JP7387219B2 - Composite vibration damping support frame using acoustic black hole and its design method - Google Patents

Description

The present invention relates to a composite vibration damping support structure using an acoustic black hole and a method for designing the same, and specifically relates to a vibration damping support structure that can suppress the transmission of elastic waves.

A ship has many power machines, especially in the cabin, such as a main engine, a transmission device, and other auxiliary machines, which inevitably generate vibration and noise during operation. Frequently used damping measures include changing the dimensions and stiffness of the support structure, vibration isolators and vibration damping techniques, which increase the weight and material costs of the support structure and also make it difficult to place and install the support structure. Even higher demands are placed on them. Therefore, it is expected to develop a new support structure that ensures good vibration damping effects without increasing weight or size.

The ideal acoustic black hole structure (ABH) has a cross-sectional thickness that is a power function.
where h(x) is the thickness of the acoustic black hole structure at x, ε is a constant, the power exponent m is a positive rational number, and _h0 is the acoustic black hole structure attenuated by is the local thickness of the structure ( _h0 for an ideal acoustic black hole is 0). When the change in the thickness of the structure satisfies a power function curve with an index of 2 or more, the basic requirements of a structure-acoustic black hole can be met. In ideal conditions, the bending waves have zero reflection and all the bending waves conducted into the ABH region are "swallowed", but in actual manufacturing, it is difficult for the structural thickness to vary to zero according to the power index; The thickness is cut off at the tip. Even the slightest local thickness can increase the reflection coefficient of a structure by more than 50%, weakening the collective effect of an acoustic black hole, and pasting damping material in the area of the acoustic black hole can significantly increase the reflection coefficient. can effectively absorb energy and suppress vibration.

Damping masses are generally strips and are placed at the joints of plates along the vibration transmission path of the structure, so that sudden changes in the steady structure (mass, stiffness, etc.) can cause impedance mismatches in the structure and lead to bending waves. It exhibits a good reflective effect against.

The present invention relates to a composite vibration damping support structure using an acoustic black hole and its design method, which controls vibrations generated from a power machine by utilizing the collective effect of elastic waves caused by an acoustic black hole, thereby dissipating vibration energy and suppressing waves. In addition to suppressing propagation, the damping layer and vibration isolator are provided to improve the damping effect.

It is an object of the present invention to provide a damping support structure that reduces vibration transmission in power mechanical structures.

In order to achieve the above object, the present invention adopts the following technical solutions.

A composite vibration damping support frame based on an acoustic black hole, including a support frame body, the support frame body being at least one door frame-like frame body consisting of a top plate and at least two vertical brackets; A web is connected to the rear side of the body, a vibration isolator is connected to the lower end, and a one-dimensional acoustic black hole wedge structure 1 and a one-dimensional acoustic black hole wedge structure 2 are provided at both ends of the face plate from front to back, respectively. , the bracket is provided with at least two small-diameter two-dimensional acoustic black holes 1 in the upper part, at least two large-diameter two-dimensional acoustic black holes 2 in the lower part, and the web is provided with at least two two-dimensional acoustic black holes 2 in the lower part. A dimensional acoustic black hole array is provided, and three one-dimensional acoustic black hole wedge structures are provided at each end of the web, the one-dimensional acoustic black hole wedge structure one, the one-dimensional acoustic black hole wedge structure two, the one-dimensional acoustic The black hole wedge structure 3, the 2-dimensional acoustic black hole structure 1, and the 2-dimensional acoustic black hole structure 2 are each covered with an attenuation layer on the side surface corresponding to the two-dimensional acoustic black hole array.

More preferably, the top plate and the web are both rectangular steel plates, the bracket is a right-angled trapezoidal steel plate, and the vibration isolator is hollow or solid structural steel with a rectangular cross section.

More preferably, the cross section of the acoustic black hole is
where h ₀ is between 0.2 and 1 mm. A one-dimensional acoustic black hole has a wedge structure whose cross section is stretched in the normal direction, and a two-dimensional acoustic black hole has a hollow structure whose cross section rotates around the y-axis.

