A Local Resonant Metamaterial Based on Electromagnetic Branch Circuit Damping

Abstract

This invention relates to a locally resonant metamaterial, aiming to provide a locally resonant metamaterial based on electromagnetic branch circuit damping to achieve control over the bandgap characteristics of the metamaterial. The technical solution is a locally resonant metamaterial based on electromagnetic branch circuit damping, characterized in that: the locally resonant metamaterial is composed of multiple cells arranged coaxially and connected end-to-end; each cell includes a rubber spring assembly, an upper cell shell and a lower cell shell connected in sequence, a resonator installed between the lower cell shell and the upper cell shell, and a branch circuit connecting a pair of coils in the resonator.

Description

Technical Field

[0001] This invention relates to a local resonant metamaterial, and more particularly to a local resonant metamaterial based on electromagnetic branch circuit damping. Background Technology

[0002] The bandgap frequency of traditional phononic crystals is affected by the Bragg condition, meaning the lattice size must be approximately half the wavelength of the elastic wave. Therefore, relatively large cell sizes are required to achieve lower bandgap frequencies, which limits the applications of phononic crystals in certain areas. To overcome this limitation, Liu Zhengyou et al. first proposed the concept of locally resonant metamaterials in 2000. They periodically arranged cells composed of a high-density core coated with soft rubber in an elastic medium and discovered a low-frequency bandgap lower than the Bragg bandgap, namely the locally resonant bandgap. The discovery of this bandgap extended the range of phononic crystal modulated waves to the subwavelength band. This principle can be used to realize low-frequency bandgap and perform low-frequency vibration isolation. However, once traditional locally resonant metamaterials are fabricated, the bandgap frequency and width are not easily changed, making it impossible to isolate harmonic components outside the bandgap frequency band. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings in the above-mentioned background technology and provide a local resonant metamaterial based on electromagnetic branch circuit damping, so as to achieve the control of the bandgap characteristics of the metamaterial.

[0004] The technical solution provided by this invention is:

[0005] A local resonant metamaterial based on electromagnetic branch circuit damping is characterized in that: the local resonant metamaterial is composed of multiple cells arranged coaxially and connected end to end in sequence; each cell includes a rubber spring assembly, an upper cell shell and a lower cell shell connected in sequence, a resonator installed between the lower cell shell and the upper cell shell, and a branch circuit connecting a pair of coils in the resonator.

[0006] The resonator includes two permanent magnets with opposite polarities, coaxially fixed between the lower and upper cell housings by a fixing component, and a coil wound around the outer circumference of the two permanent magnets and supported by the lower cell housing.

[0007] The upper cell shell and the lower cell shell are positioned by interlocking with each other through a snap-fit ​​structure; and are connected as one unit by a number of bolts arranged parallel to the axis.

[0008] The fixing components include a central bolt that passes through the axis of the two permanent magnets and connects the upper cell shell and the lower cell shell as a whole, a washer located between the two permanent magnets, and two sleeves; the sleeves are a first sleeve located between the upper cell shell and the first permanent magnet and a second sleeve located between the lower cell shell and the second permanent magnet.

[0009] The lower cell housing is coaxially arranged with an inner ring. Several vibration-damping straight beams are evenly distributed radially along the circumferential direction of the inner wall of the lower cell housing and connected to the outer wall of the inner ring of the lower cell. The upper and lower parts of the inner wall of the inner ring of the lower cell are respectively made with annular grooves and annular bosses. The winding cylinder of the coil is embedded and fixed in the annular grooves and the annular bosses.

[0010] The inner wall of the upper cell shell is connected to a partition perpendicular to the axis, and a central bolt hole is opened in the center of the partition; a coil lead-out hole is opened in the wall of the upper cell shell.

[0011] The snap-fit ​​structure includes an annular groove formed on the inner wall of the bottom of the upper cell shell and a top boss located on the top of the lower cell shell and cooperating with the annular groove.

[0012] In the branch circuit, the positive output terminal of the power operational amplifier is grounded through a first resistor, the second resistor is connected between the input terminal and the positive output terminal of the power operational amplifier, and the third resistor is connected between the input terminal and the negative output terminal of the power operational amplifier; one end of the coil is connected to the negative output terminal of the power operational amplifier, and the other end is grounded.

[0013] The branch circuit simultaneously connects the coils of all cells in the local resonant metamaterial.

