Acoustic black hole vibration absorbing wing-coupled beam system and adjusting method

Abstract

The application provides an acoustic black hole vibration-absorbing wing coupled beam system and an adjusting method, wherein the acoustic black hole vibration-absorbing wing coupled beam system comprises a beam and further comprises acoustic black hole vibration-absorbing wings arranged on the beam; the acoustic black hole vibration-absorbing wing is in a strip shape, comprises a first end and a second end, the first end is connected to the beam, and the second end is a free end; the first end is a gradual starting end of an acoustic black hole structure, and the second end is a tail end of the acoustic black hole structure; a straight line where a long axis of the acoustic black hole vibration-absorbing wing is located intersects with a straight line where a long axis of the beam is located; two acoustic black hole vibration-absorbing wings, i.e., a first acoustic black hole vibration-absorbing wing and a second acoustic black hole vibration-absorbing wing, are connected to the same point of the beam; and the first acoustic black hole vibration-absorbing wing and the second acoustic black hole vibration-absorbing wing are symmetrically arranged with the long axis of the beam and a straight line perpendicular to the long axis of the beam as the symmetric axes. The application can be widely applied in the field of beam system vibration reduction.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction technology, particularly to the field of vibration reduction technology for beams. Background Technology

[0002] Acoustic black hole (ABH) structures are designed based on power-law thickness, which can effectively control the propagation of flexural waves within the structure. ABH structures can achieve the convergence and localization of mid-to-high frequency vibration energy, demonstrating excellent vibration control potential in the mid-to-high frequency range.

[0003] However, traditional Absorbed Boom (ABH) designs typically place the energy directly on the main structure, guiding and concentrating vibrational energy in the thin-walled region by gradually reducing the thickness of the main structure's cross-section along its length in a power-law manner. From an ideal vibration control perspective, the energy concentration effect is optimal when the ABH edge thickness approaches zero. However, in practical engineering contexts, structural strength and fatigue performance are factors that cannot be ignored. Therefore, the stress concentration, stiffness reduction, and insufficient load-bearing capacity caused by excessive thickness reduction in the ABH region significantly limit the engineering applicability of most ABH structures.

[0004] Furthermore, the excitations in engineering applications are highly complex, and the excitation directions are often multi-dimensional. Traditional ABH structures primarily absorb transverse bending waves, and these structures have strong directional limitations in controlling vibration response. Therefore, typical ABH structures mainly rely on the directional convergence of bending waves along specific paths, making it difficult to effectively address vibration control requirements under multi-dimensional or complex excitation conditions, thus limiting their adaptability in real-world applications. Maintaining the wave regulation advantages of ABH structures while improving their structural robustness and expanding their adaptability in vibration control dimensions has become a core challenge in driving the application of this structure in engineering. Summary of the Invention

[0005] To improve the structural robustness under vibration operating conditions and expand the adaptability of vibration control dimensions, this invention provides an acoustic black hole vibration-absorbing wing coupled beam system and adjustment method.

[0006] The technical solution of the present invention is as follows:

[0007] An acoustic black hole vibration-absorbing wing coupled beam system includes a beam and an acoustic black hole vibration-absorbing wing disposed on the beam. The acoustic black hole vibration-absorbing wing is elongated and includes a first end and a second end. The first end is connected to the beam, and the second end is a free end. The first end is the starting end of the gradual transition of the acoustic black hole structure, and the second end is the tail end of the acoustic black hole structure. The line containing the major axis of the acoustic black hole vibration-absorbing wing intersects the line containing the major axis of the beam.

[0008] The system includes two acoustic black hole absorbing wings connected to the same point on the beam: a first acoustic black hole absorbing wing and a second acoustic black hole absorbing wing; the first acoustic black hole absorbing wing and the second acoustic black hole absorbing wing are symmetrically arranged with the major axis of the beam and a straight line perpendicular to the major axis of the beam as the axis of symmetry.

[0009] Optionally, the acoustic black hole vibration-absorbing wing coupling beam system includes a vibration-absorbing wing mounting frame; the first end of the vibration-absorbing wing is connected to the vibration-absorbing wing mounting frame; and the vibration-absorbing wing mounting frame is connected to the beam.

[0010] Optionally, a transmission gear is provided on the vibration-absorbing wing mounting frame; the transmission gear is connected to the first end of the vibration-absorbing wing.

[0011] Optionally, a drive motor is provided on the vibration-absorbing wing mounting frame; a transmission mechanism is provided between the drive motor and the transmission gear.

[0012] Optionally, the drive motor includes a stepper motor.

