A local resonant elastic metamaterial plate-like structure with ultra-low frequency vibration reduction characteristics

Abstract

A local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics, including an annular base frame plate, a central mass column passing through the base frame plate in the axial direction, the central mass column consisting of a middle mass column and umbrella-shaped mass columns symmetrically connected at both ends of the middle mass column, the side of the middle mass column is connected to the inner wall of the base frame plate through a thin strip structure, the two umbrella-shaped mass columns are respectively located above and below the base frame plate, and the base frame plate, the thin strip structure and the central mass column are all made of the same single material. The invention has a lighter mass under the same size, and can produce ultra-low frequency band gap characteristics, and has a controllable band gap range for elastic waves. The band gap can be adjusted by adjusting the height of the central mass column, the horizontal width of the thin strip structure and the wall thickness of the base frame plate. Compared with the Bragg scattering type plate structure, it has good processing and manufacturing and low cost advantages. The present invention can be used for vibration reduction of precision instruments and effectively protect important structures against low-frequency vibrations.

Description

Technical Field

[0001] The invention belongs to the technical field of vibration reduction, and in particular relates to a local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics. Background Art

[0002] While the construction of buildings, roads and bridges brings convenience to people's lives, the vibration caused by construction will interfere with the normal use of precision instruments and high-precision equipment in adjacent areas, affecting the normal development of scientific research and industrial work. At present, the rating and research on the level of vibration and noise caused by construction are not comprehensive enough, and there is even less research on the impact of ultra-low frequency micro-vibration on precision instruments and equipment. There is no efficient vibration reduction device to reduce low-frequency micro-vibration. The vibration reduction and isolation measures for precision instruments and equipment are relatively simple, and the vibration reduction effect for ultra-low frequency bands is extremely limited, which cannot meet the normal use of precision instruments and equipment in a vibrating environment.

[0003] The new local resonant elastic metamaterial plate-like structure is an ultra-low frequency vibration reduction plate-like structure designed with a special structure. The elastic metamaterial theory is an extension of the local resonant phononic crystal in the phononic crystal theory, breaking through the structural limitations of the phononic crystal theory and inheriting its band gap characteristics. Existing literature has studied the method of drilling holes in the plate and then adding local resonators to reduce the vibration of the plate-like structure. For local resonators, most of them are composed of two or more materials. For this method, although the structure produces a low-frequency bandgap, its processing difficulty and manufacturing cost will increase accordingly. Summary of the invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a local resonant elastic metamaterial plate-like structure with ultra-low frequency vibration reduction characteristics, which has excellent low-frequency vibration band gap characteristics and good processing and manufacturing conditions.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics, comprising an annular basic frame plate 1, a central mass column 3 axially passing through the basic frame plate 1, the central mass column 3 consisting of a middle mass column and umbrella-shaped mass columns symmetrically connected at both ends of the middle mass column, the side of the middle mass column is connected to the inner wall of the basic frame plate 1 through a thin strip structure 2, and the two umbrella-shaped mass columns are respectively located above and below the basic frame plate 1.

[0007] The cross section of the basic frame plate 1 is a ring-shaped square, and the thin strip structure 2 is a cross structure, which is respectively connected to the center of the inner wall of the basic frame plate 1 and the outer wall of the middle mass column.

[0008] The cross-sections of the middle mass column and the umbrella-shaped mass column are both circular, and the two are connected in a coaxial manner. The radius of the umbrella-shaped mass column is 10 / 3 times the radius of the middle mass column, and the axial height of the umbrella-shaped mass column is 0.5 times the axial height of the middle mass column.

[0009] The cross-sectional radius of the middle mass column is 1.5 mm, the axial height of the middle mass column is 6 mm, the cross-sectional radius of the umbrella-shaped mass column is 5 mm, the axial height of a single umbrella-shaped mass column is 2 mm, the cross-sectional area of ​​the basic frame plate 1 is a square with a side length of 10 mm, the axial height of the frame plate is 2 mm, the wall thickness of the frame plate is 0.5 mm, the band width of the thin strip structure 2 is 0.5 mm, the axial height is 2 mm, and the angle θ between two adjacent thin strips is 90°.

[0010] The axial height of the middle mass column is greater than the axial height of the basic frame plate 1 and the thin strip structure 2 .