[0014] The beneficial effects of this invention are: by adjusting the resistance and inductance within the branch circuit, this invention changes the equivalent mass and equivalent damping of the metamaterial, thereby altering the bandgap frequency and bandgap width characteristics of the metamaterial, and ultimately effectively regulating the vibration isolation performance of the metamaterial. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the structure after the three cells are combined in an embodiment of the present invention.

[0016] Figure 2 This is a front view (sectional view) of a single cell structure in an embodiment of the present invention.

[0017] Figure 3 yes Figure 2 A schematic diagram of the three-dimensional structure.

[0018] Figure 4 This is a schematic diagram of the installation structure of the resonator in an embodiment of the present invention. Figure 2 (Cross-sectional view).

[0019] Figure 5 yes Figure 2 A schematic diagram of the upper cell shell structure.

[0020] Figure 6 yes Figure 2A schematic diagram of the lower cell shell structure.

[0021] Figure 7 This is a three-dimensional structural diagram of the upper cell shell in an embodiment of the present invention.

[0022] Figure 8 This is a schematic diagram of the front view of the lower cell shell in an embodiment of the present invention.

[0023] Figure 9 This is a three-dimensional structural diagram of the lower cell shell in an embodiment of the present invention.

[0024] Figure 10 This is a three-dimensional structural diagram of the rubber spring in an embodiment of the present invention.

[0025] Figure 11 This is a three-dimensional structural diagram of the winding drum in an embodiment of the present invention.

[0026] Figure 12 This is a schematic diagram of the three-dimensional structure of the permanent magnet in an embodiment of the present invention.

[0027] Figure 13 This is a three-dimensional structural diagram of the first sleeve or the second sleeve in an embodiment of the present invention.

[0028] Figure 14 This is a three-dimensional structural diagram of the gasket in an embodiment of the present invention.

[0029] Figure 15 This is a schematic diagram of the control circuit in an embodiment of the present invention.

[0030] The following are the labels in the diagram: Coil sleeve 1-1, First permanent magnet 1-2, Gasket 1-3, Second permanent magnet 1-4, First sleeve 1-5, Second sleeve 1-6, Coil 1-7;

[0031] Upper cell shell 2, bolt hole 2-1, partition 2-2, intermediate bolt hole 2-21, lead wire hole 2-3, annular groove 2-4.

[0032] 3. Lower cell shell, 3-1 bolt hole, 3-2 central bolt hole, 3-3 lower cell inner ring, 3-31 annular groove, 3-32 annular boss, 3-4 vibration damping straight beam, 3-5 top boss, 4 rubber spring, 5 winding drum, 6 center bolt. Detailed Implementation

[0033] The present invention will be further described below with reference to the embodiments shown in the accompanying drawings.

[0034] This invention consists of three parts: a cell shell, a resonator, and a branch circuit.

[0035] I. Localized Resonance Metamaterials

[0036] Figure 1 This is a schematic diagram of three cells glued together end to end. In reality, this type of localized resonant metamaterial is composed of multiple cells, such as... Figure 1 The method is to form a coaxial structure with its ends connected.

[0037] II. Cellular shell

[0038] Figure 2 The cell shown includes an upper cell shell 2, a lower cell shell 3, and a rubber spring 4.

[0039] The upper cell shell ( Figure 7 The upper cell shell has eight bolt holes 2-1 arranged axially in the circumferential direction. The eight bolt holes are evenly distributed in the circumferential direction of the upper cell shell. A partition 2-2 perpendicular to the axis of the upper cell shell is connected to the inner wall of the upper cell shell. A central bolt hole 2-2 is opened in the center of the partition. An annular groove 2-4 is provided on the lower side of the inner wall of the upper cell shell. A coil lead hole 2-3 penetrating the wall is provided on the circumferential surface of the upper cell shell.

[0040] The lower cell shell ( Figure 8 , Figure 9 The lower cell housing (as shown) also has eight bolt holes 3-1 evenly distributed along its circumference, parallel to the housing axis. A central bolt hole 3-2 is located at the center of the lower cell housing. The top boss 3-6 of the lower cell housing protrudes upwards to engage with the annular groove 1-1, thus ensuring accurate positioning with the upper cell housing. The bolt holes in the lower cell housing correspond to the bolt holes in the upper cell housing, have the same diameter, and are fixed by bolts. A lower cell inner ring is coaxially arranged within the lower cell housing. Several (preferably 20) radially extending damping beams 3-4 are evenly distributed along the circumference of the lower cell housing's inner wall, connecting to the outer wall 3-3 of the lower cell inner ring, thereby supporting the lower cell inner ring. An annular groove 3-31 is provided on the upper part of the inner wall of the lower cell inner ring, and an annular boss 3-32 extending inward in the direction of the inner diameter is made on the lower part of the inner wall of the lower cell inner ring; the winding cylinder 5, which is fitted with coils 1-7, is simultaneously engaged in the groove and the support plate, thereby realizing the installation and positioning of the coil.