[0013] Optionally, the free vibration equation of the acoustic black hole vibration-absorbing wing coupled beam system is:

[0014] ;

[0015] Where, ω k For the k-th natural frequency, u k M is the displacement vector matrix corresponding to the mode. total Let K be the global quality matrix. total The global stiffness matrix is:

[0016] ;

[0017] in,

[0018] ;

[0019] ;

[0020] ;

[0021] B(x) is the strain-displacement matrix, D(x) is the material stiffness matrix, subscript 1 represents the first acoustic black hole absorbing wing, subscript 2 represents the second acoustic black hole absorbing wing, and subscript 3 represents the beam;

[0022] The element stiffness matrix is ​​located at the connection point between the first acoustic black hole vibration absorber and the beam. Represented as :

[0023] ;

[0024] Wherein, the subscript 13 represents the value of the corresponding parameter at the connection point between the first acoustic black hole vibration-absorbing fin and the beam. ;

[0025] k nxp k is the normal stiffness at the connection point between the acoustic black hole vibration absorber and the beam. bxp K represents the bending stiffness at the connection point between the acoustic black hole vibration-absorbing fin and the beam. nxp R is the torsional stiffness at the connection point between the acoustic black hole vibration-absorbing fin and the beam. 1n R 2n and R 3n Let be the basis function vector at the connection point between the acoustic black hole vibration absorber and the beam;

[0026] The subscript 23 represents the value of the corresponding parameter at the connection point between the second acoustic black hole absorbing wing and the beam. Represented as :

[0027] ;

[0028] in, .

[0029] Regarding the adjustment method for the acoustic black hole absorbing wing coupled beam system as described above, the adjustment method involves simultaneously adjusting the minimum angle between the line containing the major axis of the first acoustic black hole absorbing wing and the line containing the major axis of the beam, and the minimum angle α between the line containing the major axis of the second acoustic black hole absorbing wing and the line containing the major axis of the beam.

[0030] The adjustment method includes the following steps:

[0031] S1. Set the initial value of a, and measure the current vibration velocity at the observation point of the beam;

[0032] S2, increase a, and measure the current vibration velocity at the observation point of the beam;

[0033] S3. Determine whether the current vibration velocity measured in step S2 has increased compared to the current vibration velocity measured in step S1. If it has increased, execute steps S311 and S312. If it remains unchanged or decreases, execute steps S321 and S322.

[0034] S311. Set a to 90° and measure the current vibration velocity at the observation point of the beam;

[0035] S312. Compare the current vibration velocity measured in step S311 with the vibration velocity measured in step S1;

[0036] S321, Increase a, and measure the current vibration velocity at the observation point of the beam;

[0037] S322. Determine whether the current vibration velocity measured in step S321 has increased compared to the current vibration velocity measured in the previous step S321. If it remains unchanged or decreases, repeat steps S321 and S322.

[0038] The technical effects of this invention are as follows:

[0039] The beam system of this invention does not incorporate acoustic black hole structures on the main beam structure. Instead, vibration reduction is achieved through two acoustic black hole vibration-absorbing wings attached to the beam without altering its structure. Each acoustic black hole vibration-absorbing wing is elongated, comprising a first end and a second end. The first end is connected to the beam, while the second end is a free end. The first end forms the starting point of the acoustic black hole structure, and the second end forms its tail end. The long axis of the acoustic black hole vibration-absorbing wing intersects with the long axis of the beam. The acoustic black hole vibration-absorbing wing itself is an acoustic black hole structure. This arrangement effectively transmits vibrations from the beam to the acoustic black hole vibration-absorbing wing for damping. Furthermore, by adjusting the angle between the long axis of the acoustic black hole vibration-absorbing wing and the long axis of the beam, it can accommodate vibrations of different directions and frequencies on the beam, thereby effectively reducing vibrations. Therefore, the technical solution of this invention achieves its objective.

[0040] The further effects of the above-mentioned alternative methods will be explained in detail below with reference to specific implementation methods. Attached Figure Description

[0041] Figure 1 This is a model analysis diagram of the coupled beam system for the acoustic black hole vibration-absorbing wing.

[0042] Figure 2 This is a structural diagram of the first angle of an embodiment of the acoustic black hole vibration-absorbing wing coupled beam system.

[0043] Figure 3 This is a structural diagram from the second angle of an embodiment of the acoustic black hole vibration-absorbing wing coupled beam system.

[0044] Figure 4 This is a structural diagram of the vibration-absorbing wing mounting bracket.

[0045] Figure 5 Vibration mode diagrams of the coupled beam system with the acoustic black hole absorbing wing under different excitation frequencies.

[0046] Figures 6 to 10In the diagram, ABH represents the acoustic black hole absorbing fin. The ABH angle refers to the smallest angle between the line containing the major axis of the acoustic black hole absorbing fin and the line containing the major axis of the beam. The excitation angle (e.g., 10-degree excitation) refers to the smallest angle between the excitation direction and the axis of the beam.

[0047] Figure 6 The vibration velocity response curves (2-2500Hz) are shown for different ABH angle states under 10-degree excitation.

[0048] Figure 7 The vibration velocity response curves (2-2500Hz) are shown for different ABH angle states under 30-degree excitation.

