A two-dimensional magnetic lattice vibration experimental device and method

Abstract

The present invention discloses a two-dimensional magnetic lattice vibration experimental device and method. It includes an oscillating component, a shooting component and an oscillator mechanism. The oscillator mechanism is provided with a plurality of oscillators with magnets. The oscillating component is used to touch the oscillator to oscillate and conduct a two-dimensional lattice vibration experiment. The shooting component is used to shoot the two-dimensional lattice vibration experiment. The oscillator mechanism includes two different "spring-magnet" oscillators. Each "spring-magnet" oscillator includes a closely wound spring, a columnar hollow magnet and a rubber ring. The upper end of the closely wound spring is provided with a columnar hollow magnet, and the lower end of the closely wound spring is inserted into a square acrylic plate. The present invention is used to "macroscopically" simulate the phonon and lattice wave phenomena in the crystal lattice. By adjusting parameters such as the vibration amplitude and frequency, the physical experiment teaching of the phonon band theory is made more intuitive. By changing the periodicity and spatial structure of the magnetic oscillator, the characteristic differences of the two-dimensional lattice vibration mode and the mechanical wave behavior under different interactions can be shown.

Description

Technical Field

[0001] The present invention relates to a research method for two-dimensional lattice wave propagation, and in particular to an experimental device for simulating two-dimensional lattice vibrations based on a "spring-magnet" magnetic lattice for displaying and studying two-dimensional lattice vibrations and a method for using the same. Background Art

[0002] In a crystal, atoms are arranged periodically to form a lattice. There are mutual forces between them, and they make tiny vibrations near the equilibrium position under the action of the force. When the crystal vibrates due to external forces, the vibration will propagate inside it in the form of waves. According to the phonon band theory, affected by factors such as the distribution of atoms in the crystal, waves of certain frequencies can propagate in the crystal, while waves of certain frequencies will attenuate and disappear within a very short distance and cannot propagate. There are band gaps and passbands in wave propagation. This phenomenon is also often used in the production of frequency-selective sound insulation materials.

[0003] Since the process of wave propagation is the collective behavior of microscopic atomic vibrations, it is difficult to present it intuitively, and the bandgap and passband phenomena are also very abstract. In university physics experimental teaching, common vibration experiments such as simple pendulums and coupled pendulums cannot be directly linked to the above phenomena, and there is a lack of experimental devices that can directly demonstrate the above phenomena. It is very necessary to design an intuitive and easy-to-understand experimental device, teaching content and method. Summary of the invention

[0004] In order to solve the experimental teaching problem pointed out in the background technology, the present invention proposes an experimental device and method based on a "spring-magnet" oscillator for demonstrating and studying two-dimensional lattice vibrations, which is used to simulate two-dimensional lattice vibration experiments.

[0005] The present invention uses springs, magnets, and acrylic plates as basic components, and arranges magnets and springs into a periodic two-dimensional structure according to the holes of the acrylic plate, analogous to a microscopic atomic lattice. A motor is used to drive an external magnet to apply a periodic force to the two-dimensional lattice, simulating the lattice vibration caused by the external force on the crystal, "macroscopicizing" the lattice interaction and lattice vibration, demonstrating the phenomenon and studying its characteristics.

[0006] The technical solution adopted by the present invention is:

[0007] 1. A two-dimensional lattice vibration experimental device of a "spring-magnet" oscillator:

[0008] It includes a vibration component, a shooting component and a vibrator mechanism;

[0009] It includes a vibrator mechanism, on which a plurality of vibrators are distributed, each vibrator is provided with a magnet, and the plurality of vibrators influence each other by magnetism;

[0010] It includes a vibration-starting component, which is located on the side of the vibrator mechanism and is used to touch the vibrator in the vibrator mechanism to start the vibration and then conduct a two-dimensional grid point vibration experiment;

[0011] It includes a shooting component, which is located above the vibrator mechanism and is used for shooting the two-dimensional grid point vibration experimental conditions of the vibrator mechanism.

[0012] The vibrator mechanism includes a square acrylic plate and two different types of "spring-magnet" vibrators arranged on the square acrylic plate. The square acrylic plate is provided with array-distributed holes for installing the "spring-magnet" vibrators. Each "spring-magnet" vibrator includes a densely wound spring, a columnar hollow magnet and a rubber ring. The upper end of the densely wound spring is fitted with a columnar hollow magnet through a rubber ring, and the lower end of the densely wound spring is inserted into the square acrylic plate. In one of the "spring-magnet" vibrators, only one columnar hollow magnet is fitted with a rubber ring on the upper end of the densely wound spring, and in the other "spring-magnet" vibrator, two columnar hollow magnets are fitted with a rubber ring on the upper end of the densely wound spring.