[0041] The rubber spring ( Figure 10 The inner and outer diameters of the spring (as shown) are the same as the inner and outer diameters of the upper cell shell, respectively, and the bottom end of the rubber spring is connected (preferably by adhesive) to the top end of the upper cell shell.

[0042] III. Harmonic Oscillator Figure 4 (As shown)

[0043] The resonator includes a winding cylinder 1-1, a first permanent magnet 1-2, a gasket 1-3, a second permanent magnet 1-4, a first sleeve 1-5, a second sleeve 1-6, and a coil 1-7.

[0044] The inner diameter of the first sleeve 1-5 is matched with the outer diameter of the center bolt (for clearance fit) and is arranged coaxially with the center bolt. The top end of the first sleeve 1-5 abuts against the bottom end of the upper cell shell.

[0045] The inner diameter of the second sleeve 1-6 is matched with the outer diameter of the center bolt (for clearance fit) and is arranged coaxially with the center bolt. The bottom end of the second sleeve 1-6 abuts against the top end of the lower cell shell.

[0046] The top end of the first permanent magnet 1-2 abuts against the bottom end of the first sleeve 1-5, and the bottom end abuts against the top end of the gasket 1-3. The inner diameter of the first permanent magnet 1-2 is compatible with the center bolt (with clearance fit). The upper end of the first permanent magnet 1-2 is the S pole, and the lower end is the N pole.

[0047] The top end of the second permanent magnet 1-4 abuts against the bottom end of the shim 1-3, and the bottom end abuts against the top end of the second sleeve 1-6. The inner diameter of the second permanent magnet 1-4 is matched with the center bolt (clearance fit). The upper end of the second permanent magnet 1-4 is the N pole, and the lower end is the S pole. The first permanent magnet 1-2 and the second permanent magnet 1-4 have the same thickness, the same inner diameter, and the same outer diameter. The distance between the two permanent magnets is adjusted by the shim 1-3.

[0048] The central bolt 6 is inserted into the central bolt hole of the upper cell shell, the two sleeves, the two permanent magnets, the washer, and the central bolt hole of the lower cell shell. After being fixed by the fastening nut, these components are connected as one.

[0049] The outer circumference of the winding spool 1-1 is provided with two annular protrusions spaced apart (see...). Figure 4 The upper protrusion is supported and fixed by the annular groove 3-31 on the upper part of the inner wall of the lower cell inner ring 3-3 during installation, while the lower protrusion is supported and fixed by the annular boss 3-32 on the lower part of the inner wall of the lower cell inner ring during installation. The groove opening formed between the two protrusions faces the outer circumference and is used for winding coil 1-7. A lead hole 5-1 is provided on the upper end face of the winding cylinder, and the lead hole passes through the groove.

[0050] The coils 1-7 are wound clockwise evenly in the winding drum, and the coil connectors are led out through the outlet hole 5-1 and the lead hole 2-3.

[0051] IV. Branch Circuits Figure 15 (As shown)

[0052] The circuit includes resistors R, R1, and R2, coils 1-7, and a power operational amplifier U1 (preferably model OPA-541). In this system, R1 = R2, and the value of resistor R is the negative resistance. The positive terminal of the power amplifier is grounded through the first resistor R1, the second resistor R2 is connected between the input terminal and the positive output terminal of the amplifier, and resistor R is connected between the input terminal and the negative output terminal of the amplifier. One end of coils 1-7 is connected to the negative output terminal of the amplifier, and the other end is grounded; during operation, inductance, resistance, and voltage are generated in the coils, respectively. The function of the branch circuit is to provide negative equivalent resistance, which, when connected to the coils, is used to control the resistance of the coils and, consequently, the resistance of the resonator. The resistance of the resonator affects the position and width of its bandgap, thereby controlling its natural frequency.

[0053] Obviously, the branch circuit can simultaneously connect the coils of all cells in the local resonant metamaterial; that is, the coils of all cells in the local resonant metamaterial are connected in parallel to the branch circuit.

[0054] Working principle

[0055] 1) When metamaterials are subjected to external excitation, the shells of each cell are first caused to vibrate.

[0056] 2) The cell shell is affected by external vibration (external excitation source). The vibration is transmitted to the inner ring of the cell through the strip damping beam, and finally to the harmonic oscillator. The strip damping beam is used as a damping spring at this time.

