Compact cylinder superstructure plate with vibration control

Abstract

A compact cylinder superstructure plate with vibration control comprises a homogeneous thin plate structure and a plurality of local resonance cylinders vertically arranged on the homogeneous thin plate structure, and the local resonance cylinders are evenly distributed on a circle with the center of the homogeneous thin plate structure as the circle center and the radius being R, outward transmission of elastic waves is restrained through the coupling effect between the local resonance cylinders, and vibration control of the multi-pole mode is achieved. The elastic wave response of the homogeneous thin plate is controlled in the annular structure through multi-pole coupling resonance between the local resonance cylinders, a symmetric protection mechanism is applied, high-precision low-transmission vibration control is achieved, the structure is simple and compact, and machining is convenient.

Description

Technical Field

[0001] The present invention relates to a technology in the field of vibration control, in particular to a compact column superstructure plate with vibration control function. Background Art

[0002] With the development trend of precision, integration and intelligence of thin plate precision devices, my country's demand for high-precision and high-sensitivity precision devices is increasing. In a complex mechanical environment, the weak vibration of thin plate precision devices can easily affect the shape and positioning accuracy of the device, thereby causing manufacturing errors and misalignment of precision functional devices. High-precision modal and vibration control of thin plate structures and isolating vibration outside the functional / operating area is an important way to achieve high-precision and high-sensitivity functional applications of thin plate precision devices. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention proposes a compact column superstructure plate with vibration control, which controls the elastic wave response of the homogeneous thin plate within the annular structure through multipole coupling resonance between local resonant columns, and applies a symmetrical protection mechanism to achieve high-precision and low-transmission vibration control while having a simple and compact structure and easy processing.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention 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 evenly distributed on a circle with a radius R and a center of the homogeneous thin plate structure as the center of the circle, and the coupling effect between the local resonance columns is used to suppress the outward transmission of elastic waves, thereby realizing vibration control of multipole modes.

[0006] The vibration control mentioned above means that the resonant mode of the compact cylindrical superstructure plate is directly controlled by the multipole parameter L, specifically: the polarization form of the resonant mode satisfies Where: L is the multipole parameter.

[0007] The present invention relates to a method for realizing the above-mentioned compact column superstructure plate, comprising:

[0008] 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 radius of vibration control 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.

[0009] The resonant frequency of the resonant structure column structure plate Where: k *is the wave number of the reverse design, the density is ρ, 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 requirements of step S1, determine the corresponding number of resonant columns and the thin plate structure and material parameters, and substitute the multipole scattering theory to reversely design the parameters of the resonant columns, specifically including:

[0011] 2.1 According to scattering theory Among them: function ξ(r)=H 0 (kR)-H 0 (ikR), H 0 (k * R) is the zero-order Hankel function, the real part Re S L Corresponding to k * is the wave number of the reverse design, the imaginary part ImS L The resonance characteristics of the corresponding oscillator, N is the number of local resonance cylinders, β = 1, 2, ... N.

[0012] 2.2 Arrangement radius R based on resonant cylinder cluster cluster , the multipole parameter L, when the real part Re S L = 0 to determine the resonance frequency parameters of the local resonance column Among them: Young's modulus E of metal material parameters, and radius R of oscillator cluster arrangement.

[0013] S3, based on the geometry and material parameters obtained in step S2, substitute them into the numerical model to verify whether the preset target requirements of step S1 are met, specifically: the resonance frequency parameter h of the local resonance cylinder established based on S2 * and R, establish the corresponding three-dimensional solid model in the numerical simulation software, and 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 error of and f is within the acceptable range. Technical Effects

[0014] The present invention achieves effective control of the target frequency, target range and resonance mode by designing the resonance frequency and position of the local resonance cylinder, thereby limiting the resonance to the inside of the annular cluster surrounded by the local resonance cylinder, thereby suppressing vibration outside the annular cluster. Compared with the prior art, the present invention can achieve high-precision vibration control effects by arranging a small number of cylinders in an annular manner, and the structure is more compact. Based on the continuum bound state, the approximate zero transmission of elastic waves is achieved, which makes it easy to achieve micro-amplitude vibration control on the outside of the structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the structure of the present invention;

[0016] In the figure: homogeneous thin plate structure 1, local resonance cylinder 2;

[0017] Figure 2 for Figure 1 Top view;

[0018] In the figure: R is the radius of the circular ring structure of the cylinder structure;

[0019] Figure 3 It is an out-of-plane displacement field diagram of a numerically simulated homogeneous thin plate structure in an embodiment;

[0020] Figure 4 It is the sample diagram of the experiment of the embodiment;

[0021] Figure 5 Response spectra of the cylindrical superstructure plate in the embodiment of the invention are shown in simulation (a) and experiment (b);

[0022] Figure 6 This is an example diagram of the displacement field test effect of the experimental test surface in the embodiment. DETAILED DESCRIPTION

[0023] like Figure 1 and Figure 2 As shown, this embodiment relates to a compact column superstructure plate with vibration control, including: a homogeneous thin plate structure 1 and a plurality of local resonance columns 2 vertically arranged thereon, wherein: the plurality of local resonance columns 2 are evenly distributed on a circle with a radius R with the center of the homogeneous thin plate structure 1 as the center, and the coupling effect between the local resonance columns 2 is used to suppress the outward transmission of elastic waves, thereby realizing vibration control of the multipole mode.