[0013] The height of the topmost columnar hollow magnets of all the "spring-magnet" vibrators on the square acrylic plate is kept consistent, forming a two-dimensional lattice vibration system.

[0014] The shooting assembly includes a U-shaped acrylic frame and a shooting device; the vibrator mechanism is arranged in the U-shaped acrylic frame built above, and the shooting device is installed on the top of the U-shaped acrylic frame above the vibrator mechanism, and the shooting device is arranged toward the vibrator mechanism.

[0015] The vibration component includes a horizontal vibrator, a plastic nesting component and a power supply. The horizontal vibrator is electrically connected to the power supply. The output end of the horizontal vibrator is fixedly connected to the plastic nesting component. The plastic nesting component is used to contact and push the columnar hollow magnet in the "spring-magnet" vibrator on the square acrylic plate.

[0016] The horizontal vibrator is a mechanical device that can reciprocate in any set horizontal direction, is driven by the power supply connection, and is equipped with an amplitude adjustment gear and a speed adjustment module to make the vibration frequency continuously adjustable between 2 and 30 Hz.

[0017] 2. A two-dimensional lattice vibration method of a two-dimensional lattice vibration experimental device of a "spring-magnet" oscillator:

[0018] Build a number of n × n The two-dimensional grid of "spring-magnet" oscillators, n is a natural number greater than 3, and a "spring-magnet" oscillator located at the edge of a square acrylic plate is driven by a horizontal oscillator to make a frequency of fThe periodic directional motion is continuously transmitted by the magnetic force of the cylindrical hollow magnets between adjacent "spring-magnet" oscillators, which in turn induces the vibration of the two-dimensional grid points. The photographic equipment of the shooting component is used to collect the images and observe the propagation effect of the vibration in the grid points and the mechanical waves formed.

[0019] The present invention arranges magnets together so that there is a magnetic interaction force between them. This force decreases as the distance between the magnets increases, and has similar characteristics to the force between atoms. The magnet is fixed to the upper end of the spring, and the spring can provide a restoring force for the magnet to return the magnet to an equilibrium position. The superposition of the magnet interaction and the spring restoring effect has a good analogy with the characteristics of the force between atoms in the crystal, making the "spring-magnet" combination a device for making a macroscopic lattice vibration experiment, filling the gap in the existing two-dimensional lattice vibration experiment.

[0020] The present invention connects a cylindrical hollow magnet and a tightly wound spring through a rubber ring to form a plurality of "spring-magnet" vibrators, and evenly makes circular holes on a square acrylic plate so that the circular holes are arranged in a square array on the acrylic plate. Then a certain number of "spring-magnet" vibrators are inserted into the circular holes, keeping the springs naturally upright and the magnets at the same horizontal height to form a periodic two-dimensional square array. After the grid is built, it is equipped with a customized horizontal oscillator and connectors to provide a stable and adjustable vibration amplitude and frequency for the magnetic two-dimensional square array for research, and equipped with a U-shaped acrylic plate and shooting equipment to shoot and record the experimental phenomena for data analysis.

[0021] The present invention can be used for "macroscopic" simulation of phonon and lattice wave phenomena in crystal lattices, and by adjusting parameters such as vibration amplitude and frequency, the physical experiment teaching of phonon energy band theory is made more intuitive.

[0022] The present invention can show the characteristic differences of two-dimensional lattice vibration modes and mechanical wave behaviors under different interactions by changing the periodicity and spatial structure of magnetic oscillators. It is not only beneficial to experimental teaching, but also can provide reference for the application of vibration and sound isolation technology.

[0023] The beneficial effects of the present invention are:

[0024] The present invention designs a two-dimensional lattice vibration experimental device of a "spring-magnet" oscillator, and builds a "macroscopic" experimental system with springs and magnets as main materials to simulate the phenomenon of lattice waves caused by microscopic crystal lattice vibration. By changing the vibration frequency, scale and spatial structure of the "spring-magnet" oscillator, the observation and study of different lattice vibration modes and mechanical waves can be achieved. At the same time, if the elastic lattice wave theory modeling is adopted, the solution of lattice mechanical wave propagation is simulated and calculated. Based on the experimental device, the vibration mode and mechanical wave image of specific frequency and structure are observed, and the relationship between the actual observation results and theoretical modeling can be studied through image processing software analysis.