More preferably, one-dimensional acoustic black hole wedge structures are distributed on the edges of both ends of the top plate and the web, and two sets of one-dimensional acoustic black hole wedges of different sizes are distributed on the edges of both ends of the top plate. The structures are distributed, and the width of each structure is half the width of the top plate.

More preferably, the array form of the two-dimensional acoustic black hole array 3 is a rectangular array or a circular array, and the number of two-dimensional acoustic black holes in each array is 4 to 6.

More preferably, the distance from the edge of the two-dimensional acoustic black hole structure 1, the two-dimensional acoustic black hole structure 2, and the two-dimensional acoustic black hole array 3 to the edge of the plate, the edge of two adjacent acoustic black holes The distance is greater than 0.3r, which ensures structural strength and improves the damping effect.

More preferably, said damping layer has a thickness of 4 to 10 times the local thickness of the acoustic black hole and is a viscoelastic damping material.

More preferably, said connection is a weld.

In order to achieve the above object, other technical solutions adopted by the present invention are as follows.

A method for designing a composite vibration damping support frame using an acoustic black hole, the method comprising:
Step S1 of measuring the vibration line spectrum of the power machine using a vibration test system and determining the vibration suppression start frequency f;
Determine the power law m (generally m is 2.0 to 2.5), and if m is large, the reflection coefficient when vibration is transmitted to the boundary can be significantly reduced; step S2, which is difficult to manufacture and may not satisfy the smoothness condition at low frequencies;
Step S3 of calculating the feature size r of the acoustic black hole (length for a one-dimensional acoustic black hole, radius for a two-dimensional acoustic black hole),
S3-1: Converting from the damping start frequency of the acoustic black hole collective effect
is obtained and determined, where h is the thickness of the flat plate, ρ ₁ is the density of the material, E ₁ is the Young's modulus of the material, v is the Poisson's ratio of the material, and the one-dimensional acoustic black hole wedge structure ( 1-1), one-dimensional acoustic black hole wedge structure three (3-1), two-dimensional acoustic black hole structure one (2-1), and two-dimensional acoustic black hole array (3-2), damping start frequency f The feature size _r1 of the acoustic black hole can be calculated by substituting
S3-2: For the acoustic black hole of the top plate (1) and bracket (2), a larger set of one-dimensional acoustic black hole wedge structure 1 (1-2) and two-dimensional acoustic black hole structure 2 (2- 2) parameters
radius, determined by
Step S3 of determining
Step S4 of calculating a cross-sectional function of an acoustic black hole,
S4-1: 1-dimensional acoustic black hole wedge structure 1 (1-1), 1-dimensional acoustic black hole wedge structure 3 (3-1), 2-dimensional acoustic black hole structure 1 (2-1), 2-dimensional acoustic black hole Calculate the cross-sectional function h ₁ (x) of the array (3-2), ε ₁ is determined by the plate thickness h and the characteristic size r ₁ of the acoustic black hole,
and
S4-2: Calculate the cross-sectional functions of one-dimensional acoustic black hole wedge structure 2 (1-2) and two-dimensional acoustic black hole structure 2 (2-2),
Step S4, which is
Calculate the reflection coefficient as the ratio of the output amount and input amount of the bending wave,
Here, x ₀ , x are the starting and ending points of the cross section of the acoustic black hole, and E ₁ , E ₂ , ρ ₁ , ρ ₂ , η ₁ , η ₂ are the Young's modulus and density of the plate and damping layer, respectively. , is the loss factor, δ is the thickness of the damping layer,
is the wave number, where c is the wave speed at the wave plate, f is the wave frequency,
If no damping is applied, the very small local thickness of the acoustic black hole also increases the reflection coefficient and reduces the wave-gathering effect of the acoustic black hole. Quickly evaluate the reflection coefficient of each acoustic black hole structure using the one-dimensional acoustic black hole reflection coefficient formula,
When the damping layer is not covered, the damping loss coefficient of the acoustic black hole and the supporting structure is relatively small, and the damping effect of the supporting structure is reduced due to the unavoidable local thickness of the acoustic black hole. is not clear, and by placing an attenuation layer in the central region of the acoustic black hole, the reflection coefficient of the acoustic black hole structure can be effectively suppressed.
The radius (or length) of the damping layer must be larger than 0.5 times the feature size r of the acoustic black hole, and most of the vibrational energy will be dissipated in the central region of the acoustic black hole. must be pasted in the central area of the acoustic black hole to cover all possible areas,
A thicker damping layer δ can enhance the damping effect of the acoustic black hole, and in order to achieve both the damping effect of the acoustic black hole and economic efficiency, the loss coefficient of the damping material is generally set to be larger than 0.5. and a step S5 of setting the thickness of the damping layer to 4 to 10 times the local thickness h ₀ and controlling the reflection coefficient within the damping frequency band to within 0.5;
Smoothness condition:
Verify,
If the smoothness condition and the reflection coefficient control requirements are not satisfied, step S6 is included in which S2 and subsequent steps are repeated until the condition requirements are satisfied.

