Compact cylinder superstructure panel with vibration control

Abstract

The application discloses a compact column superstructure plate with vibration control, comprising a homogeneous thin plate structure and a plurality of local resonance columns vertically arranged on the homogeneous thin plate structure, wherein the plurality of local resonance columns are uniformly arranged on a circle with the center of the homogeneous thin plate structure as the center and a radius R, and the elastic wave transmission is inhibited by the coupling effect between the local resonance columns to realize vibration control of a multipole mode. The application controls the elastic wave response of the homogeneous thin plate in the annular structure by the multipole coupling resonance between the local resonance columns, applies a symmetric protection mechanism, and realizes high-precision and low-transmission vibration control while the structure is simple, compact and convenient to process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vibration control, and particularly relates to a compact column superstructure plate with vibration control. BACKGROUND

[0002] With the development trend of thin plate precision devices, the demand for high-precision and high-sensitivity precision devices in China is increasing. In a complex mechanical environment, the weak vibration of a thin plate precision device can easily affect the shape and positioning accuracy of the device, and further cause manufacturing errors and precision functional device misalignment. High-precision modal and vibration control of the thin plate structure and isolation of the vibration outside the functional / operation area are important ways to achieve high-precision and high-sensitivity functional applications of the thin plate precision device. SUMMARY

[0003] The present application proposes a compact column superstructure plate with vibration control, which controls the elastic wave response of the homogeneous thin plate in the ring structure by the multipole coupling resonance between the local resonance columns, and realizes high-precision and low-transmission vibration control by applying the symmetry protection mechanism while the structure is simple and compact and easy to process.

[0004] The present application is realized by the following technical solutions:

[0005] The present application relates to a compact column superstructure plate with vibration control, comprising: a homogeneous thin plate structure and a plurality of local resonance columns vertically arranged thereon, wherein: the plurality of local resonance columns are uniformly arranged on a circle with the center of the homogeneous thin plate structure as the center and a radius R, and the coupling effect between the local resonance columns is used to suppress the transmission of elastic waves outward, and the vibration control of the multipole mode is realized.

[0006] The vibration control refers to that the resonance mode of the compact column superstructure plate is directly regulated by the multipole parameter L, and specifically, the polarization form of the resonance mode satisfies Wherein: L is the multipole parameter.

[0007] The present application relates to the implementation method of the above-mentioned compact column superstructure plate, comprising:

[0008] S1, determining the target frequency, mode and position range of the thin plate structure vibration source control, specifically: determining the arrangement radius R of the resonance column cluster according to the vibration control requirement radius cluster , determining the multipole parameter L according to the mode requirement control, and determining the resonance frequency of the resonance structure column structure plate according to the vibration control frequency.

[0009] The resonance frequency of the resonance structure column structure plate Wherein: k *The wave number of the inverse design is k, the density of the homogeneous thin plate structure is p, the stiffness of the homogeneous thin plate structure is D, and the thickness of the homogeneous thin plate structure is h.

[0010] S2, based on the target demand of step S1, the number of corresponding resonance columns and the parameters of the thin plate structure and the material are determined, and the parameters of the resonance column are designed by substituting the multipole scattering theory, specifically including:

[0011] 2.1 According to the scattering theory Wherein, the function

[0012] ξ(r) = H0(kR) - H0(ikR), H0(k * R) is the zero-order Hankel function, the real part Re S L Corresponding to k * The wave number of the inverse design is k, the imaginary part Im S L Corresponding to the resonance characteristics of the resonator, N is the number of local resonance columns, and beta = 1, 2,..., N.

[0013] 2.2 Based on the arrangement radius R cluster of the resonance column cluster, the multipole parameter L, when the real part Re S L = 0, the resonance frequency parameters of the local resonance column are determined Wherein: the metal material parameter Young's modulus E, the resonator cluster arrangement radius R.