[0025] The present invention can simulate crystal lattice vibrations under general laboratory conditions, analogically express microscopic phonons in various directly observable vibration modes, and demonstrate the forbidden band and passband behaviors of mechanical wave propagation. It can not only be used as a physical experiment teaching device, but also provide experimental research methods for practical applications. The study of lattice vibrations and mechanical wave propagation can provide solutions for the improvement of vibration isolation and sound insulation technology. By simulating two-dimensional lattice vibrations, the vibration characteristics of periodic elastic recovery media are revealed, which helps to understand the propagation mode of vibrations and sound waves in materials with similar structures. If the collective behavior of periodic structures can be accurately grasped, the material structure can be designed more effectively to weaken or prevent the propagation of vibrations and sound waves, thereby improving the vibration isolation and sound insulation effects of the materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a schematic diagram of a "spring-magnet" oscillator.

[0027] Figure 2 It is a schematic diagram of a square acrylic plate.

[0028] Figure 3 It is a schematic diagram of the shooting device.

[0029] Figure 4 It is a schematic diagram of the horizontal oscillator, plastic nested components and power supply combination.

[0030] Figure 5 It is a schematic diagram of the combination of a square acrylic plate and a 5×5 "spring-magnet" vibrator.

[0031] Figure 6 It is a schematic diagram of the two-dimensional lattice vibration experimental setup.

[0032] Figure 7 yes n × n Schematic diagram of the square two-dimensional elastic lattice theory.

[0033] In the figure: 1. tightly wound spring, 2. cylindrical hollow magnet, 3. rubber ring, 4a. first "spring-magnet" vibrator, 4b. second "spring-magnet" vibrator, 5. square acrylic plate, 6. U-shaped acrylic plate frame, 7. horizontal oscillator, 8. plastic nesting assembly, 9. power supply, 10. shooting equipment. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0035] like Figure 6 As shown, the device includes a vibration-starting component, a shooting component and a vibrator mechanism.

[0036] It includes a vibrator mechanism, on which a plurality of vibrators are distributed, each vibrator is provided with a magnet, and the plurality of vibrators influence each other by magnetism;

[0037] It includes a vibration-starting component, which is located on the side of the vibrator mechanism and is used to touch the vibrator in the vibrator mechanism to start the vibration and then conduct a two-dimensional grid point vibration experiment;

[0038] It includes a shooting component, which is located above the vibrator mechanism and is used for shooting the two-dimensional grid point vibration experimental conditions of the vibrator mechanism.

[0039] like Figure 5 As shown, the vibrator mechanism includes a square acrylic plate 5 and two different "spring-magnet" vibrators, a first "spring-magnet" vibrator 4a and a second "spring-magnet" vibrator 4b, arranged on the square acrylic plate 5. Figure 2 As shown, the square acrylic plate 5 is provided with holes for installing the "spring-magnet" vibrators in a uniform array, such as Figure 1 As shown, each of the first "spring-magnet" vibrator 4a and the second "spring-magnet" vibrator 4b includes a closely wound spring 1, a columnar hollow magnet 2 and a rubber ring 3, the upper end of the closely wound spring 1 is fixedly mounted with the columnar hollow magnet 2 through the rubber ring 3, and the lower end of the closely wound spring 1 is inserted into the square acrylic plate 5 through the rubber ring 3; in one of the first "spring-magnet" vibrators 4a, only one columnar hollow magnet 2 is fixedly mounted with the rubber ring 3 on the upper end of the closely wound spring 1, and in the other second "spring-magnet" vibrator 4b, two columnar hollow magnets 2 are fixedly mounted with the rubber ring 3 on the upper end of the closely wound spring 1, and the two columnar hollow magnets 2 are coaxially arranged up and down.

[0040] like Figure 1As shown, the "spring-magnet" vibrator includes two types: the first "spring-magnet" vibrator 4a is composed of a group of columnar hollow magnets 2, a rubber ring 3 and a tightly wound spring 1; the second "spring-magnet" vibrator 4b is composed of two groups of columnar hollow magnets 2, a rubber ring 3 and a tightly wound spring 1. Among them, the rubber ring 3 is fixed between the tightly wound spring 1 and the columnar hollow magnet 2 to play a tightening role, and one or two groups of columnar hollow magnets 2 are installed on the tightly wound spring 1 to change the mass of the "spring-magnet" vibrator and the magnitude of the interaction force.