The operating principle of the present invention is as follows. The present invention utilizes the acoustic black hole effect to change the phase velocity and group velocity of waves in the structure by changing the structural impedance, and realizes the aggregation of waves in a local region of the structure. In a thin plate structure, if the change in impedance is achieved by varying the thickness of the plate in some exponential form, the velocity of the bending wave gradually decreases with decreasing thickness, the wavelength is compressed, and the amplitude is increases and ideally the wave velocity decreases to zero so that no reflections occur. Also, by utilizing the principle of impedance mismatch, the vibration isolators in the support structure suppress the propagation of vibration waves generated by the power machinery to the hull structure. In the process of vibrations being transmitted from the faceplate to the hull, the acoustic black hole cannot absorb the bending waves completely because of the local thickness of the acoustic black hole, and some waves will "escape" and , the bracket and the web have lower bending stiffness than the vibration isolator and reflect some of the bending waves, and the reflected bending waves propagate inside the bracket and the web and re-enter the acoustic black hole region, thereby The wave aggregation effect of the acoustic black hole increases.

The acoustic black hole has the first cutoff frequency
It does not work at all when the excitation is lower than the first cutoff frequency, and since the characteristic length of the acoustic black hole is longer than the half wavelength of the bending wave in the flat plate, the acoustic black hole effect is It gradually begins to function. In the design method of composite damping support structure, acoustic black holes with relatively large feature sizes are calculated based on the first cutoff frequency, and the feature sizes of other acoustic black holes are calculated based on the first cutoff frequency derived from the smoothness condition. 2 cutoff frequency
Calculated from. The number of two-dimensional acoustic black holes in the bracket and the array configuration and number of acoustic black holes in the web are determined by the size and ease of placement of the support structure.

Vibrations caused by the power machine are transmitted from the face plate to the bracket or web. As vibrational waves propagate over the bracket, the waves collect within the acoustic black hole structure. Due to the wave aggregation effect of the acoustic black hole, the wave width in the central region of the acoustic black hole is relatively large, and a damping layer is pasted on the surface of the acoustic black hole region, and the damping layer uses shear deformation to transfer mechanical energy. Converts into thermal energy and consumes vibrational energy.

The beneficial effects of the present invention are as follows.