[0014] S3, based on the geometric and material parameters obtained in step S2, the numerical model is substituted to verify whether the preset target demand of step S1 is met, specifically: based on the resonance frequency parameters h * of the local resonance column obtained in S2, a corresponding three-dimensional entity model is established in the numerical simulation software, the arrangement radius R cluster of the resonance column ring under the specified control demand is verified, the numerical simulation frequency f sim and the error of f are within an acceptable range.

[0015] Technical effects

[0016] The present application realizes effective control of target frequency, target range and resonance mode by designing the resonance frequency and position of the local resonance column, achieves the effect of limiting resonance within the annular cluster surrounded by the local resonance column, and thereby suppresses vibration outside the annular cluster. Compared with the prior art, the present application can realize high-precision vibration control effect by arranging a small number of columns in a ring, and the structure is more compact. Based on the continuum bound state, the elastic wave is approximately zero-transmitted, and the micro-amplitude vibration control of the outside of the structure is easy to realize. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 It is a structural schematic diagram of the present application;

[0018] In the figure: homogeneous thin plate structure 1, local resonance column 2;

[0019] Figure 2 For Figure 1 Top view;

[0020] In the figure: R is the radius of the ring structure of the column structure;

[0021] Figure 3 For the out-of-plane displacement field diagram of the homogeneous thin plate structure in the numerical simulation of the embodiment;

[0022] Figure 4 For the sample diagram of the experimental sample in the embodiment;

[0023] Figure 5 For the response spectrum of the simulation (a) and experiment (b) of the column superstructure plate in the embodiment;

[0024] Figure 6 For the test effect example diagram of the experimental test surface displacement field in the embodiment. DETAILED DESCRIPTION

[0025] As Figure 1 and Figure 2 shown, the present embodiment relates to a compact column superstructure plate with vibration control, comprising: a homogeneous thin plate structure 1 and a plurality of locally resonant columns 2 vertically arranged thereon, wherein: a plurality of locally resonant columns 2 are uniformly arranged on a circle with the center of the homogeneous thin plate structure 1 as the center and the radius R, and the coupling effect between the locally resonant columns 2 suppresses the transmission of elastic waves outward, realizing the vibration control of the multipole mode.

[0026] The homogeneous thin plate structure 1 is an equal-thickness thin plate of uniform material, with a thickness of h=2mm and a stiffness of D.

[0027] In the embodiment, the control equation of the resonance frequency of the local resonance column is designed according to the target requirement The local resonance column forms a ring with a radius R.

[0028] In the embodiment, the radius R is the position of the ring formed by the local resonance column in the control area, which is 70mm.

[0029] In the embodiment, the column superstructure plate is processed by a high-precision numerical control machine tool, and the material used is 7075 aviation aluminum alloy.

[0030] After theoretical design analysis and experimental verification, the vibration control target frequency is 4655Hz, the mode is six-pole, and the annular radius is 70mm. The overall thickness of the thin plate structure is 2mm, and the cylinder radius is set to 2.5mm. Based on the multi-pole scattering theory, the resonant frequency of the cylinder structure is inversely designed, and the cylinder height is obtained as 310mm. Based on the above inverse design parameters, the out-of-plane displacement field of the structure is obtained by numerical simulation, as shown in Figure 3 As can be seen from the figure, the cylinder superstructure plate of the embodiment can confine the elastic wave in the annular ring with a specified frequency of 4655Hz and a range of R=70mm, without transmitting to the outside of the annular ring, and the field diagram is a six(L=3) pole mode, which meets the design requirements of frequency, range and mode control.

[0031] As shown in Figure 4 The resonant structure cylinder structure plate of the above theoretical design is prepared, including a homogeneous thin plate structure 1 and a local resonant cylinder 2.

[0032] As shown in Figure 5 The response spectrum of simulation and experiment is shown, and the peak frequency of the response spectrum observed in the experiment is 4652Hz. The frequency error between the experiment and the theoretical-simulation design is less than 1%.