[0041] The topmost columnar hollow magnets 2 of all the "spring-magnet" oscillators on the square acrylic plate 5 are kept at the same height, forming a two-dimensional lattice vibration system.

[0042] like Figure 2 As shown, the square acrylic plate 5 has circular holes distributed in a square lattice with a spacing of 20 mm, and the diameter of the circular holes is 3 mm. By installing a rubber ring 3 on the other end of the "spring-magnet" vibrator tightly wound spring 1, it can be inserted into the circular hole of the square acrylic plate 5 to make a two-dimensional grid of the "spring-magnet" vibrator.

[0043] like Figure 5 As shown, the "spring-magnet" vibrator is inserted into the circular hole of the square acrylic plate 5, and the spring is naturally straightened and the magnet height of each "spring-magnet" vibrator is consistent. By selecting the circular hole of the square acrylic plate 5, the vibrator grid points with different periods are made. By the specific combination of the first "spring-magnet" vibrator 4a and the second "spring-magnet" vibrator 4b, the physical properties of the vibrator grid points are changed.

[0044] The columnar hollow magnet 2 is installed into the circular hole of the plastic nesting component 8, and the position of the horizontal vibrator 7 is adjusted and fixed, and attention is paid to keeping the height of the plastic nesting component 8 and the columnar hollow magnet 2 at the top of the "spring-magnet" vibrator consistent.

[0045] In addition, a U-shaped acrylic plate frame 6 and a shooting assembly of a shooting device 10 are provided to observe the motion state of all the "spring-magnet" vibrators. Figure 3 As shown, the shooting assembly includes a U-shaped acrylic frame 6 and a shooting device 10; the vibrator mechanism is arranged in the U-shaped acrylic frame 6 built above, and the shooting device 10 is installed on the top of the U-shaped acrylic frame 6 above the vibrator mechanism, and the shooting device 10 is arranged downward toward the vibrator mechanism.

[0046] like Figure 3 As shown, the U-shaped acrylic plate frame 6 and the shooting device 10 constitute a simple shooting device for the experiment. The shooting device 10 adopts a shooting angle facing forward and can perform high frame rate shooting to capture details in a short time for image analysis.

[0047] like Figure 4As shown, the vibrator assembly includes a horizontal vibrator 7, a plastic nested assembly 8 and a power supply 9. The horizontal vibrator 7 and the power supply 9 are electrically connected. The output end of the horizontal vibrator 7 and the plastic nested assembly 8 are fixedly connected. The plastic nested assembly 8 is non-magnetic. The plastic nested assembly 8 is used to contact and push the columnar hollow magnet 2 in any "spring-magnet" vibrator on the square acrylic plate 5.

[0048] like Figure 4 As shown, the horizontal vibrator 7 performs periodic equal-amplitude vibration under the power supply of the power supply 9, and the amplitude is adjustable in four levels, namely 15 mm, 20 mm, 25 mm and 30 mm. The vibration frequency is continuously adjustable in the range of 2-30 Hz. The material of the plastic nesting component 8 can reduce the interference with the magnetic field and play the role of connecting the horizontal vibrator 7 and the "spring-magnet" vibrator.

[0049] The horizontal vibrator 7 is a mechanical device that can reciprocate in any set horizontal direction, is connected and driven by a power supply 9, and is equipped with an amplitude adjustment gear and a speed adjustment module to make the vibration frequency continuously adjustable within a range of 2-30 Hz.

[0050] In the specific implementation, first insert one end of the tightly wound spring 1 into the hole of the columnar hollow magnet 2, and connect them through the rubber ring 3 to form a "spring-magnet" vibrator. By changing the number of columnar hollow magnets 2, different "spring-magnet" vibrators are made, and the other ends of the tightly wound springs 1 of several "spring-magnet" vibrators are inserted into the array holes on the square acrylic plate 5 in turn, and are also connected through the rubber ring 3. The height of the columnar hollow magnet at the top of each "spring-magnet" vibrator is kept consistent, and such a group of vibrators forms a two-dimensional lattice vibration system.

