated panel fH (Hz), based on the Helmholtz resona-

ffiffiffiffiffiffiffiffiffi SD SRld <sup>r</sup>

) is the sound propagation velocity through the medium (air), S<sup>D</sup>

tor principle, is according to the studies [1, 20] given by an expression:

) is the cross-sectional area of the cavity, SR (m<sup>2</sup>

<sup>f</sup> <sup>H</sup> <sup>¼</sup> <sup>c</sup> 2π

(hole spacing), l (m) is the thickness of the perforated plate, and d (m) is the

Figure 1 illustrates an arrangement of a frame-based element in the form of linear structures (wire construction) overlapping the nanofibrous membrane over its entire back surface. Each shape of the frame borders the area of the oscillating

, (9)

: (10)

, (11)

) is the area of the resonator

<sup>f</sup> m,n <sup>¼</sup> <sup>1</sup> 2 CM

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane

<sup>f</sup> m,n <sup>¼</sup> <sup>π</sup>Rf <sup>0</sup>,i

work [18] is given by the relation

DOI: http://dx.doi.org/10.5772/intechopen.82615

2. Acoustic element design

hole.

(m<sup>2</sup>

25

where c (m s�<sup>1</sup>

distance from the reflective wall.

2.1 Principle of acoustic element

sides of the rectangle.

where CM (m s�<sup>1</sup> ) is the velocity of transverse wave propagating on the membrane given by the relationship

$$\mathbf{C}\_{M} = \sqrt{\frac{\nu}{m\_{sq}}},\tag{3}$$

where msq (kg m�<sup>2</sup> ) is the basis weight of the membrane.

To calculate the membrane base frequencies according to formula Eq. (2), it is necessary first to determine the velocity of the transverse wave propagating on the membrane CM. This is not possible without knowledge of the radially acting tensioning force v that causes the diaphragm tension on the circular frame. The CM and ν values are not known, so Eq. (2) cannot be applied to the calculation. By adjusting it, however, the necessary relationships can be obtained.

For determining the angular velocity ω0,i (s�<sup>1</sup> ), the following formula is commonly used:

ω0,i ¼ 2πf <sup>0</sup>,i : (4)

By putting it in relation Eq. (2), the equation Eq. (4) can be rewritten as follows:

$$2\pi f\_{0,i} = \frac{a\_{0,i}C\_M}{R} \,. \tag{5}$$

After the conversion of this relationship, it is possible to express the relation

$$f\_{0,i} = \frac{a\_{0,i}C\_M}{2\pi R} \Rightarrow \frac{f\_{0,i}}{a\_{0,i}} = \frac{C\_M}{2\pi R}.\tag{6}$$

The ratio CM <sup>2</sup>π<sup>R</sup> is constant since the membrane radius and the velocity of the wave propagation by the membrane do not change. Thus, the ratio of frequency and relevant constant of the vid is constant as follows:

$$\frac{f\_{0,1}}{a\_{0,1}} = \frac{f\_{0,2}}{a\_{0,2}} = \frac{f\_{0,3}}{a\_{0,3}} = \frac{f\_{0,4}}{a\_{0,4}}.\tag{7}$$

From the abovementioned relationships Eqs. (4)–(6), it is obvious that the radius of the membrane R is inversely proportional to the frequency f0,i and with the increasing radius of the membrane, the own frequency falls.

#### 1.2.2 Resonance frequency of rectangular membrane

The membrane is tensioned in the x-axis and y-axis direction by a tension ν applied per unit length. The rectangular membrane with sides a and b and axes x and y is tensioned in axial direction by forces:

$$F\_{\mathfrak{x}} = \mathfrak{b}.\nu, F\_{\mathfrak{y}} = \mathfrak{a}.\nu \tag{8}$$

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane DOI: http://dx.doi.org/10.5772/intechopen.82615

For the rectangular membrane, its resonant frequency fm,n (Hz) according to the work [18] is given by the relation

$$f\_{m,n} = \frac{1}{2} \mathcal{C}\_{\mathcal{M}} \sqrt{\left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2},\tag{9}$$

where m and n are vids in each axis and a and b (m) are the dimensions of the sides of the rectangle.

The nodal lines of the circle in the simplest case of symmetry are concentric circles, the node lines of the rectangle pointing in the simplest case in the direction of the membrane stresses (perpendicular to the sides of the shape) and dividing the rectangle into the same parts in either direction or in both directions. In a more complex case, the node line is guided along the diagonal rectangle. The constant tension of the membrane ν was achieved by observing the constant conditions during the electrospinning of nanofibrous membrane to the grid support. The optical method according to study [19] determined the base resonant frequency of the circular membrane f0,i. Assuming a constant value ν and thus CM, then the relation Eq. (9) can be modified by assigning the relation Eq. (2) as follows:

$$f\_{m,n} = \frac{\pi R f\_{0,i} \sqrt{\left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2}}{a\_{0,i}}.\tag{10}$$

## 2. Acoustic element design

If the assumption of axially symmetrical vibrations is fulfilled, then the following relation (2) applies, from which it is possible to determine the base membrane frequencies f0,i (Hz) using the constant of the vid a0,i (equal to 2.4048 for f0,1,