[0033] As shown in Figure 6 The out-of-plane displacement response at 4652Hz directly observed in the experiment is shown, and the out-of-plane displacement field outside the annularly arranged cylinder is approximately zero. The mode is the six-pole mode predicted in the embodiment by theory and simulation, which realizes the original design purpose, and is consistent with the numerical result displacement field shown in Figure 3

[0034] Compared with the prior art, the application does not change the mechanical properties of the homogeneous thin plate structure, and realizes the vibration control of the specified region, mode and frequency on the homogeneous thin plate structure by designing the resonant frequency and position of the local resonant cylinder and the coupling relationship with the homogeneous thin plate structure. The elastic wave does not leak outside the structure, and the vibration suppression in the in-plane compact space of the homogeneous thin plate structure is realized. The application designs the resonant frequency of the local resonant cylinder based on the multi-pole scattering theory, focuses on the vibration suppression of the specified target frequency, fully utilizes the anti-phase resonance characteristics of the local resonant cylinder, greatly improves the suppression of the bending vibration of the homogeneous thin plate structure, provides a new idea for high-precision vibration suppression of compact space thin plate precision devices, and has important engineering application value.

[0035] The above specific embodiments can be adjusted in different ways without departing from the principles and purposes of the application, and the protection scope of the application is subject to the claims and is not limited by the above specific embodiments. Each implementation scheme within the scope is subject to the constraints of the application.​

Claims

1. A method for realizing a compact cylindrical superstructure plate with vibration control, characterized in that: The compact cylindrical superstructure plate comprises a homogeneous thin plate structure and a plurality of local resonance cylinders vertically arranged thereon, wherein the plurality of local resonance cylinders are evenly distributed on a circle with a radius R, with the center of the homogeneous thin plate structure as the center. The coupling effect between the local resonance cylinders suppresses the outward transmission of elastic waves, thereby achieving vibration control of the multipole mode. The method includes: S1. Determine the target frequency, mode and position range of the thin plate structure vibration source control. Specifically, determine the arrangement radius R of the resonant column cluster according to the required vibration control radius. cluster , determine the multipole parameter L according to the modal demand control, and determine the resonant frequency of the resonant structure column structure plate according to the vibration control frequency; S2. Based on the target requirements of step S1, determine the corresponding number of resonant cylinders and the thin plate structure and material parameters, and substitute the multipole scattering theory to inversely design the parameters of the resonant cylinders, specifically including: 6.1 According to scattering theory , where: L is the multipole parameter, function , is the zero-order Hankel function, the real part Corresponding k * The wave number for reverse design, imaginary part Corresponding to the resonance characteristics of the oscillator, N is the number of local resonance cylinders, , i is the imaginary unit; 6.2 Arrangement Radius R of Resonant Cylinder Cluster cluster , the multipole parameter L, when the real part Determine the resonance frequency parameters of the local resonance cylinder , where: Young's modulus E of metal material parameters, radius of oscillator cluster arrangement R, wave number k of reverse design * , the stiffness D of the homogeneous thin plate structure, the thickness h of the homogeneous thin plate structure; S3. Based on the geometric and material parameters obtained in step S2, the parameters are substituted into the numerical model to verify whether the preset target requirements of step S1 are met, thereby realizing a compact column superstructure plate.

2. The method according to claim 1, wherein: The vibration control mentioned above means that the resonance mode of the compact cylindrical superstructure plate is directly controlled by the multipole parameter L, specifically: the polarization form of the resonance mode satisfies .

3. The method according to claim 1, wherein: The resonant frequency of the resonant structure column structure plate , where: density is .

4. The method according to claim 1, wherein: The step S3 is specifically as follows: based on the resonance frequency parameters and R of the local resonance cylinder established in S2, a corresponding three-dimensional solid model is established in the numerical simulation software to verify the arrangement radius R of the resonance cylinder ring of the specified control requirement. cluster , numerical simulation frequency f under multipole parameter L sim The errors of and f are within the acceptable range.

Images