[0049] Figure 8 The vibration velocity response curves (2-2500Hz) are shown for different ABH angle states under 50-degree excitation.

[0050] Figure 9 The vibration velocity response curves (2-2500Hz) are shown for different ABH angle states under 70-degree excitation.

[0051] Figure 10 The vibration velocity response curves (2-2500Hz) are shown for different ABH angle states under 90-degree excitation.

[0052] Figures 11 to 15 In this context, the ABH angle refers to the smallest angle between the line containing the major axis of the acoustic black hole absorbing fin and the line containing the major axis of the beam.

[0053] Figure 11 The vibration velocity at the observation point corresponding to different ABH angles under 35Hz excitation.

[0054] Figure 12 The vibration velocity at the observation point corresponding to different ABH angles under 62Hz excitation.

[0055] Figure 13 The vibration velocity at the observation point corresponding to different ABH angles under 295Hz excitation.

[0056] Figure 14 The vibration velocity at the observation point corresponding to different ABH angles under 730Hz excitation.

[0057] Figure 15 The vibration velocity at the observation point corresponding to different ABH angles under 1500Hz excitation.

[0058] Figure 16 This is a flowchart of the adjustment method for the acoustic black hole vibration-absorbing wing coupled beam system.

[0059] The markings in the image are explained as follows:

[0060] 101. First acoustic black hole vibration-absorbing wing; 102. Beam; 103. Second acoustic black hole vibration-absorbing wing;

[0061] 201. First acoustic black hole vibration-absorbing wing; 202. Beam; 203. Second acoustic black hole vibration-absorbing wing;

[0062] 401. Transmission gear; 402. Stepper motor; 403. Worm gear; 404. Vibration-absorbing wing mounting bracket. Detailed Implementation

[0063] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0064] Figure 2 and Figure 3 The specific structure of an embodiment of the acoustic black hole vibration-absorbing wing coupled beam system of the present invention is shown from both positive and negative perspectives. For example... Figure 2 and Figure 3 As shown, the acoustic black hole absorbing wing coupled beam system of the present invention includes a beam 202 and a first acoustic black hole absorbing wing 201 and a second acoustic black hole absorbing wing 203 disposed on the beam 202. The first acoustic black hole absorbing wing 201 and the second acoustic black hole absorbing wing 203 (hereinafter referred to as acoustic black hole absorbing wing when describing their common characteristics) have the same structure and dimensions, and both have an acoustic black hole structure. That is, the elongated acoustic black hole absorbing wing has two ends: a first absorbing wing end and a second absorbing wing end. The first absorbing wing end is the starting end of the gradual change of the acoustic black hole structure, and the second absorbing wing end is the tail end of the acoustic black hole structure. The starting end of the gradual change of the acoustic black hole structure is a cross-section (e.g., Figure 1 The section shown is parallel to the long axis of the acoustic black hole's vibration-absorbing fin, at the end with the greatest thickness; the tail end of the acoustic black hole structure is at the end with the smallest thickness. The first end of the vibration-absorbing fin is connected to beam 202, and the second end of the vibration-absorbing fin is a free end. Figure 2 and Figure 3 As shown, the line containing the major axis of the acoustic black hole absorbing wing intersects the line containing the major axis of beam 202, and the major axes of the first acoustic black hole absorbing wing 201, the second acoustic black hole absorbing wing 203, and the major axis of beam 202 are in the same plane. Figure 2 and Figure 3 As shown, the first acoustic black hole absorbing wing 201 and the second acoustic black hole absorbing wing 203 are symmetrically arranged with the major axis of beam 202 and the straight line perpendicular to the major axis of beam 202 as the axis of symmetry.

[0065] like Figure 2 and Figure 3 As shown, the first acoustic black hole vibration-absorbing wing 201 and the second acoustic black hole vibration-absorbing wing 203 are connected to the beam 202 via a vibration-absorbing wing mounting bracket. Specifically, the first end of the vibration-absorbing wing is connected to the vibration-absorbing wing mounting bracket. Figure 4The specific structure of the vibration-absorbing wing mounting bracket 404 and its connection relationship with the first end of the vibration-absorbing wing are shown. The vibration-absorbing wing mounting bracket 404 includes two mating parts forming a hollow structure. The hollow part accommodates the beam 202 through which it passes. The two mating parts are fastened to the beam 202 using screws or other fastening measures. A transmission gear 401 is provided on the vibration-absorbing wing mounting bracket 404, and the transmission gear 401 is connected to the first end of the vibration-absorbing wing. A stepper motor 402 is also provided on the vibration-absorbing wing mounting bracket 404. The stepper motor 402 drives the oscillation of the acoustic black hole vibration-absorbing wing through a worm gear 403 meshing with the transmission gear 401. That is, the angle between the line containing the major axis of the acoustic black hole vibration-absorbing wing and the line containing the beam 202 can be adjusted and locked by the stepper motor 402.