[0051] Then, the plastic nested component 8 is installed on the vibration head of the horizontal vibrator 7. The horizontal vibrator 7 generates frequency-adjustable vibration under the drive of the power supply 9. The other end of the combined plastic nested component 8 is put on a "spring-magnet" vibrator on the edge to stimulate the vibration of the "spring-magnet" vibrator and drive the two-dimensional lattice vibration system to vibrate.

[0052] The U-shaped acrylic plate frame 6 is placed on the square acrylic plate 5 and the two-dimensional lattice vibration system, and the shooting device 10 is installed on the top of the U-shaped acrylic plate frame 6. The shooting device 10 is used to face the "spring-magnet" vibrator two-dimensional lattice vibration system through the U-shaped acrylic plate frame to shoot and record the vibration conditions, thereby forming a "spring-magnet" vibrator two-dimensional lattice vibration experimental device.

[0053] In a specific implementation, the closely wound spring 1 is a slender helical stainless steel spring with a length of 40.0 mm, an outer diameter of 1.5 mm, and a wire diameter of 0.2 mm. The cylindrical hollow magnet 2 is a strong neodymium iron boron magnet with an outer diameter of 6.0 mm, an inner diameter of 3.0 mm, and a height of 3.0 mm. The rubber ring 3 is an annular ring with an outer diameter of 3.0 mm, an inner diameter of 1.5 mm, and a height of 1.5 mm. The square acrylic plate 5 is a transparent hard plate with a length and width of 450 mm and a thickness of 10 mm, and circular holes with a square dot matrix distribution at 20 mm intervals, and the diameter of the circular holes is 3 mm. The U-shaped acrylic plate frame 5 is a transparent hard plate with a length of 500 mm, a width of 400 mm, a height of 600 mm, and a thickness of 20 mm.

[0054] The shooting equipment can be in various forms, such as mobile phones, cameras, etc., which can be placed on the U-shaped acrylic board frame.

[0055] The horizontal vibrator 7 is a mechanical device that can reciprocate in any horizontal direction, is driven by a power connection, and is equipped with an amplitude adjustment gear and a speed adjustment module, so that the vibration frequency can be continuously adjusted between 2 and 30 Hz. The plastic nesting component 8 can be connected to the horizontal vibrator 7 and can be sleeved on the cylindrical hollow magnet, so that the horizontal vibrator directly drives the cylindrical hollow magnet to move.

[0056] The implementation method of the device of the present invention is to closely build a number of n × n The two-dimensional grid of the "spring-magnet" oscillator, n is a natural number greater than 3, which can be set n =3,4,…20, a "spring-magnet" oscillator located on the edge of the square acrylic plate 5 is driven by a horizontal oscillator to make a frequency of f The periodic directional motion is continuously transmitted by the magnetic force of the cylindrical hollow magnet 2 between the adjacent "spring-magnet" oscillators, which in turn induces the vibration of the two-dimensional grid points. The photographic equipment of the shooting component is used to collect the images and observe the propagation effect of the vibration in the grid points and the mechanical waves formed.

[0057] After photographic recording, image processing software can be used to assist in analysis, observe and study the effects of vibration frequency and the spatial structure of the "spring-magnet" oscillator on wave propagation, and make a comparative analysis with the two-dimensional elastic lattice wave theory.

[0058] like Figure 7 As shown in the figure, the x and y coordinate axes and the position coordinates and numbers of each grid point are marked in the square grid point schematic diagram. The x-axis number is represented by p+j, and the y-axis number is represented by q+k, where p, q, j, and k are arbitrary integers. d is the interval period. There is an interaction force between adjacent grid points, and there is no direct interaction force between non-adjacent grid points.

[0059] The working principle of the present invention is as follows:

[0060] according to n × n Square two-dimensional elastic lattice theory, assuming that for the particle numbered (j, k), the mass is m j,k , with the counterclockwise rotation as the positive angle direction, the interaction proportional coefficients along the 0°, 45°, 90° and 135° directions are denoted as k j,k,1 , k j,k,2 , k j,k,3 , k j,k,4 .