[0011] The basic frame plate 1, the thin strip structure 2 and the central mass column 3 are all made of the same single material.

[0012] The basic frame plate 1, the thin strip structure 2 and the central mass column 3 form a symmetrical structure as a whole.

[0013] The thin strip structure 2 connects the basic frame plate 1 and the middle mass column, and is a symmetrically distributed structure with the same angle as the axis based on the middle mass column.

[0014] Compared with the prior art, the local resonant elastic metamaterial plate structure of the present invention has a lighter mass than the traditional vibration isolation plate structure of the same size, and can produce ultra-low frequency band gap characteristics, and has a controllable band gap range for elastic waves. Its band gap can be adjusted by adjusting the height of the whole center mass column, the horizontal width of the thin strip structure and the wall thickness of the basic frame plate. In addition, this structure uses a single material. Compared with other phononic crystal structures that add local resonators by drilling holes on the plate body, the local resonant elastic metamaterial plate structure of the present invention has good processing and manufacturing advantages, as well as low cost advantages.

[0015] The local resonant elastic metamaterial plate structure of the present invention has potential application value in the protection of precision instruments and can effectively control the ultra-low frequency vibrations to which the precision instruments are subjected. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic structural diagram of a unit cell of a novel local resonant elastic metamaterial plate-like structure of the present invention.

[0017] Figure 2 It is the energy band diagram of the unit cell of the novel local resonant elastic metamaterial plate-like structure of the present invention.

[0018] Figure 3 This is a structural diagram of the novel local resonant elastic metamaterial plate-like structure of the present invention.

[0019] Figure 4 It is a frequency response function curve diagram of the novel local resonant elastic metamaterial plate-like structure of the present invention. DETAILED DESCRIPTION

[0020] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0021] like Figure 1 As shown, a new type of local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics includes an annular basic frame plate 1 and a central mass column 3 passing through its axis, the inner wall of the basic frame plate 1 and the outer wall of the central mass column 3 are connected by a thin strip structure 2, and the basic frame plate 1, the thin strip structure 2 and the central mass column 3 are all made of the same single material.

[0022] In this embodiment, the basic frame plate 1 is a frame plate structure with a square cross-section and no material in the center. The thin strip structure 2 connects the basic frame plate 1 and the central mass column 3, and is a symmetrical distribution structure based on the central mass column 3 with the same angle as the axis, forming a cross-shaped symmetrical structure as a whole.

[0023] Specifically, the central mass column 3 is composed of a middle mass column in the basic frame plate 1 and umbrella-shaped mass columns located above and below the outside of the basic frame plate 1 and symmetrically distributed. The middle mass column is connected to the thin-strip structure 2 and is connected to the umbrella-shaped mass column in a coaxial manner. The cross-section of the middle mass column is circular, and the cross-section of the symmetrical umbrella-shaped mass column is also circular.

[0024] In the present invention, the axial height of the middle mass column needs to be greater than the axial height of the basic frame plate 1 and the thin strip structure 2 , and the cross-section of the umbrella-shaped mass column is the inscribed circle of the basic frame plate 1 .

[0025] In the embodiment of the present invention, the cylindrical radius of the middle mass column of the central mass column 3 is 1.5 mm, the cylindrical height of the middle mass column is 6 mm, the cylindrical radius of the symmetrical umbrella-shaped mass column is 5 mm, the height of the single-sided umbrella-shaped mass column is 2 mm, the square cross-section side length of the basic frame plate 1 is 10 mm, the axial height of the frame plate is 2 mm, the wall thickness of the frame plate is 0.5 mm, the band width of the thin strip structure 2 is 0.5 mm, the axial height is 2 mm, and the angle θ between two adjacent thin strips is 90°

[0026] The present invention uses silicone rubber as the overall material of the structure, and the specific material parameters are: density ρ = 1300kg / m 3 , shear modulus E = 1.175 × 10 5 Pa, Poisson's ratio μ = 0.469. Figure 2 It can be seen that the structure has a band gap in the range of 0-70Hz, where the band gap is 35-45Hz.

[0027] The novel local resonant elastic metamaterial plate-like structure of the present invention is obtained by extending the unit cell of the novel local resonant elastic metamaterial plate-like structure in two mutually perpendicular directions parallel to the plate surface, such as Figure 3 shown.