[0066] The meshing of gear 401 and worm 403 has a relatively large transmission ratio, providing a speed reduction function and lowering the torque requirements of stepper motor 402. Meanwhile, the acoustic black hole absorbing wing only contains a thickness-gradient region with low added mass; therefore, using a small stepper motor to drive the angle adjustment mechanism avoids excessive accumulation of added mass. The self-locking characteristic generated by the lead angle of worm 403 being smaller than the friction angle limits excessive rotation of the acoustic black hole absorbing wing.

[0067] Figure 1 A model of the acoustic black hole vibration absorber coupled beam system is shown, where the first acoustic black hole vibration absorber 101 corresponds to Figure 2 The first acoustic black hole absorbing wing 201, beam 102 corresponds to Figure 2 Beam 202 in the middle, the second acoustic black hole absorbing wing 103 corresponds to Figure 2 The second acoustic black hole absorbing wing 202. The following is about... Figure 1 The model shown is analyzed.

[0068] For simplicity, the first acoustic black hole absorbing wing 101 is defined as beam 1, i.e., k=1; the second acoustic black hole absorbing wing 102 is defined as beam 2, i.e., k=2; and beam 102 is defined as beam 3, i.e., k=3. According to Timoshenko's beam theory, the axial displacement of the beam corresponding to number k... and lateral displacement They are respectively:

[0069] (1)

[0070] In Equation 1, k=0, 1, and 2 correspond to beam 1, beam 2, and beam 3, respectively. h and L are the thickness and length of the corresponding numbered beams.

[0071] The strain-displacement relationship of each beam (beam 1, beam 2, and beam 3) can be defined as follows, and the relevant normal stress and shear stress can be calculated as follows:

[0072] (2)

[0073] Where εxx represents the strain of the beam with the corresponding number (superscript), γxz represents the shear strain of the beam with the corresponding number (superscript), and σ xx τ represents the normal stress of the beam corresponding to the number (superscript). xz This indicates the shear stress of the beam with the corresponding number (superscript). This describes the rotation angle of the cross section of the beam corresponding to number (k), E k G is the Young's modulus of the beam corresponding to number (k). k It is the shear modulus of the beam corresponding to number (k).

[0074] The expressions for the strain energy U1 and kinetic energy T1 of beam 1 are as follows:

[0075] (3)

[0076] (4)

[0077] Among them, U ABH U represents the strain energy of the first acoustic black hole absorbing fin. D The strain energy represents the damping layer installed at the free end of the vibration-absorbing fins near the first acoustic black hole. The natural frequency is given. Beams 1 and 2 have the same structure, dimensions, and materials; therefore, the derivation of U2 and T2 follows equations (3)-(4), respectively. Beam 3 is a uniform beam containing only a uniform structure; therefore, U3 can be written as:

[0078] (5)

[0079] In equations (3) and (5), the tensile stiffness matrix is ​​denoted as A. 11 The bending-stretching coupling matrix is ​​denoted as B. 11 The bending stiffness matrix is ​​denoted as D. 11 The moment of inertia is denoted as I. i (i=1, 2, 3). The detailed expression is as follows:

[0080] (6)

[0081] (7)

[0082] Where κ represents the shear correction factor (with a value of 5 / 6), ρ represents the density of the beam, and h represents the thickness of the beam section. The model assumes that the material is isotropic and homogeneous, hence I² = 0.

[0083] Q 11 and Q 55 It is given by the following formula:

[0084] (8)

[0085] Among them, E k It is the Young's modulus of the beam corresponding to number (k), ν k It is the Young's modulus and Poisson's ratio corresponding to beam number (k).

[0086] The model was established by applying Timoshenko beam theory and the energy principle. The system's Lagrangian function is expressed as:

[0087] (9)

[0088] Where W is the work done by the external point force applied to beam 3. The formula for W is:

[0089] (10)

[0090] Where F is the external force and δ(x) is the corresponding Dirac increment function.

[0091] Geometric analysis methods directly use non-uniform rational B-splines (NURBS) commonly used in CAD to represent geometry and displacement. The basis functions can be defined as:

[0092] (11)

[0093] (12)

[0094] Where, ω i Let ξ be the weighting factor, ξ be the parameter space, and N be the weighting factor. i,p (ξ) is the B-spline basis function along the ξ direction.

[0095] NURBS curves are described by combining control points with NURBS curves:

[0096] (13)

[0097] Where n1, n2, and n3 (the subscripts correspond to the beam code numbers) are the number of control points for the isogeometric analysis of beams 1, 2, and 3, respectively; p1, p2, and p3 (the subscripts correspond to the beam code numbers) are the orders of the NURBS basis functions of beams 1, 2, and 3, respectively; and P... i，1 P i，2 P i，3 (The numbers in the lower right corner correspond to the code numbers of the beams) and represent the positions of the i-th control points of beams 1, 2, and 3, respectively.