[0061] For a given particle, its amplitudes (u, v) in the x and y directions satisfy the following relationship:

[0062] m j,k u' p+j,q+k = k j,k,1 (u p+j+1,q+k -u p+j,q+k )

[0063] + k j,k,2 (u p+j+1,q+k+1 -u p+j,q+k + v p+j+1,q+k+1 -v p+j,q+k ) / 2

[0064] + k j,k,4 (u p+j-1,q+k+1 -u p+j,q+k + v p+j-1,q+k+1 -v p+j,q+k ) / 2

[0065] + k j-1,k,1 (u p+j-1,q+k -u p+j,q+k )

[0066] + k j-1,k-1,2 (u p+j-1,q+k-1 -u p+j,q+k + v p+j-1,q+k-1 -v p+j,q+k ) / 2

[0067] + k j+1,k-1,4 (u p+j+1,q+k-1 -u p+j,q+k + v p+j+1,q+k-1 -v p+j,q+k ) / twenty one)

[0068] m j,k v' p+j,q+k = k j,k,3 (v p+j,q+k+1 -vp+j,q+k )

[0069] + k j,k,2 (v p+j+1,q+k+1 -v p+j,q+k + u p+j+1,q+k+1 -u p+j,q+k ) / 2

[0070] + k j,k,4 (v p+j-1,q+k+1 -v p+j,q+k + u p+j-1,q+k+1 -u p+j,q+k ) / 2

[0071] + k j-1,k,3 (v p+j,q+k-1 -v p+j,q+k )

[0072] + k j-1,k-1,2 (v p+j-1,q+k-1 -v p+j,q+k + u p+j-1,q+k-1 -u p+j,q+k ) / 2

[0073] + k j+1,k-1,4 (v p+j+1,q+k-1 -v p+j,q+k + u p+j+1,q+k-1 -u p+j,q+k ) / twenty two)

[0074] Among them, m j,k u' p+j,q+k Indicates mass m j,k and the second-order derivative of the x-direction displacement with time u' p+j,q+k The product of j, k v' p+j,q+k Indicates mass m j,k and the second-order derivative v' of the displacement in the y direction with time p+j,q+k The product of, j and k are positive integers, p and q are any non-negative integers, u' p+j,q+k It represents the second-order derivative of the displacement of the particle numbered (p+j,q+k) along the x direction with time, that is, the vibration acceleration, v' p+j,q+k It represents the second-order derivative of the displacement of the particle numbered (p+j,q+k) along the y direction with time, that is, the vibration acceleration. In order to simplify the symbolic form, p and q are abbreviated and m is used instead. j,k represents the mass of the particle numbered (p+j,q+k), u p+j,q+k Indicates the displacement of the particle numbered (p+j,q+k) along the x direction, v p+j,q+k Indicates the displacement of the particle numbered (p+j,q+k) along the y direction. Similarly, u p+j,q+k+1represents the displacement of the particle numbered (p+j,q+k+1) along the x direction, v p+j,q+k+1 Indicates the displacement of the particle numbered (p+j,q+k+1) along the y direction, u p+j,q+k-1 represents the displacement of the particle numbered (p+j,q+k-1) along the x direction, v p+j,q+k-1 Indicates the displacement of the particle numbered (p+j,q+k-1) along the y direction, u p+j+1,q+k Indicates the displacement of the particle numbered (p+j+1,q+k) along the x direction, v p+j+1,q+k Indicates the displacement of the particle numbered (p+j+1,q+k) along the y direction, u p+j-1,q+k represents the displacement of the particle numbered (p+j-1,q+k) along the x direction, v p+j-1,q+k Indicates the displacement of the particle numbered (p+j-1,q+k) along the y direction, u p+j-1,q+k-1 represents the displacement of the particle numbered (p+j-1,q+k-1) along the x direction, v p+j-1,q+k-1 Indicates the displacement of the particle numbered (p+j-1,q+k-1) along the y direction, u p+j-1,q+k+1 represents the displacement of the particle numbered (p+j-1,q+k+1) along the x direction, v p+j-1,q+k+1 Indicates the displacement of the particle numbered (p+j-1,q+k+1) along the y direction, u p+j+1,q+k-1 represents the displacement of the particle numbered (p+j+1,q+k-1) along the x direction, v p+j+1,q+k-1 Indicates the displacement of the particle numbered (p+j+1,q+k-1) along the y direction, u p+j+1,q+k+1 Indicates the displacement of the particle numbered (p+j+1,q+k+1) along the x direction, v p+j+1,q+k+1 It indicates the displacement of the particle numbered (p+j+1,q+k+1) along the y direction.