The present invention dissipates the vibration energy generated by the power machine while supporting the power machine, and comprehensively utilizes the energy gathering effect of an acoustic black hole, damping vibration damping design technology, and the principle of impedance mismatch to reduce bending waves. By performing control and dissipation of vibration energy, the purpose of vibration damping can be achieved, and it has promising future potential and can be applied to support structures of various power machines on ships. The present invention has a more obvious vibration damping effect than a general support structure, with an average vibration damping effect of 7 dB or more in a frequency band of 500 Hz or more, and a damping band gap of 70%. , has important application value in vibration damping and noise reduction of marine power machinery. The size of the one-dimensional acoustic black holes at both ends of the face plate and the web is not the same, and the radius of the two sets of upper and lower acoustic black holes on the bracket is also not the same, which allows the damping frequency band of the acoustic black hole to be wide. Become. Also, the introduction of damping mass and damping improves the collective effect of acoustic black holes. Since the waves are concentrated within the black hole region, a damping layer is provided only in this region rather than the entire support structure body, which reduces material usage and manufacturing costs. In addition, compared to ordinary brackets, the mass of the support structure body is reduced even with the same thickness because the acoustic black hole structure is introduced. Since we adopted an acoustic black hole structure in place of the damping hole structure of the support structure, it does not affect the strength of the support structure compared to damping hole type support structures, and can be attached elastically or rigidly. The power machine can be supported when the power machine is installed, and vibration transmission of the power machine can be reduced.

FIG. 2 is a structural schematic diagram of a rectangular array form of the present invention. FIG. 2 is a structural schematic diagram of a circular array form of the present invention. FIG. 3 is a top view of the face plate of the present invention. FIG. 3 is an AA arrow view of the face plate of the present invention. It is a left view of the bracket of this invention. FIG. 3 is a view taken along the arrow BB of the bracket of the present invention. 1 is a front view of a web in a rectangular array configuration of the present invention; FIG. FIG. 2 is a CC arrow view of a rectangular array web of the present invention. FIG. 2 is a front view of a web in the form of a circular array of the present invention. FIG. 3 is a DD view of a circular array web of the present invention. It is a flowchart of the design method of this invention.

As shown in FIGS. 1 to 10, the composite vibration damping support frame using an acoustic black hole of the present invention supports a power machine of a ship and consumes vibration energy in a transmission path. Top plate 1, bracket 2, web 3, vibration isolator 4, one-dimensional acoustic black hole wedge structure 1-1, one-dimensional acoustic black hole wedge structure two 1-2, and one-dimensional acoustic black hole wedge structure three 3-1. , a bracket two-dimensional acoustic black hole 1 2-1, a two-dimensional acoustic black hole structure 2-2, a web two-dimensional acoustic black hole array 3-2, and a damping layer 5.

The weight of the power machine is supported by the top plate 1, brackets 2 and webs 3.

The top plate 1 is made of steel and has a rectangular shape. The lower end surface of the top plate 1 and the upper end surfaces of the bracket 2 and the web 3 are connected by welding. The upper plate 1 has a one-dimensional acoustic black hole wedge structure 1-1 and a one-dimensional acoustic black hole wedge structure 2 1-2 on both edges, and a damping layer 5 is provided on the plane of the one-dimensional acoustic black hole area. is pasted.

The bracket 2 is made of steel, has a right-angled trapezoidal shape, has an upper end surface connected to the top plate 1 by welding, and one end surface connected to the web 3 by welding. A hole structure 1 2-1 and a two-dimensional acoustic black hole structure 2-2 are provided, the smaller set of the two-dimensional acoustic black hole structure 2-1 is placed close to the upper base of the trapezoid, and the larger set The two-dimensional acoustic black hole structure 22-2 is placed close to the upper base of the trapezoid. A damping layer 5 is pasted on one side of the plane of the two-dimensional acoustic black hole region.

The web 3 is made of steel, has a rectangular shape, has an upper end surface connected to the top plate 1 by welding, is connected to one end surface of the bracket 2 by welding, and has a two-dimensional acoustic black A hole array 3-2 is attached, and a damping layer 5 is pasted on one side of the plane of the two-dimensional acoustic black hole region.

The cross section of the vibration isolator 4 is rectangular, and the width of the cross section is 5 to 10 times the thickness of the web 3 or the bracket 2. The vibration isolator 4 is provided at the lower end of the bracket 2 and the web 3, and The lower end surfaces of the webs 3 and 3 are welded to the center of the connection surface of the vibration isolator 4, respectively.