[0098] NURBS functions are used to describe the geometric parameters and displacements of beams 1, 2, and 3:

[0099] (14)

[0100] (15)

[0101] Where q is the state vector, x i Indicates geometric position, u i w i and φ i R represents the axial displacement, lateral displacement, and section rotation angle of the i-th control point, respectively. i，p1 R i，p2 and R i，p3 Let represent the basis functions corresponding to beam 1, beam 2, and beam 3, respectively.

[0102] The stiffness matrix of beam 1 can be expressed as:

[0103] (16)

[0104] The stiffness matrix of beam 2 can be expressed as:

[0105] (17)

[0106] The stiffness matrix of beam 3 can be expressed as:

[0107] (18)

[0108] B(x) is the strain-displacement matrix of the beam, and D(x) is the material stiffness matrix of the beam, where subscripts 1, 2, and 3 correspond to beam 1, beam 2, and beam 3, respectively. L ABH1 L is the length of beam 1. ABH2 L is the length of beam 2. uni It is the length of beam 3.

[0109] Beam 1 and beam 3 are coupled using a rigid connection point, as are beam 2 and beam 3. The element stiffness matrix of the rigid connection point between beam 1 and beam 3 can be expressed as:

[0110] (19)

[0111] (20)

[0112] The element stiffness matrix of the rigid connection point between beam 2 and beam 3 can be expressed as:

[0113] (twenty one)

[0114] (twenty two)

[0115] Where, knxp Let k be the normal stiffness at the connection point of beams 1, 2, and 3. bxp Let K be the bending stiffness at the connection point of beams 1, 2, and 3. nxp R represents the torsional stiffness at the connection points of beams 1, 2, and 3. 1n R 2n and R 3n Let be the basis function vectors at the connection points of beams 1, 2, and 3.

[0116] Global stiffness matrix K total Defined as:

[0117] (twenty three)

[0118] Global mass matrix M total Defined as:

[0119] (twenty four)

[0120] The free vibration equations of the acoustic black hole vibration-absorbing coupled beam system are as follows:

[0121] (25)

[0122] Where, ω k For the k-th natural frequency, u k This is the displacement vector matrix corresponding to the mode.

[0123] The effectiveness of the free vibration equation of the acoustic black hole vibration-absorbing wing coupled beam system is verified by simulation comparison below. The calculation results of the system of the present invention based on equation (25) (marked as "the present invention" in Table 1) are compared with the calculation results based on the FEM method (finite element analysis, such as COMSOL simulation, divides the solution domain into finite elements, constructs interpolation functions to approximate the field quantity in each element, and then integrates the overall equation to obtain an approximate solution) (marked as "FEM" in Table 1). The comparison results are shown in Table 1.

[0124] Table 1

[0125]

[0126] The data in Table 1 is as follows: Figure 1 The natural frequencies of the acoustic black hole absorbing wing coupled beam system are shown for different included angles φ. The results in Table 1 show that the calculation results based on equation (25) are accurate.

[0127] To analyze the vibration state of the acoustic black hole vibration-absorbing wing coupled beam system of this invention, simulation analysis was used to compare the vibration modes of the system with those of a single uniform beam. The comparison results are as follows: Figure 5 As shown. Figure 5The simulation conditions shown are: the excitation force is 10N, and the excitation direction θ is 90 degrees. It's 30 degrees. (For example...) Figure 5 As shown, on a single uniform beam, bending waves are uniformly distributed. Therefore, the observation point (protected end) will inevitably experience relatively large displacement. In the acoustic black hole vibration-absorbing fin coupled beam system of this invention, the vibration modes are mainly concentrated on the acoustic black hole vibration-absorbing fin. That is, the external excitation first induces beam vibration, and then the vibration is absorbed by the acoustic black hole vibration-absorbing fin, so that the vibration energy is dissipated through the acoustic black hole vibration-absorbing fin.

[0128] In real-world engineering environments, the characteristics of external excitations are complex and diverse, with frequencies and directions often uncertain. To further analyze the vibration characteristics of the acoustic black hole absorbing wing coupled to the beam system of this invention under complex environments, different excitations and the angle between the acoustic black hole absorbing wing and the beam (…) were investigated. The vibration of the system was analyzed under the following conditions. The specific parameter settings are shown in Table 2.

[0129] Table 2

[0130]

[0131] In Table 2, the uniform beam refers to beam 3, the ABH beam refers to the acoustic black hole absorbing wing, and the two columns on the right are the parameters of the ABH beam.