[0075] Substitute the following tentative solution into the above formulas (1) and (2):

[0076] u p+j,q+k =A j,k exp i((p+j) γ x +(q+k) γ y -ωt) (3)

[0077] v p+j,q+k =B j,k exp i((p+j) γ x +(q+k) γ y -ωt) (4)

[0078] Where i is the imaginary unit, A j,k and B j,kis the particle amplitude, ω is the vibration angular frequency, γ x and γ y is the component of the reduced wave vector along the x and y directions. When the number of grid points is large enough, the two-dimensional periodic boundary condition is used, and the above equation can be converted into the solution of the eigenvalue equation:

[0079] (S(γ x , γ y )-ω 2 I)A=0 (5)

[0080] Among them, I is the unit matrix, A is the displacement matrix, and S is the lattice action matrix. From this, we can solve the γ corresponding to the known ω angular frequency. x and γ y , and then we can analyze the vibration modes of two-dimensional lattices, mechanical wave properties, band gaps and passbands, etc.

[0081] Specifically, by solving equation (5), we can calculate the γ corresponding to any angular frequency ω: x and γ y In general, a value of angular frequency ω can be obtained with a series of solvable γ x and γ y This means that for this angular frequency ω, the vibration displacement of each elastic grid point can be expressed by the corresponding wave equations (3) and (4), showing the permeability of this angular frequency. When one of the elastic grid points is driven by an external fixed angular frequency ω, it will cause the vibration of all grid points in the entire range, forming a propagable lattice wave. However, under certain mass and elastic distribution conditions, some angular frequency ω values ​​do not have a solution in equation (5). x and γ y value. At this time, equations (3) and (4) will produce dissipative terms, becoming functions that gradually decay with spatial extension, rather than wave equations. This shows that the elastic grid is impassable to this angular frequency. When an external fixed angular frequency ω is used to drive one of the elastic grid points, the vibration will gradually decay and stop in a smaller range, forming a localized vibration. This is the wave propagation and localized behavior caused by the vibration mode. The corresponding ω and γ x and γ y The relationship is called the band relationship. The band relationship that passes the lattice wave is called the passband, and the band relationship that blocks the lattice wave is called the forbidden band.

[0082] During the implementation, on the one hand, the parameter to be regulated is the frequency of driving the lattice point vibration, corresponding to the angular frequency ω. On the other hand, when making two-dimensional elastic lattices, the mass of each lattice point and the strength of the surrounding interaction force can be adjusted as needed. This adjustment will change the specific values ​​of each term in equations (1) and (2), affect the S matrix, and ultimately affect the energy band relationship. By adjusting the vibration frequency, experimental demonstration, observation and research of passband and forbidden band can be achieved, and the vibration mode of two-dimensional elastic lattices can be explored.

[0083] The implementation of the specific embodiment is as follows:

[0084] Figure 6 The complete schematic diagram of the device of the present invention is shown. According to the research needs, build the required periodicity and structure of the "spring-magnet" vibrator two-dimensional grid. After building the "spring-magnet" vibrator two-dimensional grid array with a specific period and structure, set the end fixing point position of the horizontal vibrator 7 of the driving part to adjust the amplitude of the vibration. Insert a vibrator magnet into the hollow of the plastic nesting component 8 of the driving part, and fix the horizontal vibrator 7 to ensure that the amplitude of the driven vibrator is obvious and will not be attracted to other vibrators. Slowly adjust the power transformer knob to adjust the vibration frequency of the horizontal vibrator 7. Adjust the vibration direction according to experimental needs.

[0085] After setting the vibration amplitude, frequency and direction, the vibration video of the two-dimensional "spring-magnet" vibrator grid is recorded by the shooting equipment. The vibration and mechanical wave propagation of the array are analyzed and recorded using the image software. The image software can track and record the motion function of any "spring-magnet" vibrator over time on the two-dimensional plane. The "time-displacement" data of the "spring-magnet" vibrator is obtained through processing and analysis. Then, through Fourier transform analysis, the vibration spectrum of the "spring-magnet" vibrator can be obtained, including the vibration amplitude and frequency. By analyzing the motion of each "spring-magnet" vibrator, the vibration mode and mechanical wave propagation characteristics of the two-dimensional grid can be obtained, and the distribution of the vibration frequency, amplitude and direction of the vibrator in the two-dimensional plane can be obtained.

[0086] By adjusting the vibration amplitude, frequency and direction parameters of the horizontal oscillator 7, tracking, recording, analyzing and data processing are performed on each "spring-magnet" oscillator to obtain the movement of the "spring-magnet" oscillator under different parameter conditions, as well as the collective behavior of the "spring-magnet" oscillator lattice driven by different amplitudes and frequencies, such as the speed, direction and amplitude attenuation of mechanical wave propagation, which helps to study the vibration problems of two-dimensional lattices and the application of phonon energy bands.