<sup>2</sup>π<sup>R</sup> <sup>a</sup>0,iCM, (2)

, (3)

), the following formula is com-

: (4)

<sup>R</sup> : (5)

<sup>2</sup>π<sup>R</sup> : (6)

: (7)

) is the velocity of transverse wave propagating on the mem-

ffiffiffiffiffiffiffi ν msq r

<sup>f</sup> <sup>0</sup>,i <sup>¼</sup> <sup>1</sup>

CM ¼

) is the basis weight of the membrane. To calculate the membrane base frequencies according to formula Eq. (2), it is necessary first to determine the velocity of the transverse wave propagating on the membrane CM. This is not possible without knowledge of the radially acting tensioning force v that causes the diaphragm tension on the circular frame. The CM and ν values are not known, so Eq. (2) cannot be applied to the calculation. By adjusting

ω0,i ¼ 2πf <sup>0</sup>,i

<sup>2</sup>π<sup>f</sup> <sup>0</sup>,i <sup>¼</sup> <sup>a</sup>0,iCM

After the conversion of this relationship, it is possible to express the relation

<sup>2</sup>π<sup>R</sup> ) <sup>f</sup> <sup>0</sup>,i

<sup>¼</sup> <sup>f</sup> <sup>0</sup>, <sup>3</sup> a0, <sup>3</sup>

From the abovementioned relationships Eqs. (4)–(6), it is obvious that the radius of the membrane R is inversely proportional to the frequency f0,i and with

The membrane is tensioned in the x-axis and y-axis direction by a tension ν applied per unit length. The rectangular membrane with sides a and b and axes x

propagation by the membrane do not change. Thus, the ratio of frequency and

<sup>¼</sup> <sup>f</sup> <sup>0</sup>, <sup>2</sup> a0,<sup>2</sup> a0,i

<sup>2</sup>π<sup>R</sup> is constant since the membrane radius and the velocity of the wave

<sup>¼</sup> <sup>f</sup> <sup>0</sup>,<sup>4</sup> a0,<sup>4</sup>

Fx ¼ b:ν, Fy ¼ a:ν (8)

<sup>¼</sup> CM

<sup>f</sup> <sup>0</sup>,i <sup>¼</sup> <sup>a</sup>0,iCM

relevant constant of the vid is constant as follows:

1.2.2 Resonance frequency of rectangular membrane

and y is tensioned in axial direction by forces:

f <sup>0</sup>, <sup>1</sup> a0, <sup>1</sup>

the increasing radius of the membrane, the own frequency falls.

By putting it in relation Eq. (2), the equation Eq. (4) can be rewritten as follows:

5.5201 for f0,2, 8.6537 for f0,3, 11.97915 for f0,4):

it, however, the necessary relationships can be obtained. For determining the angular velocity ω0,i (s�<sup>1</sup>

where CM (m s�<sup>1</sup>

Acoustics of Materials

where msq (kg m�<sup>2</sup>

monly used:

The ratio CM

24

brane given by the relationship

#### 2.1 Principle of acoustic element

The acoustic element is based on a rigid frame in the form of a perforated plate or a flexible frame in the form of linear shapes or grids, the back side of which covers a thin carrier layer with a nanofibrous membrane which is covered with frames to some extent against mechanical damage. The frame also has a visual function. The element arrangement based on a perforated panel with a nanofibrous layer wherein the area of the nanofibrous membrane is determined by the size and shape of the perforation which, in general, does not necessarily have to be repeated throughout its shape and size, and the element thus consists of many different sheets that allow vibration of the membrane resulting in the unique properties of each vibrating area. The properties of the cavity resonator also enter the system, where the thickness of the plate and its distance from the reflecting surface (wall/ ceiling application) are also important in addition to the size and spacing of the hole.

The frequency of the perforated panel fH (Hz), based on the Helmholtz resonator principle, is according to the studies [1, 20] given by an expression:

$$f\_H = \frac{c}{2\pi} \sqrt{\frac{\mathcal{S}\_D}{\mathcal{S}\_R l d}},\tag{11}$$

where c (m s�<sup>1</sup> ) is the sound propagation velocity through the medium (air), S<sup>D</sup> (m<sup>2</sup> ) is the cross-sectional area of the cavity, SR (m<sup>2</sup> ) is the area of the resonator (hole spacing), l (m) is the thickness of the perforated plate, and d (m) is the distance from the reflective wall.

Figure 1 illustrates an arrangement of a frame-based element in the form of linear structures (wire construction) overlapping the nanofibrous membrane over its entire back surface. Each shape of the frame borders the area of the oscillating

#### Figure 1.

The principle of designing the final solution of a frame-based acoustic element in the form of linear formations with a nanofibrous layer in view and cut. The gray color in cross section shows the frame (wire construction), the blue one is nanofibrous resonant membrane, and the red one is adhesive.

membrane, and, in general, the individual frame structure does not need to be repeated over the whole surface, and the element thus consists of many different borders that allow vibration of the membrane resulting in the unique properties of each oscillating surface.