[0132] Figures 6 to 10 The results corresponding to the structural parameters in Table 2 are shown, illustrating the effects of applying excitation at different angles and the angles between the acoustic black hole absorbing fins and the beam. For example... Figures 6 to 10 As shown, for a low-frequency excitation of 10 degrees (2-100Hz), the introduction of the acoustic black hole absorbing fins adds a peak around 35Hz, which is lowest when the angle between the acoustic black hole absorbing fins and the beam is 90°. Near the second-order resonance region, setting the angle between the acoustic black hole absorbing fins and the beam to 30° provides some vibration reduction. With increasing excitation frequency, the vibration reduction effect varies depending on the angle between the acoustic black hole absorbing fins and the beam, but the vibration velocity at the observation point on the right is significantly reduced. This phenomenon is due to the structural characteristics of the acoustic black hole. Under low-frequency excitation, the wavelength of the bending wave is relatively long. The structural vibration is dominated by large bending, and the distribution of violent vibration points is diffuse; the vibration concentration efficiency of the thin-walled region of the acoustic black hole is not fully utilized. As the excitation frequency increases, the excitation causes the system to vibrate violently. The special structure of the acoustic black hole absorbing fins begins to show its advantages; a large amount of energy is concentrated in the thin-walled region, and then the energy concentrated in this region is dissipated through a damping material with a high loss factor. Therefore, the vibration of the beam was mitigated.

[0133] from Figures 6 to 10 The results show that the angle between the acoustic black hole vibration absorber and the beam remains constant, but the system response differs under different excitation directions. For example, from... Figures 6 to 10 As can be seen, for the additional excitation directions of 10°, 30°, 50°, and 70° at 300Hz, there is a relatively high peak value at a 90-degree angle between the acoustic black hole absorbing fin and the beam. However, when the excitation direction is 90°, the vibration velocity is actually the lowest at this 90-degree angle. That is, there exists an angle that results in the lowest vibration velocity at the observation point for the current excitation direction and frequency. The vibration of the system can be reduced by adjusting the angle between the acoustic black hole absorbing fin and the beam, utilizing the aforementioned principle.

[0134] Figures 11 to 15 The results show that the vibration velocity at observation points on the beam changes under different single-frequency excitations at different angles between the acoustic black hole absorbing fins and the beam. This phenomenon arises from the complex interaction between wave propagation dynamics and structural modes. In the coupled system of beam 3 with beams 1 and 2, the coupling angle (i.e., the angle between the acoustic black hole absorbing fins and the beam) alters the wave propagation path and boundary conditions from beam 3 to beams 1 and 2. At different angles, the wave's incident, reflection, and transmission behaviors change: when the coupling angle is optimized, the wave energy enters beams 1 and 2 efficiently and is dissipated, resulting in good vibration reduction; however, when the angle is mismatched, the wave may be partially reflected back to beam 3, leading to energy dispersion and a decrease in vibration reduction. Furthermore, the excitation frequency also affects the optimal coupling angle: at high frequencies, the wavelength is short, the angle is sensitive to wave steering, and the local effects of the acoustic black hole play a dominant role, requiring a specific angle to achieve energy concentration; at low frequencies, the wavelength is longer, the overall system modes play a major role, and the coupling angle affects the overall stiffness and mass distribution, thus altering the resonance characteristics. Therefore, even if the excitation angle and coupling angle are fixed, frequency changes will alter the coupling mechanism between the wave and the structure, resulting in different optimal solutions for vibration reduction at high and low frequencies.

[0135] The above analysis shows that, overall, the introduction of acoustic black hole vibration absorbers can reduce the peak vibration velocity at the damping end. Appropriate parameter design and selection can ensure that the added acoustic black hole vibration absorbers produce a stable vibration reduction effect. It is important to note that the angle between the acoustic black hole vibration absorber and the beam under different excitation directions will affect the vibration reduction performance. Furthermore, even if the excitation direction remains unchanged, different excitation frequencies will alter the angle between the most effective acoustic black hole vibration absorber and the beam.

[0136] This invention further provides an adjustment method for an acoustic black hole absorbing wing coupled beam system. The adjustment method involves simultaneously adjusting the minimum angle between the line containing the major axis of the first acoustic black hole absorbing wing and the line containing the major axis of the beam, and the minimum angle between the line containing the major axis of the second acoustic black hole absorbing wing and the line containing the major axis of the beam, that is, adjusting the coupling angle of beam 1, beam 2 and beam 3.

[0137] Figure 16The flow chart of the adjustment method of the present invention is shown, and the following is a detailed description of the steps in the flow chart.

[0138] For clarity and brevity, Figure 16 The specific terminology used in the illustrated process is explained uniformly. The included angle refers to the minimum angle between the line containing the major axis of the acoustic black hole absorbing wing and the line containing the major axis of the beam. Since the first and second acoustic black hole absorbing wing are symmetrically arranged, adjusting the included angle means simultaneously adjusting the angle between the first and second acoustic black hole absorbing wing. Unless otherwise specified, any change in included angle refers to simultaneously and with the same amplitude adjusting the minimum included angle between the first and second acoustic black hole absorbing wing and the beam.