[0087] Through the explanation of the above implementation process, the present invention is more fully applied to the observation of mechanical wave propagation in a two-dimensional magnetic oscillator lattice array, forming a relatively complete experimental device and experimental method, demonstrating the innovation, integrity and advancement of the present invention, as well as its operability in application.

Claims

1. A "spring-magnet" oscillator two-dimensional lattice vibration experimental device, characterized in that: It includes a vibration component, a shooting component and a vibrator mechanism; A vibrator mechanism, wherein a plurality of vibrators are distributed on the vibrator mechanism, each vibrator is provided with a magnet, and the plurality of vibrators influence each other by magnetism; The vibrator mechanism comprises a square acrylic plate (5) and two different types of "spring-magnet" vibrators arranged on the square acrylic plate (5); the square acrylic plate (5) is provided with array-distributed holes for mounting the "spring-magnet" vibrators; each type of "spring-magnet" vibrator comprises a closely wound spring (1), a columnar hollow magnet (2) and a rubber ring (3); the upper end of the closely wound spring (1) is sleeved with the columnar hollow magnet (2) via the rubber ring (3); the lower end of the closely wound spring (1) is inserted into the square acrylic plate (5); in one type of "spring-magnet" vibrator (4a), only one columnar hollow magnet (2) is sleeved on the upper end of the closely wound spring (1) via the rubber ring (3); in another type of "spring-magnet" vibrator (4b), two columnar hollow magnets (2) are sleeved on the upper end of the closely wound spring (1) via the rubber ring (3); The vibration-starting component is located on the side of the vibrator mechanism and is used to touch the vibrator in the vibrator mechanism to start the vibration and then conduct a two-dimensional grid vibration experiment; The shooting component is located above the oscillator mechanism and is used to shoot the two-dimensional grid point vibration experimental conditions of the oscillator mechanism.

2. A "spring-magnet" oscillator two-dimensional lattice vibration experimental device according to claim 1, characterized in that: The topmost columnar hollow magnets (2) of all the "spring-magnet" vibrators on the square acrylic plate (5) are kept at the same height, forming a two-dimensional lattice vibration system.

3. The "spring-magnet" oscillator two-dimensional lattice vibration experimental device according to claim 1, characterized in that: The shooting assembly comprises a U-shaped acrylic plate frame (6) and a shooting device (10); the vibrator mechanism is arranged in the U-shaped acrylic plate frame (6) built above, the shooting device (10) is installed on the top of the U-shaped acrylic plate frame (6) above the vibrator mechanism, and the shooting device (10) is arranged towards the vibrator mechanism.

4. The "spring-magnet" oscillator two-dimensional lattice vibration experimental device according to claim 1, characterized in that: The vibration component comprises a horizontal vibrator (7), a plastic nesting component (8) and a power supply (9); the horizontal vibrator (7) and the power supply (9) are electrically connected; the output end of the horizontal vibrator (7) and the plastic nesting component (8) are fixedly connected; the plastic nesting component (8) is used to contact and push the columnar hollow magnet (2) in the "spring-magnet" vibrator on the square acrylic plate (5).

5. The "spring-magnet" oscillator two-dimensional lattice vibration experimental device according to claim 4 is characterized in that: The horizontal vibrator (7) is a mechanical device capable of reciprocating along any set horizontal direction, is connected and driven by the power source (9), and is equipped with an amplitude adjustment gear and a speed adjustment module, so that the vibration frequency can be continuously adjusted within a range of 2-30 Hz.

6. A two-dimensional lattice point vibration method applied to the two-dimensional lattice point vibration experimental device of the "spring-magnet" vibrator according to claim 1, characterized in that: In the center of the square acrylic plate (5), a number of n × n The "spring-magnet" vibrator two-dimensional grid, n is a natural number greater than 3, and a "spring-magnet" vibrator located on the edge of the square acrylic plate (5) is driven by a horizontal vibrator to make a frequency of f The periodic directional movement is continuously transmitted by the magnetic force of the cylindrical hollow magnets (2) between the adjacent "spring-magnet" vibrators, thereby inducing the vibration of the two-dimensional grid points. The photographic equipment of the shooting component is used to collect the images and observe the propagation effect of the vibration in the grid points and the mechanical waves formed.

Images