[0028] refer to Figure 3 and Figure 4 , Figure 3 A represents the response, B is the longitudinal excitation point, and C is the bending and torsion excitation point. Figure 4 It is the transmission spectrum of a semi-infinite periodic structure formed by the extension of 7X7 unit cells. It can be seen that there is a region in the frequency domain where the vibration attenuation is lower than 0dB, which corresponds to the ultra-low frequency band gap in the band structure. It should be noted that in the simulation of the transmission characteristics, three excitation methods were adopted, namely longitudinal excitation, bending excitation and torsional excitation, so what is obtained from the transmission spectrum is the band gap under the three excitation methods, which is wider than the complete band gap in the band structure, but corresponds to the complete band gap in the band structure.

[0029] It can be seen that the use of the novel local resonant elastic metamaterial plate-like structure of the present invention can make the plate-like structure produce a low-frequency band gap, and effectively control the ultra-low frequency vibration of the plate-like structure.

[0030] Therefore, the local resonant elastic metamaterial plate structure of the present invention can be applied to shock absorption and vibration isolation of precision mechanical instruments and equipment, and can protect the precision instruments and equipment from normal use during ultra-low frequency vibration.

[0031] The present invention is lighter than the traditional plate structure with the same size, and can produce ultra-low frequency band gap characteristics, with a controllable band gap range for elastic waves. The band gap can be adjusted by adjusting the height of the central mass column, the horizontal width of the thin strip structure and the wall thickness of the base frame. Compared with the Bragg scattering type plate structure, it has good processing and manufacturing and low cost advantages. The present invention has potential advantages in precision instrument vibration reduction and can effectively protect important structures against low-frequency vibration.

Claims

1. A local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics, comprising a ring-shaped basic frame plate (1), It is characterized in that The central mass column (3) passes through the foundation frame plate (1) in the axial direction. The central mass column (3) is composed of a middle mass column and umbrella-shaped mass columns symmetrically connected to both ends of the middle mass column. The side surface of the middle mass column is connected to the inner wall of the foundation frame plate (1) through a thin strip structure (2). The two umbrella-shaped mass columns are respectively located above and below the foundation frame plate (1). The cross section of the basic frame plate (1) is a ring-shaped square, and the thin strip structure (2) is a cross-shaped structure, which is respectively connected to the center of the inner wall of the basic frame plate (1) and the outer wall of the middle mass column; The basic frame plate (1), the thin strip structure (2) and the central mass column (3) are all made of the same single material.

2. According to claim 1, the local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics, It is characterized in that The cross-sections of the middle mass column and the umbrella-shaped mass column are both circular, and the two are connected in a coaxial manner. The radius of the umbrella-shaped mass column is 10 / 3 times the radius of the middle mass column, and the axial height of the umbrella-shaped mass column is 0.5 times the axial height of the middle mass column.

3. According to claim 2, the local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics, It is characterized in that The cross-sectional radius of the middle mass column is 1.5 mm, the axial height of the middle mass column is 6 mm, the cross-sectional radius of the umbrella-shaped mass column is 5 mm, the axial height of a single umbrella-shaped mass column is 2 mm, the cross-sectional area of ​​the basic frame plate (1) is a square with a side length of 10 mm, the axial height of the frame plate is 2 mm, the wall thickness of the frame plate is 0.5 mm, the band width of the thin strip structure (2) is 0.5 mm, the axial height is 2 mm, and the angle θ between two adjacent thin strips is 90°.

4. According to claim 1, the local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics, It is characterized in that The axial height of the middle mass column is greater than the axial heights of the basic frame plate (1) and the thin strip structure (2).

5. According to claim 1, the local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics, It is characterized in that The basic frame plate (1), the thin strip structure (2) and the central mass column (3) form a symmetrical structure as a whole.

6. The local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics according to claim 1, It is characterized in that The thin strip structure (2) connects the basic frame plate (1) and the middle mass column, and is a symmetrically distributed structure with the middle mass column as the axis.

7. The local resonant elastic metamaterial plate structure with ultra-low frequency vibration reduction characteristics according to claim 1, It is characterized in that The circular cross-section of the umbrella-shaped mass column is an inscribed circle of the cross-section shape of the basic frame plate (1).

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