[0139] S1. Set the initial included angle

[0140] In this step, a stepper motor is used to drive the acoustic black hole absorbing blades to rotate, thereby setting the included angle to an initial value and fixing the acoustic black hole absorbing blades. The initial value is selected within the range of greater than 0° and less than 90°. According to... Figures 6 to 15 The pattern can be displayed by setting the initial value to a small angle, such as 10°.

[0141] The current vibration velocity (first vibration velocity) is measured and obtained at the observation point of beam 3.

[0142] S2, Increase the included angle

[0143] After completing step S1, the included angle is further increased. That is, the included angle after fixing the acoustic black hole vibration absorber in this step is greater than the initial included angle in step S1. Then, the current vibration velocity (second vibration velocity) is measured and obtained at the observation point of beam 3.

[0144] S3. Has the vibration velocity increased?

[0145] In this step, it is determined whether the second vibration velocity measured in step S2 is greater than the first vibration velocity measured in step S1. If the second vibration velocity measured in step S2 is greater than the first vibration velocity measured in step S1, then steps S311 and S312 are executed; if the second vibration velocity measured in step S2 is less than or equal to the first vibration velocity measured in step S1, then steps S321 and S322 are executed.

[0146] S311, Set the included angle to 90°

[0147] In this step, the acoustic black hole vibration absorber is driven to rotate and the included angle is fixed at 90°. Then, the current vibration velocity (third vibration velocity) is measured and obtained at the observation point of beam 3.

[0148] S312, Compare vibration reduction results

[0149] In this step, the third vibration velocity measured in step S311 is compared with the first vibration velocity measured in step S1, and the angle corresponding to the lower vibration velocity is taken as the final result (input to the "Get Result" step).

[0150] S321, Increase the included angle

[0151] In this step, the included angle is further increased based on the angle set in the previous step, and the acoustic black hole absorbing fins are fixed after the angle is increased, maintaining the increased included angle. Then, the current vibration velocity (fourth vibration velocity) is measured and obtained at the observation point of beam 3.

[0152] S322. Has the vibration velocity increased?

[0153] In this step, it is determined whether the fourth vibration velocity measured in step S321 has increased compared to the current vibration velocity measured in the previous step S321. If it remains unchanged or decreases, steps S321 and S322 are repeated. If the fourth vibration velocity has increased compared to the current vibration velocity measured in the previous step S321, the current vibration velocity measured in the previous step S321 is taken as the final result, i.e., the angle corresponding to the lower vibration velocity is taken as the final result, and input to the "Obtain Result" step. "The current vibration velocity measured in the previous step S321" includes two cases: one is when there is no loop execution from step S3 to step S322, in which case "the current vibration velocity measured in the previous step S321" refers to the current vibration velocity measured in step S2; the other is when there is a loop execution from step S321 to step S322, in which case "the current vibration velocity measured in the previous step S321" refers to the current vibration velocity obtained in step S321 of the previous loop.

[0154] Results

[0155] In this step, the final result obtained in the previous steps is used as the result for subsequent processing.

[0156] The following two embodiments further illustrate the adjustment method of the present invention.

[0157] Example 1:

[0158] The external excitation frequency is 34 Hz.

[0159] S1. Set the initial included angle

[0160] With the initial included angle set at 10°, the current vibration velocity is obtained as 0.3506 m / s.

[0161] S2, Increase the included angle

[0162] Increasing the included angle to 20° yields a current vibration velocity of 0.3486 m / s.

[0163] S3. Has the vibration velocity increased?

[0164] No, 0.3506m / s > 0.3486m / s.

[0165] S321, Increase the included angle

[0166] Increasing the included angle to 30° yields a current vibration velocity of 0.3464 m / s.

[0167] S322. Has the vibration velocity increased?

[0168] No, 0.3486m / s > 0.3464m / s.

[0169] S321, Increase the included angle

[0170] Increasing the included angle to 40° yields a current vibration velocity of 0.3453 m / s.

[0171] S322. Has the vibration velocity increased?

[0172] No 0.3464m / s >0.3453m / s.

[0173] S321, Increase the included angle

[0174] Increasing the included angle to 50° yields a current vibration velocity of 0.3454 m / s.

[0175] S322. Has the vibration velocity increased?

[0176] Yes, 0.3454m / s > 0.3453m / s.

[0177] Results

[0178] The included angle should be adjusted to 40°.

[0179] Example 2:

[0180] The external excitation frequency is 295 Hz.

[0181] S1. Set the initial included angle

[0182] With the initial included angle set at 10°, the current vibration velocity is obtained as 0.1459 m / s.

[0183] S2, Increase the included angle

[0184] Increasing the included angle to 20° yields a current vibration velocity of 0.1638 m / s.

[0185] S3. Has the vibration velocity increased?

[0186] Yes, 0.1638m / s > 0.1459m / s.

[0187] S311, Set the included angle to 90°

[0188] With the included angle set to 90°, the current vibration velocity is obtained as 0.7545 m / s.

[0189] S312, Compare vibration reduction results

[0190] 0.7545 m / s > 0.1459 m / s.