The damping layer 5 is a viscoelastic damping material, which can be composed of suitable additive fillers and solvents such as asphalt, water solubilized, latex, epoxy resin, etc., and the steel plate and the damping layer 5 are bonded with a high-strength adhesive. It becomes an integrated structure.

The design method of a composite damping support frame using an acoustic black hole includes the following steps (see FIG. 11).
S1: Measure the vibration line spectrum of the power machine using a vibration test system, and determine the vibration damping start frequency f.
S2: Determine the power law m (generally m is 2.0 to 2.5). If m is large, the reflection coefficient when vibration is transmitted to the boundary can be significantly reduced, but if m is The larger the size, the more difficult it is to manufacture, and the smoothness condition may not be satisfied at low frequencies.
S3: Calculate the feature size r of the acoustic black hole (length for a one-dimensional acoustic black hole, radius for a two-dimensional acoustic black hole).
S3-1: Converting from the damping start frequency of the acoustic black hole collective effect
is obtained and determined, where h is the thickness of the flat plate, _ρ1 is the density of the material, _E1 is the Young's modulus of the material, v is the Poisson's ratio of the material, and the one-dimensional acoustic black hole wedge structure -1 -1. For the one-dimensional acoustic black hole wedge structure 3-1, the two-dimensional acoustic black hole structure 2-1, and the two-dimensional acoustic black hole array 3-2, substitute the damping start frequency f into the equation to calculate the acoustic black The feature size r ₁ of the hole can be calculated,
S3-2: For the acoustic black hole of the top plate 1 and bracket 2, set the parameters of the larger set of one-dimensional acoustic black hole wedge structure 1-1-2 and two-dimensional acoustic black hole structure 2-2.
Determined by the radius
Determine.
S4: Calculate the cross-sectional function of the acoustic black hole.
S4-1: Cross sections of one-dimensional acoustic black hole wedge structure 1-1, one-dimensional acoustic black hole wedge structure 3-1, two-dimensional acoustic black hole structure 2-1, and two-dimensional acoustic black hole array 3-2. Function h ₁ (x)
Calculated by, ε ₁ is determined by the plate thickness h and the feature size r ₁ of the acoustic black hole,
It is.
S4-2: Calculate the cross-sectional functions of one-dimensional acoustic black hole wedge structure 21-2 and two-dimensional acoustic black hole structure 22-2,
It is.
S5: Calculate the reflection coefficient as the ratio of the output amount and input amount of the bending wave,
Here, x ₀ , x are the starting and ending points of the cross section of the acoustic black hole, and E ₁ , E ₂ , ρ ₁ , ρ ₂ , η ₁ , η ₂ are the Young's modulus and density of the plate and damping layer, respectively. , is the loss factor, δ is the thickness of the damping layer,
is the wave number, where c is the wave speed at the wave plate, f is the wave frequency,
If no damping is applied, the very small local thickness of the acoustic black hole also increases the reflection coefficient and reduces the wave-gathering effect of the acoustic black hole. We quickly evaluate the reflection coefficient of each acoustic black hole structure using the one-dimensional acoustic black hole reflection coefficient formula.

If the damping layer is not covered, the damping loss coefficient of the acoustic black hole and the supporting structure is relatively small, and the local thickness of the acoustic black hole is unavoidable, so the damping effect of the supporting structure is It is not obvious that by laying a damping layer in the central region of the acoustic black hole, the reflection coefficient of the acoustic black hole structure can be effectively suppressed.
The radius (or length) of the damping layer must be larger _than 0.5 times the feature size r of the acoustic black hole, and most of the vibrational energy will be dissipated in the central region of the acoustic black hole. must be pasted in the central area of the acoustic black hole to cover all possible areas,
A thicker damping layer δ can enhance the damping effect of the acoustic black hole, and in order to achieve both the damping effect of the acoustic black hole and economic efficiency, the loss coefficient of the damping material is generally set to be larger than 0.5. The thickness of the damping layer is set to 4 to 10 times the local thickness h ₀ and the reflection coefficient within the damping frequency band is controlled within 0.5.
S6: Smoothness condition:
Verify,
If the smoothness condition and the reflection coefficient control requirements are not met, S2 and subsequent steps are repeated until the condition requirements are met.

