Phononic crystal simulation device and method, phononic crystal detection method, galton plate

Abstract

The present disclosure provides a phononic crystal simulation device and method, a phononic crystal detection method and a Galton plate. The present disclosure adopts a signal generation system composed of a signal source, a power amplifier and a loudspeaker, an acoustic wave receiving system composed of a microphone, a signal amplifier and an oscilloscope, and improves the nail array structure of the Galton plate to simulate the phononic crystal structure, so that the mechanism of the Bragg scattering type and the local resonance type for forming the band gap of the phononic crystal and the band gap characteristics of the phononic crystal can be conveniently and accurately explored from the experimental point of view. In addition, the present disclosure uses the Galton plate to simulate the phononic crystal. Since the phononic crystal and the Galton plate have great structural commonality, the Galton plate has a periodic nail array structure. The Galton plate is used as a simulation model of a two-dimensional phononic crystal to explore the band gap characteristics, and accurate research results can be obtained.

Description

Technical Field

[0001] This disclosure relates to the field of signal processing, particularly to the field of acoustic wave shielding and the field of solid-state physics teaching in university physics experimental courses, and discloses a phonon crystal simulation device and method, a phonon crystal detection method, and a Galton plate. Background Technology

[0002] In a crystal structure, the region where electrons can move freely is called the "conduction band," and between adjacent conduction bands is an energy gap region where electrons cannot move; this region is called the "forbidden band." Phonons are energy quanta that describe lattice vibrations. In a crystal structure, they reflect the properties of lattice wave propagation. Similar to the motion of electrons in a crystal structure, they also have forbidden bands and conduction bands, but their formation mechanisms are different.

[0003] Phononic crystals are a concept proposed in recent years, referring to materials or structures with periodic distributions of elastic constants and density, and possessing band gap characteristics. Currently, most university physics textbooks lack corresponding feasible research projects in the solid-state physics chapters. Summary of the Invention

[0004] This disclosure provides at least one phonon crystal simulation apparatus and method, phonon crystal detection method, and Galton plate for simulating phonon crystals.

[0005] According to one aspect of this disclosure, a phonon crystal simulation device is provided, including a signal source, a power amplifier, a loudspeaker, a Galton board, a microphone, a signal amplifier, and an oscilloscope;

[0006] The signal source is used to generate signals;

[0007] The power amplifier is connected to the signal source, performs power amplification on the signal, and sends the amplified signal to the speaker.

[0008] The loudspeaker is disposed at the notch of the Galton plate and is connected to the power amplifier; under the action of the amplified signal, the loudspeaker emits sound waves of a specific frequency into the Galton plate;

[0009] The Galton plate is used to simulate a phononic crystal;

[0010] The microphone is used to detect sound waves inside the Galton plate;

[0011] The signal amplifier amplifies the detected sound wave signal and sends the amplified sound wave signal to the oscilloscope.

[0012] The oscilloscope is connected to the signal amplifier and is used to detect the amplitude-frequency characteristics of the amplified acoustic signal and generate an amplitude-frequency characteristic diagram; wherein the amplitude-frequency characteristic diagram is used to determine the bandgap characteristics of the phononic crystal.

[0013] In one possible implementation, the Galton plate includes a vibrator, a plate wall, and a cover plate; wherein the vibrator is disposed on a bottom plate within a cavity formed by the plate wall and the cover plate; and both the plate wall and the cover plate are provided with sound-absorbing inner walls.

[0014] In one possible implementation, the oscillator is arranged according to a periodic structure; the periodic structure includes a square structure and a triangular structure; the horizontal spacing of the lattice units formed by the oscillator is a first preset length, and the vertical spacing of the lattice units formed by the oscillator is a second preset length.

[0015] In one possible implementation, the oscillator includes a Bragg scattering oscillator or a localized resonance oscillator;

[0016] The Bragg scattering oscillator includes a columnar body, made of materials including PVC and wood; the columnar body includes a cylindrical, T-shaped, or cross-shaped columnar body;

[0017] The resonant oscillator includes a resonant body; the resonant body includes an empty rubber tube or a resonant column filled with particles.

