CN110725471B - Variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance unit - Google Patents
Variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance unit Download PDFInfo
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- CN110725471B CN110725471B CN201911006120.1A CN201911006120A CN110725471B CN 110725471 B CN110725471 B CN 110725471B CN 201911006120 A CN201911006120 A CN 201911006120A CN 110725471 B CN110725471 B CN 110725471B
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- E—FIXED CONSTRUCTIONS
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- E04C—STRUCTURAL ELEMENTS; BUILDING MATERIALS
- E04C3/00—Structural elongated elements designed for load-supporting
- E04C3/02—Joists; Girders, trusses, or trusslike structures, e.g. prefabricated; Lintels; Transoms; Braces
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- E—FIXED CONSTRUCTIONS
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- E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
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- E04B1/62—Insulation or other protection; Elements or use of specified material therefor
- E04B1/74—Heat, sound or noise insulation, absorption, or reflection; Other building methods affording favourable thermal or acoustical conditions, e.g. accumulating of heat within walls
- E04B1/82—Heat, sound or noise insulation, absorption, or reflection; Other building methods affording favourable thermal or acoustical conditions, e.g. accumulating of heat within walls specifically with respect to sound only
- E04B1/84—Sound-absorbing elements
- E04B1/8404—Sound-absorbing elements block-shaped
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- E—FIXED CONSTRUCTIONS
- E04—BUILDING
- E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
- E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
- E04B1/62—Insulation or other protection; Elements or use of specified material therefor
- E04B1/74—Heat, sound or noise insulation, absorption, or reflection; Other building methods affording favourable thermal or acoustical conditions, e.g. accumulating of heat within walls
- E04B1/82—Heat, sound or noise insulation, absorption, or reflection; Other building methods affording favourable thermal or acoustical conditions, e.g. accumulating of heat within walls specifically with respect to sound only
- E04B1/84—Sound-absorbing elements
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Abstract
The invention discloses a variable cross-section acoustic metamaterial beam with a two-degree-of-freedom local resonance unit, which belongs to the technical field of mechanical vibration and noise control and mainly aims to solve the problem that the local resonance band gap of a constant cross-section acoustic metamaterial in the prior art is narrow, so that the effective frequency range of vibration and noise reduction of the constant cross-section acoustic metamaterial is small, and the practical application of the acoustic metamaterial in engineering is limited.
Description
Technical Field
The invention belongs to the technical field of mechanical vibration and noise control, and particularly relates to a variable cross-section acoustic metamaterial beam with a two-degree-of-freedom local resonance unit.
Background
The acoustic metamaterial is a local resonance type phonon crystal (periodic structure) with extraordinary physical properties (negative mass density, negative elastic modulus and the like) which are different from materials in the nature. The low-frequency local resonance band gap can be generated in a sub-wavelength band of the structure size, and the characteristic can realize the effect of blocking low-frequency vibration noise through a small-size structure. However, the local resonance band gap bandwidth of the traditional equal-section acoustic metamaterial is narrow, so that the effective frequency range of vibration and noise reduction is small, and the bottleneck greatly limits the wide application of the acoustic metamaterial in engineering practice.
Disclosure of Invention
The invention aims to solve the problem that the effective frequency range of vibration and noise reduction of an equal-section acoustic metamaterial is small due to the narrow local resonance band gap bandwidth of the equal-section acoustic metamaterial in the prior art, so that the practical application of the acoustic metamaterial in engineering is limited, and further provides a variable-section acoustic metamaterial beam with a two-degree-of-freedom local resonance unit.
A variable cross-section acoustic metamaterial beam with a two-degree-of-freedom local resonance unit comprises M stepped beam assemblies, wherein M is a positive integer, the M stepped beam assemblies are sequentially arranged along the length direction, and two adjacent stepped beam assemblies are fixedly connected;
furthermore, the stepped beam assembly comprises a stepped beam main body and two-degree-of-freedom local resonance units, each two-degree-of-freedom local resonance unit is fixedly connected to one stepped beam main body, and the stepped beam main bodies in two adjacent stepped beam assemblies are fixedly connected;
furthermore, the ladder beam main body comprises a thin beam section and a thick beam section, the thin beam section and the thick beam section are both cuboids, one end of the thin beam section and one end of the thick beam section are integrally arranged, and the other end of the thick beam section in the front ladder beam main body and the other end of the thin beam section in the back ladder beam main body in the two adjacent ladder beam main bodies are fixedly connected;
furthermore, the two-degree-of-freedom local resonance unit comprises an upper rubber column, a first mass block, a lower rubber column and a second mass block, wherein the upper rubber column, the first mass block, the lower rubber column and the second mass block are all cylinders, the upper rubber column, the first mass block, the lower rubber column and the second mass block are sequentially arranged from top to bottom, the bottom end of the upper rubber column is bonded with the top end of the first mass block, the bottom end of the first mass block is bonded with the top end of the lower rubber column, the bottom end of the lower rubber column is bonded with the top end of the second mass block, and the top end of the upper rubber column is bonded with the lower surface of the thin beam section;
further, the end face diameter value of the upper rubber column is L1, the width value of the lower surface of the thin beam section is L2, and L1 is L2;
furthermore, the center of the end face of the upper rubber column is coaxial with the center of the lower surface of the thin beam section;
furthermore, the end surface diameter values of the upper rubber column, the first mass block, the lower rubber column and the second mass block are the same;
further, the height of the upper rubber column is smaller than that of the lower rubber column;
further, the height of the second mass block is smaller than that of the first mass block;
further, the value range of M is 4-10.