Claims (9)

A composite vibration damping support frame using an acoustic black hole including a support frame main body,
The support frame body is at least one door frame-like frame body composed of a top plate (1) and at least two vertical brackets (2), and the frame body has a web (3) on the rear side. A vibration isolator (4) is connected to the lower end, and a one-dimensional acoustic black hole wedge structure 1 (1-1) and a one-dimensional acoustic black hole wedge structure 2 (1-2) are connected to both ends of the upper plate (1). ) are provided from front to back, respectively, and the bracket (2) is provided with at least two small-diameter two-dimensional acoustic black holes (2-1) in the upper part, and at least two large-diameter two-dimensional acoustic black holes (2-1) in the lower part. A dimensional acoustic black hole 2 (2-2) is provided, and said web (3) is provided with at least two two-dimensional acoustic black hole arrays (3-2), one at each end of said web (3). A three-dimensional acoustic black hole wedge structure (3-1) is provided, the one-dimensional acoustic black hole wedge structure one (1-1), the one-dimensional acoustic black hole wedge structure two (1-2), and the two-dimensional acoustic black hole. Structure 1 (2-1), 2-dimensional acoustic black hole structure 2 (2-2), and 1-dimensional acoustic black hole wedge structure 3 (3-1) are each connected to a 2-dimensional acoustic black hole array (3-2). A composite vibration damping support frame characterized in that a damping layer (5) is covered on the corresponding side surface. The top plate (1) and the web (3) are both rectangular steel plates, the bracket (2) is a right-angled trapezoidal steel plate, and the vibration isolator (4) is a hollow or solid structural steel plate with a rectangular cross section. The composite vibration damping support frame using an acoustic black hole according to claim 1. The cross section of the acoustic black hole is
, where h ₀ is 0.2 to 1 mm,
The one-dimensional acoustic black hole has a wedge structure with a cross section stretched in the normal direction, and the two-dimensional acoustic black hole has a cross section with a concave structure rotated around the y-axis. A composite vibration damping support frame using the acoustic black hole described in 1. Two sets of one-dimensional acoustic black hole wedge structure 1 (1-1) and one-dimensional acoustic black hole wedge structure 2 (1-2) of different sizes are distributed on the edges of both ends of the top plate (1). , the width of each of these is half the width of the top plate (1), the composite vibration damping support frame using an acoustic black hole according to claim 1. Claim characterized in that the array form of the two-dimensional acoustic black hole array 3 (3-2) is a rectangular array or a circular array, and the number of two-dimensional acoustic black holes in each array is 4 to 6. A composite vibration damping support frame using the acoustic black hole described in 1. Distance from the edge of the two-dimensional acoustic black hole structure 1 (2-1), the two-dimensional acoustic black hole structure two (2-2), and the two-dimensional acoustic black hole array 3 (3-2) to the edge of the plate , wherein the distance between the edges of two adjacent acoustic black holes is greater than 0.3r, where r is the characteristic size of the acoustic black holes. Composite vibration damping support frame. Acoustic black according to claim 1, characterized in that the damping layer (5) has a thickness between 4 and 10 times the local thickness h ₀ of the acoustic black hole and is a viscoelastic damping material. Composite vibration damping support frame with holes. The composite vibration damping support frame using an acoustic black hole as claimed in claim 1, wherein the connection is by welding. A method for designing a composite vibration damping support frame using an acoustic black hole according to any one of claims 1 to 8, comprising:
Step S1 of measuring the vibration line spectrum of the power machine using a vibration test system and determining the vibration suppression start frequency f;
Determine the power law m (m is 2.0 to 2.5), and if m is large, the reflection coefficient when vibration is transmitted to the boundary can be significantly reduced, but the larger m is, the more difficult it is to manufacture. step S2, which is difficult and may not satisfy the smoothness condition at low frequencies;