[0018] In one possible implementation, the signal amplifier includes: a first resistor, a second resistor, a third resistor, a fourth resistor, a first capacitor, a second capacitor, and an operational amplifier;

[0019] One end of the microphone is grounded, and the other end is connected to one end of the first resistor and the first capacitor. The other end of the first resistor is connected to the power supply. The other end of the first capacitor is connected to one end of the second resistor. The other end of the second resistor is connected to one end of the third resistor and the inverting input terminal of the operational amplifier. The other end of the third resistor is connected to the output terminal of the operational amplifier. One end of the second capacitor is connected to the non-inverting input terminal of the operational amplifier, and the other end of the second capacitor is connected to ground. One end of the fourth resistor is connected to the non-inverting input terminal of the operational amplifier, and the other end of the fourth resistor is connected to ground. The output terminal of the operational amplifier is connected to the oscilloscope.

[0020] In one possible implementation, the microphone, signal amplifier, and oscilloscope have a frequency range of 200–7000 Hz.

[0021] According to another aspect of this disclosure, a Galton plate is provided, comprising the Galton plate described in any of the preceding claims.

[0022] According to another aspect of this disclosure, a phonon crystal simulation method is provided, applied to the phonon crystal simulation apparatus described in any of the preceding claims, comprising:

[0023] A signal is generated using the signal source and sent to the power amplifier;

[0024] The power amplifier receives the signal sent by the signal source, performs power amplification on the signal, and sends the amplified signal to the speaker.

[0025] The loudspeaker, under the influence of the amplified signal, emits sound waves of a specific frequency into the Galton plate; the Galton plate is used to simulate a phonon crystal.

[0026] The microphone is used to detect sound waves inside the Galton plate;

[0027] The signal amplifier is used to amplify the sound wave signal detected by the microphone, and the amplified sound wave signal is sent to the oscilloscope.

[0028] The amplitude-frequency characteristics of the amplified acoustic signal are detected using the oscilloscope, and an amplitude-frequency characteristic diagram is generated; wherein, the bandgap characteristics of the phononic crystal can be determined by the change between the amplitude-frequency characteristic diagram corresponding to the Galton plate including the oscillator and the amplitude-frequency characteristic diagram corresponding to the Galton plate excluding the oscillator.

[0029] According to another aspect of this disclosure, a method for detecting phonon crystals is provided, comprising:

[0030] Using the phonon crystal simulation method described above, the first amplitude-frequency response diagram of the signal is determined, and the first amplitude response diagram of the signal is determined using the first amplitude-frequency response diagram;

[0031] The oscillator in the Galton plate is removed, and the second amplitude-frequency characteristic diagram of the signal is determined using the above-mentioned phonon crystal simulation method. The second amplitude-frequency characteristic diagram of the signal is then used to determine the second amplitude characteristic of the signal.

[0032] The bandgap characteristics of the phononic crystal are determined using the first amplitude characteristic and the second amplitude characteristic.

[0033] The phonon crystal simulation apparatus and method disclosed herein employ a signal generation system consisting of a signal source, a power amplifier, and a loudspeaker, and a sound wave receiving system consisting of a microphone, a signal amplifier, and an oscilloscope. An improved Galton plate pin array structure is used to simulate the phonon crystal structure, enabling convenient and accurate experimental investigation of the mechanisms of Bragg scattering and local resonance in phonon crystal bandgap formation and the bandgap characteristics of phonon crystals. Furthermore, this disclosure utilizes a Galton plate to simulate the phonon crystal. Due to the significant structural similarities between phonon crystals and Galton plates—Galton plates possessing a periodic pin array structure—using the Galton plate as a simulation model for two-dimensional phonon crystals to investigate bandgap characteristics yields accurate research results.