[0024] The homogeneous thin plate structure 1 is a thin plate of uniform material with a thickness of h=2 mm and a rigidity of D.

[0025] In this embodiment, the control equation of the resonant frequency of the local resonant cylinder 2 designed according to the target requirements is: The radius of the circle formed by the local resonance cylinder is R.

[0026] In this embodiment, the radius R is 70 mm, which is the position of the circle surrounded by the local resonance cylinders in the control area.

[0027] In this embodiment, the column super-structure plate is formed by high-precision CNC machine tools, and the material used is 7075 aviation aluminum alloy.

[0028] After theoretical design analysis and experimental verification, the vibration control target frequency is 4655Hz, the mode is hexapole, and the ring radius is 70mm. The overall thickness of the thin plate structure is 2mm, and the column radius is set to 2.5mm. Based on the multipole scattering theory, the resonant frequency of the column structure is inversely designed, and the column height is 310mm. Based on the above inverse design parameters, the out-of-plane displacement field of the structure is obtained by numerical simulation method, as shown in Figure 3 As shown in the figure, the cylindrical superstructure plate of this embodiment can confine the elastic wave within a circular ring with a specified frequency of 4655 Hz and a range of R = 70 mm, without transmitting to the outside of the ring, and the field pattern is a six (L = 3) pole mode, meeting the design requirements of frequency, range and mode control targets.

[0029] like Figure 4 As shown, the resonant structure column structure plate designed according to the above theory is prepared, which includes a homogeneous thin plate structure 1 and a local resonant column 2.

[0030] like Figure 5 As shown, the response spectra of simulation and experiment, the peak frequency of the response spectrum observed in the experiment is 4652Hz, and the frequency error between the experiment and the theoretical-simulation design is less than 1%.

[0031] like Figure 6 As shown in the figure, the out-of-plane displacement response at 4652 Hz directly observed in the experiment, the outer displacement field of the outer side of the annularly arranged column is approximately zero. The mode is the hexapole mode predicted by the theory and simulation in the embodiment, achieving the original design purpose, which is consistent with Figure 3 The numerical results shown are consistent with the displacement field.

[0032] Compared with the prior art, the present invention designs the resonance frequency and position of the local resonance column and the coupling relationship with the homogeneous thin plate structure without changing the mechanical properties of the homogeneous thin plate structure. Vibration control of a specified area, specified mode and frequency on the homogeneous thin plate structure is achieved, and elastic wave leakage does not occur on the outside of the structure, thereby achieving vibration suppression in the compact space within the surface of the homogeneous thin plate structure. The present invention designs the resonance frequency of the local resonance column based on the multipole scattering theory, focuses on the vibration suppression of the specified target frequency, and makes full use of the anti-phase resonance characteristics of the local resonance column, which greatly improves the suppression of the bending vibration of the homogeneous thin plate structure, provides a new idea for the high-precision vibration suppression of thin plate precision devices in compact spaces, and has important engineering application value.

[0033] The above-mentioned specific implementations may be partially adjusted in different ways without departing from the principles and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementations. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A compact column superstructure plate with vibration control, characterized in that: include: 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 and a center of the homogeneous thin plate structure as the center of the circle, and the coupling effect between the local resonance cylinders is used to suppress the outward transmission of elastic waves, thereby realizing vibration control of the multipole mode.

2. The compact column superstructure plate with vibration control according to claim 1, characterized in that: The vibration control mentioned above means that the resonant mode of the compact cylindrical superstructure plate is directly controlled by the multipole parameter L, specifically: the polarization form of the resonant mode satisfies Where: L is the multipole parameter.

3. The compact column superstructure plate with vibration control according to claim 1, characterized in that: The resonant frequency of the resonant structure column structure plate Where: k * is the wave number of the reverse design, the density is ρ, the stiffness of the homogeneous thin plate structure is D, and the thickness of the homogeneous thin plate structure is h.

4. A method for realizing the compact column superstructure plate according to any one of claims 1 to 3, characterized in that: include: S1. Determine the target frequency, mode and position range of the vibration source control of the thin plate structure; 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 reversely design the parameters of the resonant cylinders; S3. Based on the geometry and material parameters obtained in step S2, substitute them into the numerical model to verify whether the preset target requirements of step S1 are met, thereby realizing a compact column superstructure plate.

5. The method according to claim 4, characterized in that: The step S1 is specifically as follows: determining the arrangement radius R of the resonant cylinder cluster according to the required radius of vibration control 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.

6. The method according to claim 4, characterized in that: The step S2 specifically includes: 6.1 According to scattering theory Where: function ξ(r) = H0(kR)-H0(ikR), H0(k * R) is the zero-order Hankel function, the real part Re S L Corresponding to k * is the wave number of the reverse design, the imaginary part ImS L The resonance characteristics of the corresponding oscillator, N is the number of local resonance cylinders, β = 1, 2, ... N; 6.2 Arrangement radius R based on resonant cylinder cluster cluster , the multipole parameter L, when the real part Re S L = 0 to determine the resonance frequency parameters of the local resonance column Among them: Young's modulus E of metal material parameters, and radius R of oscillator cluster arrangement.

7. The method according to claim 4, characterized in that: 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 error of and f is within the acceptable range.

Images