Step S3 of calculating the feature size r of the acoustic black hole (the feature size r of the one-dimensional acoustic black hole is the length, and the feature size r of the two-dimensional acoustic black hole is the radius), the specific contents and steps are as follows. ,
S3-1: Converting from the damping start frequency of the acoustic black hole collective effect
is obtained and determined, where h is the thickness of the flat plate, ρ ₁ is the density of the material, E ₁ is the Young's modulus of the material, v is the Poisson's ratio of the material, and the one-dimensional acoustic black hole wedge structure - ( 1-1), one-dimensional acoustic black hole wedge structure three (3-1), two-dimensional acoustic black hole structure one (2-1), and two-dimensional acoustic black hole array (3-2), damping start frequency f The feature size _r1 of the acoustic black hole can be calculated by substituting
S3-2: For the acoustic black hole on the top plate (1) and bracket (2), the larger set of one-dimensional acoustic black hole wedge structure 1 (1-2) and two-dimensional acoustic black hole structure 2 (2) -2) parameters
radius, determined by
Step S3 of determining
Step S4 of calculating the cross-sectional function of the acoustic black hole, the specific contents and steps are as follows:
S4-1: 1-dimensional acoustic black hole wedge structure 1 (1-1), 1-dimensional acoustic black hole wedge structure 3 (3-1), 2-dimensional acoustic black hole structure 1 (2-1), 2-dimensional acoustic black hole Calculate the cross-sectional function h ₁ (x) of the array (3-2), ε ₁ is determined by the plate thickness h and the feature size r ₁ of the acoustic black hole,
and
S4-2: Calculate the cross-sectional functions of one-dimensional acoustic black hole wedge structure 2 (1-2) and two-dimensional acoustic black hole structure 2 (2-2),
Step S4, which is
Calculate the reflection coefficient as the ratio of the output amount and input amount of the bending wave,
Here, x ₀ , x are the starting and ending points of the cross section of the acoustic black hole, and E ₁ , E ₂ , ρ ₁ , ρ ₂ , η ₁ , η ₂ are the Young's modulus and density of the plate and damping layer, respectively. , is the loss factor, δ is the thickness of the damping layer,
is the wave number, where c is the wave speed at the wave plate, f is the wave frequency,
If no damping is applied, the very small local thickness of the acoustic black hole also increases the reflection coefficient, reducing the wave aggregation effect of the acoustic black hole,
Quickly evaluate the reflection coefficient of each acoustic black hole structure using the one-dimensional acoustic black hole reflection coefficient formula,
If the damping layer is not covered, the damping loss coefficient of the acoustic black hole and the supporting structure is relatively small, and the local thickness of the acoustic black hole is unavoidable, so the damping effect of the supporting structure is It is not obvious that by laying a damping layer in the central region of the acoustic black hole, the reflection coefficient of the acoustic black hole structure can be effectively suppressed.
The damping layer is possible because the radius or length of the damping layer must be larger than 0.5 times the feature size r of the acoustic black hole, and most of the vibrational energy will be dissipated in the central region of the acoustic black hole. must be attached to the central area of the acoustic black hole to cover as much of the area as possible,
A thicker damping layer δ can enhance the damping effect of the acoustic black hole, and in order to achieve both the damping effect of the acoustic black hole and economic efficiency, the loss coefficient of the damping material is generally set to be larger than 0.5. and step S5 of setting the thickness of the damping layer to 4 to 10 times the local thickness h ₀ and controlling the reflection coefficient within the damping frequency band to within 0.5;
Smoothness condition:
Verify,
If the smoothness condition and the reflection coefficient control requirements are not met, the method is characterized in that it includes a step S6 of repeating S2 and subsequent steps until the requirements of the conditions are met.