[0034] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0035] The accompanying drawings are provided to better understand this solution and do not constitute a limitation of this disclosure. Wherein:

[0036] Figure 1 This is a schematic diagram of the phonon crystal simulation device according to the present disclosure;

[0037] Figure 2 This is a schematic diagram of a signal amplifier based on an embodiment of this disclosure;

[0038] Figure 3A It is based on the Bragg scattering diagram in the embodiments of this disclosure;

[0039] Figure 3B This is based on the Galton plate Bragg scattering principle diagram in the embodiments of this disclosure;

[0040] Figure 3C This is a schematic diagram of an equivalent spring system based on the principle of simulated local resonance in the embodiments of this disclosure;

[0041] Figure 4 It is based on the amplitude-frequency response curve of the sound wave received by the microphone or signal amplifier in the embodiments of this disclosure;

[0042] Figure 5A This is a physical diagram showing that the oscillator in the embodiments of this disclosure is a triangular array of wooden rods;

[0043] Figure 5B This is a graph showing the variation of the K value of a triangular array of wooden rods as the oscillator in the embodiments of this disclosure;

[0044] Figure 6A This is a physical diagram showing that the oscillators in the embodiments of this disclosure are arranged in a T-shape and a square array.

[0045] Figure 6B This is a graph showing the variation of K values ​​for a T-shaped, square array of oscillators in the embodiments of this disclosure;

[0046] Figure 7A This is a physical image of the vibrator, which is a rubber tube filled with particles arranged in a square array, according to the embodiments of this disclosure.

[0047] Figure 7B This is a graph showing the K-value variation of a square array of rubber cylinder-filled particles as the oscillator in the embodiments of this disclosure. Detailed Implementation

[0048] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0049] The technical solution of this disclosure will be described below through specific embodiments.

[0050] like Figure 1 The diagram shown is a schematic diagram of the phonon crystal simulation device of this embodiment. Specifically, the device of this embodiment may include: a signal source 110, a power amplifier 120, a speaker 130, a Galton board 140, a microphone 150, a signal amplifier 160, and an oscilloscope 170.

[0051] The signal source 110 is used to generate a signal; the power amplifier 120 is connected to the signal source 110, amplifies the signal, and sends the amplified signal to the speaker 130; the speaker 130 is disposed at the notch of the Galton plate 140 and is connected to the power amplifier 120; under the action of the amplified signal, the speaker 130 emits sound waves of a specific frequency into the Galton plate 140; the Galton plate 140 is used to simulate a phonon crystal; the microphone 150 is used to detect the sound waves inside the Galton plate 140; the signal amplifier 160 amplifies the signal of the sound waves detected by the microphone 150 and sends the amplified sound wave signal to the oscilloscope 170. The oscilloscope 170 is connected to the signal amplifier 160 and is used to detect the amplitude-frequency characteristics of the amplified acoustic signal and generate an amplitude-frequency characteristic diagram. The amplitude-frequency characteristic diagram is used to determine the bandgap characteristics of the phononic crystal. Specifically, the bandgap characteristics of the phononic crystal can be determined by the change between the amplitude-frequency characteristic diagram corresponding to the Galton plate including the oscillator and the amplitude-frequency characteristic diagram corresponding to the Galton plate excluding the oscillator.

[0052] Based on the significant structural similarities between phononic crystals and Galton plates, the Galton plate is used as a simulation model of two-dimensional phononic crystals to explore bandgap characteristics. This disclosure also reveals a similar bandgap: a collective attenuation of energy within a certain frequency range, termed the "bandgap," and a collective amplification of energy, termed the "conduction band."

[0053] like Figure 1 As shown, the Galton plate includes an oscillator, a plate wall, and a cover plate; wherein the oscillator is disposed on the bottom plate within the cavity formed by the plate wall and the cover plate; both the plate wall and the cover plate are provided with sound-absorbing inner walls. The oscillator is arranged in a periodic structure; the periodic structure includes a square structure and a triangular structure; the horizontal spacing of the lattice units formed by the oscillator is a first preset length, and the vertical spacing of the lattice units formed by the oscillator is a second preset length. Here, the first preset length and the second preset length can be equal, for example, both are 5 centimeters.

[0054] Based on the significant structural similarities between phononic crystals and Galton plates, Galton plates are used as a simulation model for two-dimensional phononic crystals, opening up a new experimental field for solid-state physics in university physics experiments. At the same time, Galton plates are given a completely new application: exploring bandgap characteristics.