Compared with the prior art, the invention has the following beneficial effects:
1. the step beam and upper rubber column bonding surface, the upper rubber column and upper mass block bonding surface, the upper mass block and lower rubber column bonding surface and the lower rubber column and lower mass block bonding surface in the device provided by the invention are stably connected, so that corresponding displacement is coordinated. The width of the lower surface of the thin beam section of the stepped beam is designed to be a flat structure with the diameter consistent with that of the cross section of the upper rubber column, so that the stepped beam and the local resonance unit are firmly and reliably bonded.
2. The invention designs a plurality of groups of stepped beam structures with different parameters, which is beneficial to researching and exploring the interaction relation between the Bragg band gap generated by the periodic arrangement of the variable cross-section beam sections and the local resonance band gap generated by the local resonance of the rubber column mass block structure. Has important theoretical and practical significance for discovering new vibration reduction and isolation technical means and ways.
3. Based on the band gap characteristic analysis result of the variable-section acoustic metamaterial beam, the variable-section design can greatly increase the width and the number of the Bragg band gaps, promote the fusion of the Bragg band gaps and the local resonance band gaps, and effectively widen the width of the local resonance band gaps, so that the bottleneck of narrow bandwidth of the local resonance band gaps is broken through, and the excellent vibration reduction and isolation effect is achieved.
4. The invention has simple structure, convenient manufacture and low cost, and saves the expenses for scientific research.
Drawings
FIG. 1 is an isometric view of the present invention;
FIG. 2 is a bottom view of the present invention;
FIG. 3 is a front view of the present invention;
FIG. 4 is a top view of the present invention;
FIG. 5 is an isometric view of a ladder beam assembly of the present invention;
FIG. 6 is a bottom view of the ladder beam assembly of the present invention;
FIG. 7 is a front view of the ladder beam assembly of the present invention;
FIG. 8 is a top view of the ladder beam assembly of the present invention;
FIG. 9 is a left side view of the ladder beam assembly of the present invention;
FIG. 10 is a graph showing the effect of broadening the band gap of the local resonance in accordance with the present invention.
In the figure, a step beam main body 1, a thin beam section 11, a thick beam section 12, a two-degree-of-freedom local resonance unit 2, an upper rubber column 21, a first mass block 22, a lower rubber column 23 and a second mass block 24 are shown.
Detailed Description
The first embodiment is as follows: the present embodiment is described with reference to fig. 1 to 4, and the variable cross-section acoustic metamaterial beam with a two-degree-of-freedom local resonance unit includes M stepped beam assemblies, where M is a positive integer, the M stepped beam assemblies are sequentially arranged along a length direction, and two adjacent stepped beam assemblies are fixedly connected to each other.
In the embodiment, when the length, the cross section size ratio and the length ratio of the thin beam section to the thick beam section of the stepped beam assembly are fixed, rubber columns and mass blocks with various structural parameters in the stepped beam assembly can be designed to be bonded into different local resonance units, the natural frequency of the local resonance units is adjusted, the position of a local resonance band gap is further changed, and the local resonance band gap is widened through the interaction of the local resonance band gap and the Bragg band gap; when the structural parameters of the local resonance unit are fixed, different unit cell lengths, cross section size ratios and length ratios of the thin beam section and the thick beam section can be designed, and the broadening of a local resonance band gap can be realized.
The second embodiment is as follows: the present embodiment is described with reference to fig. 5 and 8, and is further limited to the ladder beam assembly in the first embodiment, and in the present embodiment, the ladder beam assembly includes a ladder beam main body 1 and a two-degree-of-freedom local resonance unit 2, each two-degree-of-freedom local resonance unit 2 is fixedly connected to one ladder beam main body 1, and the ladder beam main bodies 1 in two adjacent ladder beam assemblies are fixedly connected. Other components and connection modes are the same as those of the first embodiment.