[0057] 3) The first and second permanent magnets generate opposing magnetic field lines. When the coil vibrates, it cuts the magnetic field lines, generating current and thus a Lorentz force. The Lorentz force acts as damping, and the natural frequency of the resonator can be adjusted by regulating the magnitude of the Lorentz force. When the natural frequency of the resonator is close to the frequency of the incoming elastic wave, the resonant mode of the resonator is excited. At this time, the cell shell is subjected to the force applied by the elastic wave and the reverse force of the resonator, thus maintaining the stability of the shell.

[0058] 4) The branch circuit connecting the coil has the function of providing an equivalent negative resistance, which reduces the resistance of the resonator and thus affects the current; the increase of Lorentz force leads to an increase in damping, which makes the local resonant bandgap of the resonator wider and closer to the low-frequency region, resulting in a better vibration reduction effect.

[0059] This invention proposes a locally resonant metamaterial based on electromagnetic branch circuit damping, leveraging the vibration reduction characteristics of locally resonant metamaterials. A damping beam transmits the vibrations experienced by the cell shell to the internal resonator. Under elastic wave excitation, the resonator induces a resonant mode, exerting a reaction force on the shell to counteract the external excitation force. Furthermore, a negative resistance branch circuit is connected to the coil, widening the local resonant bandgap of the resonator and achieving a better vibration reduction effect.

[0060] In general, the resonator achieves vibration reduction by coupling low-frequency, wide-range vibration waves through local resonance. The introduction of branch circuits can widen the bandgap and further enhance the vibration reduction effect.

Claims

1. A local resonant metamaterial based on electromagnetic branch circuit damping, characterized in that: The local resonant metamaterial is composed of multiple cells arranged coaxially and connected end to end; each cell includes a lower cell shell (3), an upper cell shell (2) and a rubber spring assembly (4) connected in sequence, a resonator installed between the lower cell shell and the upper cell shell, and a branch circuit connecting a pair of coils in the resonator; The resonator includes two permanent magnets with opposite polarities that are coaxially fixed between the lower cell shell and the upper cell shell by a fixing component, and a coil (1-7) wound around the outer circumference of the two permanent magnets and supported by the lower cell shell. The upper and lower cell shells are positioned by interlocking structures and are connected as a whole by a number of bolts arranged parallel to the axis. The fixing components include a central bolt (6) that passes through the axis of the two permanent magnets and connects the upper cell shell (2) and the lower cell shell as a whole, a washer located between the two permanent magnets, and two sleeves; the sleeves are a first sleeve (1-5) located between the upper cell shell and the first permanent magnet (1-2) and a second sleeve (1-6) located between the lower cell shell and the second permanent magnet (1-4). The lower cell housing (3) is coaxially arranged with a lower cell inner ring (3-3). Several vibration damping straight beams (3-4) are evenly distributed in the circumferential direction of the lower cell housing and are connected to the outer wall of the lower cell inner ring. The upper and lower parts of the inner wall of the lower cell inner ring are respectively made with annular grooves (3-31) and annular bosses (3-32). The winding cylinder (5) of the coil is embedded and fixed in the annular grooves and the annular bosses.

2. The locally resonant metamaterial based on electromagnetic branch circuit damping according to claim 1, characterized in that: The inner wall of the upper cell shell is connected to a partition (2-2) perpendicular to the axis, and a central bolt hole is provided in the center of the partition; a lead wire hole (2-3) is provided in the wall of the upper cell shell.

3. The local resonant metamaterial based on electromagnetic branch circuit damping according to claim 2, characterized in that: The snap-fit ​​structure includes an annular groove (2-4) formed on the inner wall of the bottom of the upper cell shell and a top boss (3-6) located on the top of the lower cell shell and cooperating with the annular groove.

4. The local resonant metamaterial based on electromagnetic branch circuit damping according to claim 3, characterized in that: In the branch circuit, the positive output terminal of the power operational amplifier (U1) is grounded through the first resistor (R1), the second resistor (R2) is connected between the input terminal and the positive output terminal of the power operational amplifier, and the resistor (R) is connected between the input terminal and the negative output terminal of the power operational amplifier; one end of the coil (1-7) is connected to the negative output terminal of the power operational amplifier, and the other end is grounded.

5. The local resonant metamaterial based on electromagnetic branch circuit damping according to claim 4, characterized in that: The branch circuit simultaneously connects the coils of all cells in the local resonant metamaterial.

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