[0055] Current research suggests two mechanisms for the generation of band gaps in phononic crystals: Bragg scattering and local resonance. In the former, the oscillator is made of a single material, and its periodicity plays a dominant role. In the latter, the oscillator is made of composite materials, and the resonance characteristics of a single scatterer play a dominant role. The oscillator includes either a Bragg scattering oscillator or a local resonance oscillator. The Bragg scattering oscillator can be a columnar structure or other structures of various shapes and materials, such as a solid cylindrical wooden rod, or a T-shaped or cross-shaped PVC column. The resonance oscillator can be various self-designed resonators, such as a hollow rubber tube or a resonant column filled with particles.

[0056] In some embodiments, the Bragg scattering oscillator is a solid wooden rod, which may be cylindrical, T-shaped, or cross-shaped; or, the resonant oscillator is a hollow cylinder, which may be made of rubber or paper; the hollow cylinder may be unfilled or filled with granular material, including alumina beads. In some embodiments, the frequency range of the signal amplifier is 800–7000 Hz. 800–7000 Hz is the stable operating frequency range of the signal amplifier.

[0057] The number of microphones mentioned above can be three.

[0058] In some embodiments, such as Figure 2As shown, the signal amplifier includes: a first resistor R1, a second resistor R2, a third resistor R3, a fourth resistor R4, a first capacitor C1, a second capacitor C2, and an operational amplifier OPA.

[0059] One end of the microphone's electret is grounded, and the other end is connected to one end of the first resistor R1 and the first capacitor C1. The other end of the first resistor R1 is connected to the power supply Vcc. The other end of the first capacitor C1 is connected to one end of the second resistor R2. The other end of the second resistor R2 is connected to one end of the third resistor R3 and the inverting input of the comparator operational amplifier OPA. The other end of the third resistor R3 is connected to the output of the operational amplifier OPA. One end of the second capacitor C2 is connected to the non-inverting input of the operational amplifier OPA, and the other end of the second capacitor C2 is grounded. One end of the fourth resistor R4 is connected to the non-inverting input of the operational amplifier OPA, and the other end of the fourth resistor R4 is grounded. The output of the operational amplifier OPA is connected to the oscilloscope.

[0060] This disclosure also provides a Galton plate, which is the same as the Galton plate in the above embodiments.

[0061] This disclosure also provides a phonon crystal simulation method, applied to the phonon crystal simulation device in the above embodiments, comprising the following steps:

[0062] Step 1: Generate a signal using the signal source and send it to the power amplifier.

[0063] Step 2: The power amplifier receives the signal sent by the signal source, performs power amplification on the signal, and sends the amplified signal to the speaker.

[0064] Step 3: Under the action of the amplified signal, the loudspeaker emits sound waves of a specific frequency into the Galton plate; the Galton plate is used to simulate a phonon crystal.

[0065] Step 4: Use the microphone to detect the sound waves inside the Galton plate.

[0066] Step 5: Use the signal amplifier to amplify the sound wave signal detected by the microphone, and send the amplified sound wave signal to the oscilloscope.

[0067] Step 6: Use the oscilloscope to detect the amplitude-frequency characteristics of the amplified acoustic signal and generate an amplitude-frequency characteristic diagram; wherein, the bandgap characteristics of the phononic crystal can be determined by the change between the amplitude-frequency characteristic diagram corresponding to the Galton plate including the oscillator and the amplitude-frequency characteristic diagram corresponding to the Galton plate excluding the oscillator.

[0068] This disclosure also provides a method for detecting phonon crystals, including the following steps:

[0069] Step 1: Using the phonon crystal simulation method in the above embodiments, determine the first amplitude-frequency characteristic diagram of the signal, and use the first amplitude-frequency characteristic diagram to determine the first amplitude characteristic of the signal. An oscillator is provided in the Galton plate.

[0070] Step 2: Remove the oscillator from the Galton plate, determine the second amplitude-frequency characteristic diagram of the signal using the phonon crystal simulation method in the above embodiment, and determine the second amplitude characteristic of the signal using the second amplitude-frequency characteristic diagram; in this step, no oscillator is set in the Galton plate.

[0071] Step 3: Determine the bandgap characteristics of the phononic crystal using the first amplitude characteristic and the second amplitude characteristic.

[0072] Specifically, the band gap characteristic K can be determined using the following formula:

[0073] or

[0074] In the formula, A0 represents the amplitude corresponding to the second amplitude characteristic, and A represents the amplitude corresponding to the first amplitude characteristic.