The ladder beam main part 1 fixed connection mode among two adjacent ladder beam subassemblies in this embodiment is for bonding, so set up the number of suitable increase and decrease ladder beam subassembly when being convenient for according to experiment or practical application, bond simultaneously and can not change the material nature of ladder beam main part 1 when guaranteeing firmly, still can remain certain trace buffer zone to the junction, direct fracture when avoiding the ladder beam overload, destroys single ladder beam subassembly.
The third concrete implementation mode: the present embodiment is described with reference to fig. 5, and is further limited to the ladder beam main body 1 described in the second embodiment, in the present embodiment, the one ladder beam main body 1 includes a thin beam section 11 and a thick beam section 12, the thin beam section 11 and the thick beam section 12 are both rectangular solids, one end of the thin beam section 11 is integrally disposed with one end of the thick beam section 12, and the other end of the thick beam section 12 in the previous ladder beam main body 1 in the two adjacent ladder beam main bodies 1 is fixedly connected with the other end of the thin beam section 11 in the next ladder beam main body 1. Other components and connection modes are the same as those of the first embodiment.
The fourth concrete implementation mode: the present embodiment is described with reference to fig. 1, and the present embodiment further defines the two-degree-of-freedom local resonant unit 2 described in the second embodiment, in the present embodiment, the two-degree-of-freedom local resonant unit 2 includes an upper rubber column 21, a first mass block 22, a lower rubber column 23, and a second mass block 24, the upper rubber column 21, the first mass block 22, the lower rubber column 23, and the second mass block 24 are all cylinders, and the upper rubber column 21, the first mass block 22, the lower rubber column 23, and the second mass block 24 are sequentially arranged from top to bottom, a bottom end of the upper rubber column 21 is bonded to a top end of the first mass block 22, a bottom end of the first mass block 22 is bonded to a top end of the lower rubber column 23, a bottom end of the lower rubber column 23 is bonded to a top end of the second mass block 24, and a top end of the upper rubber column 21 is bonded to a lower. Other components and connection modes are the same as those of the third embodiment.
In the embodiment, the two-degree-of-freedom local resonance unit 2 is distinguished from a common vibrator, the number of mass blocks is increased, and the mass blocks are connected through the rubber columns, so that the interaction relationship between the Bragg band gap generated by the periodic arrangement of the variable-section beam sections and the local resonance band gap generated by the local resonance of the mass block structure of the rubber columns is researched and explored more favorably.
The fifth concrete implementation mode: the present embodiment will be described with reference to fig. 6, and the present embodiment further defines the upper rubber column 21 and the thin beam segment 11 described in the fourth embodiment, in which the diameter of the end surface of the upper rubber column 21 is L1, and the width of the lower surface of the thin beam segment 11 is L2, and L1 is L2. Other components and connection modes are the same as those of the first embodiment.
In the embodiment, the width of the lower surface of the thin beam section of the stepped beam is designed to be of a flat structure with the diameter consistent with that of the cross section of the upper rubber column 21, so that the stepped beam and the local resonance unit are firmly and reliably bonded.
The sixth specific implementation mode: the present embodiment will be described with reference to fig. 9, and the present embodiment further defines the upper rubber column 21 and the thin beam segment 11 described in the fifth embodiment, and in the present embodiment, the center of the end face of the upper rubber column 21 is coaxially disposed with the center of the lower surface of the thin beam segment 11. The other components and the connection mode are the same as the fifth embodiment mode.
The seventh embodiment: the present embodiment is described with reference to fig. 1, and is further limited to the upper rubber column 21, the first mass 22, the lower rubber column 23, and the second mass 24 described in the fourth embodiment, and in the present embodiment, the end surface diameters of the upper rubber column 21, the first mass 22, the lower rubber column 23, and the second mass 24 are the same. The other components and the connection mode are the same as those of the fourth embodiment.
The specific implementation mode is eight: the present embodiment will be described with reference to fig. 1, and the present embodiment is further limited to the upper rubber column 21 and the lower rubber column 23 described in the fourth embodiment, and in the present embodiment, the height of the upper rubber column 21 is smaller than the height of the lower rubber column 23. The other components and the connection mode are the same as the fifth embodiment mode.
The specific implementation method nine: the present embodiment is described with reference to fig. 1, and is further limited to the first mass 22 and the second mass 24 described in the second embodiment, and in the present embodiment, the height of the second mass 24 is smaller than the height of the first mass 22. The other components and the connection mode are the same as the fifth embodiment mode.
In this embodiment, the first mass block 22 and the second mass block 24 have different heights and the same cross-sectional area, that is, the mass of the first mass block 22 and the mass of the second mass block 24 are different, and if the same mass block is arranged, the change of the local resonance band gap caused by the local resonance of the rubber column mass block structure is affected.