[0191] Results

[0192] The included angle should be adjusted to 10°.

[0193] It is worth noting that the above description is only a preferred embodiment of the present invention and does not limit the scope of patent protection of the present invention. The present invention can also be replaced by equivalent technologies. Therefore, all equivalent changes made based on the description and figures of the present invention, or direct or indirect applications to other related technical fields, are included within the scope of the present invention.

Claims

1. An acoustic black hole vibration-absorbing wing coupled beam system, comprising a beam, characterized in that: It also includes an acoustic black hole vibration-absorbing wing disposed on the beam; the acoustic black hole vibration-absorbing wing is elongated and includes a first end and a second end, the first end of which is connected to the beam, and the second end of which is a free end; the first end of which is the starting end of the gradual transition of the acoustic black hole structure, and the second end of which is the tail end of the acoustic black hole structure; the line containing the major axis of the acoustic black hole vibration-absorbing wing intersects the line containing the major axis of the beam; The system includes two acoustic black hole absorbing wings connected to the same point on the beam: a first acoustic black hole absorbing wing and a second acoustic black hole absorbing wing; the first acoustic black hole absorbing wing and the second acoustic black hole absorbing wing are symmetrically arranged with the major axis of the beam and a straight line perpendicular to the major axis of the beam as the axis of symmetry.

2. The acoustic black hole vibration-absorbing wing coupled beam system according to claim 1, characterized in that: It includes a vibration-absorbing wing mounting frame; the first end of the vibration-absorbing wing is connected to the vibration-absorbing wing mounting frame; the vibration-absorbing wing mounting frame is connected to the beam.

3. The acoustic black hole vibration-absorbing wing coupled beam system according to claim 2, characterized in that: A transmission gear is provided on the vibration-absorbing wing mounting frame; the transmission gear is connected to the first end of the vibration-absorbing wing.

4. The acoustic black hole vibration-absorbing wing coupled beam system according to claim 3, characterized in that: A drive motor is installed on the vibration-absorbing wing mounting frame; a transmission mechanism is provided between the drive motor and the transmission gear.

5. The acoustic black hole vibration-absorbing wing coupled beam system according to claim 4, characterized in that: The drive motor includes a stepper motor.

6. The acoustic black hole vibration-absorbing wing coupled beam system according to claim 1, characterized in that: The free vibration equation of the acoustic black hole vibration-absorbing wing coupled beam system is: ； Where, ω k For the k-th natural frequency, u k M is the displacement vector matrix corresponding to the mode. total Let K be the global quality matrix. total The global stiffness matrix is: ； in, ； ； ； B(x) is the strain-displacement matrix, D(x) is the material stiffness matrix, subscript 1 represents the first acoustic black hole absorbing wing, subscript 2 represents the second acoustic black hole absorbing wing, and subscript 3 represents the beam; The element stiffness matrix is ​​located at the connection point between the first acoustic black hole vibration absorber and the beam. Represented as : ； Wherein, the subscript 13 represents the value of the corresponding parameter at the connection point between the first acoustic black hole vibration-absorbing fin and the beam. ; k nxp k is the normal stiffness at the connection point between the acoustic black hole vibration-absorbing fin and the beam. bxp K represents the bending stiffness at the connection point between the acoustic black hole vibration-absorbing fin and the beam. nxp R is the torsional stiffness at the connection point between the acoustic black hole vibration-absorbing fin and the beam. 1n R 2n and R 3n Let be the basis function vector at the connection point between the acoustic black hole vibration absorber and the beam; The subscript 23 represents the value of the corresponding parameter at the connection point between the second acoustic black hole absorbing wing and the beam. Represented as : ； in, .

7. The adjustment method for the acoustic black hole vibration-absorbing wing coupled beam system as described in claim 1, characterized in that: The adjustment method involves simultaneously adjusting the minimum angle between the line containing the major axis of the first acoustic black hole absorbing wing and the line containing the major axis of the beam, and the minimum angle α between the line containing the major axis of the second acoustic black hole absorbing wing and the line containing the major axis of the beam. The adjustment method includes the following steps: S1. Set the initial value of a, and measure the current vibration velocity at the observation point of the beam; S2, increase a, and measure the current vibration velocity at the observation point of the beam; S3. Determine whether the current vibration velocity measured in step S2 has increased compared to the current vibration velocity measured in step S1. If it has increased, execute steps S311 and S312. If it remains unchanged or decreases, execute steps S321 and S322. S311. Set a to 90° and measure the current vibration velocity at the observation point of the beam; S312. Compare the current vibration velocity measured in step S311 with the current vibration velocity measured in step S1; S321, Increase a, and measure the current vibration velocity at the observation point of the beam; S322. Determine whether the current vibration velocity measured in step S321 has increased compared to the current vibration velocity measured in the previous step S321. If it remains unchanged or decreases, repeat steps S321 and S322.

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