The detailed implementation mode is ten: the present embodiment is described with reference to fig. 1, and the present embodiment further defines the number of the ladder beam assemblies described in the second embodiment, and in the present embodiment, the value of M ranges from 4 to 10. Other components and connection modes are the same as those of the first embodiment.
Based on the above specific embodiment, three variable cross-section acoustic metamaterial beams with unit cell lengths are designed, the length values of a single ladder beam assembly are respectively 0.35m, 0.265m and 0.257m, and a local resonance band gap broadening effect diagram is obtained through a simulation experiment, as shown in fig. 10: (a) the length of the curve corresponding to a single step beam component is 0.35m, (b) the length of the curve corresponding to a single step beam component is 0.265m, and (c) the length of the curve corresponding to a single step beam component is 0.257m, as can be seen from fig. 10, as the length of the single step beam component is reduced, the Bragg band gap in the 212-258Hz frequency band approaches to the local resonance band gap from the low frequency, so that the widths of the two local resonance band gaps of the graph in 351-407Hz and 426-617Hz are greatly widened, the vibration reduction and isolation capability of the metamaterial beam is effectively improved, and the bottleneck of narrow local resonance band gap bandwidth is also broken through. The variable cross-section acoustic metamaterial beam local resonance unit designed by the invention is easy to disassemble, and is convenient to flexibly combine with different ladder beams to obtain different vibration reduction and isolation characteristics. The materials of all structural parts of the invention are common engineering materials, thus being economical and feasible.
Claims (7)
1. A variable cross-section acoustic metamaterial beam with a two-degree-of-freedom local resonance unit comprises M stepped beam assemblies, wherein M is a positive integer, the M stepped beam assemblies are sequentially arranged along the length direction, and two adjacent stepped beam assemblies are fixedly connected;
the ladder beam assembly comprises a ladder beam main body (1) and two-degree-of-freedom local resonance units (2), each two-degree-of-freedom local resonance unit (2) is fixedly connected to one ladder beam main body (1), and the ladder beam main bodies (1) in two adjacent ladder beam assemblies are fixedly connected;
the ladder beam comprises a ladder beam main body (1) and is characterized in that the ladder beam main body (1) comprises a thin beam section (11) and a thick beam section (12), the thin beam section (11) and the thick beam section (12) are cuboids, one end of the thin beam section (11) and one end of the thick beam section (12) are integrally arranged, and the other end of the thick beam section (12) in the front ladder beam main body (1) in the two adjacent ladder beam main bodies (1) is fixedly connected with the other end of the thin beam section (11) in the rear ladder beam main body (1);
the method is characterized in that: the two-degree-of-freedom local resonance unit (2) comprises an upper rubber column (21), a first mass block (22), a lower rubber column (23) and a second mass block (24), wherein the upper rubber column (21), the first mass block (22), the lower rubber column (23) and the second mass block (24) are cylinders, the upper rubber column (21), the first mass block (22), the lower rubber column (23) and the second mass block (24) are sequentially arranged from top to bottom, the bottom end of the upper rubber column (21) is bonded with the top end of the first mass block (22), the bottom end of the first mass block (22) is bonded with the top end of the lower rubber column (23), the bottom end of the lower rubber column (23) is bonded with the top end of the second mass block (24), and the top end of the upper rubber column (21) is bonded with the lower surface of the thin beam section (11).
2. The variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance units as in claim 1, wherein: the end face diameter value of the upper rubber column (21) is L1, the width value of the lower surface of the thin beam section (11) is L2, and L1 is L2.
3. The variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance units as in claim 2, wherein: the end face circle center of the upper rubber column (21) and the lower surface circle center of the thin beam section (11) are coaxially arranged.
4. The variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance units as in claim 3, wherein: the end face diameter values of the upper rubber column (21), the first mass block (22), the lower rubber column (23) and the second mass block (24) are the same.
5. The variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance units as in claim 4, wherein: the height of the upper rubber column (21) is smaller than that of the lower rubber column (23).
6. The variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance units as in claim 5, wherein: the height of the second mass block (24) is smaller than that of the first mass block (22).
7. The variable cross-section acoustic metamaterial beam with two-degree-of-freedom local resonance units as in claim 6, wherein: the value range of M is 4-10.
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| DE102021208300A1 (en) | 2021-07-30 | 2023-02-02 | Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung eingetragener Verein | Rotating or oscillating tool fitted with metamaterials to reduce noise and vibration |
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| CN114822467B (en) * | 2022-04-25 | 2022-12-09 | 清华大学 | Phononic crystal based on gradient sound black hole structure band gap regulation and control |
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