[0075] When the value of K is greater than 1, the energy of the sound wave increases; when the value of K is less than 1, the energy of the sound wave decreases; when the value of K is equal to 1, the energy of the sound wave remains unchanged.

[0076] The principles and experimental verification process involved in this disclosure will be explained below.

[0077] principle:

[0078] (1) Band theory: In a crystal structure, the region where electrons can move freely is called the "conduction band," and between adjacent conduction bands is an energy gap region where electrons cannot move, called the "forbidden band." Phonons are quantum numbers describing lattice vibrations. In crystal structures, they reflect the properties of elastic wave propagation. Similar to the motion of electrons in crystal structures, they also have forbidden bands and conduction bands, but their motion mechanisms are different. In this simulation experiment, similar band gaps were also found. That is, energy collectively decays within a certain frequency range, which is called the "forbidden band"; while energy collectively amplifies, which is called the "conduction band."

[0079] (2) Bragg scattering: Bragg scattering is a method for studying the internal structure of matter by utilizing the scattering of X-rays by crystals. For example... Figure 3AAs shown in the figure, d represents the lattice constant, and θ represents the scattering angle. When X-rays are scattered by atoms in the crystal, diffraction fringes are observed in the observation area, thus determining the internal structure of the crystal. The Galton plate structure is used to investigate the bandgap characteristics of localized phononic crystals; its scattering mechanism is as follows: Figure 3B As shown.

[0080] To simplify the problem description, we will analyze the scattering mechanism using a plane harmonic wave as an example. Suppose a loudspeaker O emits plane harmonic waves Y1 and Y2. When Y1 and Y2 encounter an oscillator, Bragg scattering occurs, changing the propagation path to form Y1' and Y2'. The sound waves received by a microphone or signal amplifier interfere at point P. Let the path lengths of the two waves be l1 and l2, respectively. Then...

[0081]

[0082] in:

[0083]

[0084] Conditions for constructive and destructive interference:

[0085]

[0086] in

[0087] Δl=l BC +l CD ≈2dsinθ3≈2dsinθ2 (7)

[0088] Obviously, formula (7) is only a special case. The actual interference effect is the result of the participation of all oscillators. It includes the scattering of all oscillators, the result of the interference between the direct wave emitted by the loudspeaker and the scattered wave, and the result of the interference after multiple scatterings between oscillators. Their combined effect may lead to the existence of a band gap.

[0089] (3) Local Resonance Mechanism: Under the excitation of an elastic wave at a specific frequency, each oscillator resonates and interacts with the direct wave, thereby reducing the propagation of the scattered wave. Since the generation of the local resonance bandgap depends on the interaction between the resonance characteristics of the scatterer itself and the traveling wave in the matrix, its bandgap frequency is closely related to the inherent vibration characteristics of a single scatterer. In this disclosure, the phonon crystal is equivalent to a spring system, the schematic diagram of which is shown below. Figure 3C As shown in the diagram, the black spheres represent the granular material filling the composite oscillator. Under the influence of the acoustic driving force F, air resistance F1, and elastic restoring force F2, the oscillator m begins to move with a horizontal velocity v. Its principle can be described using the forced vibration equation:

[0090]

[0091] Where the sound wave driving force F = F0cosωt; the elastic restoring force F2 = -kx; and the air resistance... Its steady-state solution is

[0092] x=Acos(ωt-ψ) (9)

[0093] in:

[0094] in: The damping coefficient; The natural frequency. When the frequency of the driving force is... When forced vibrations reach their maximum amplitude, the phenomenon is called resonance.

[0095] Clearly, the formation of the band gap in a localized resonant phononic crystal is the result of the combined effects of Bragg scattering and composite oscillator resonance. When the frequency of the incident elastic wave reaches the natural frequency of the composite oscillator, the oscillator begins to resonate, thereby consuming the energy of the reflected wave and forming the band gap. When it is far from its characteristic frequency, it is equivalent to an ordinary oscillator.

[0096] Experimental methods:

[0097] (1) System calibration:

[0098] Before the experiment, the amplitude-frequency response curves of the loudspeaker, microphone, signal amplifier, and oscilloscope were calibrated in the absence of a structure, i.e., without an oscillator, as follows: Figure 4 As shown, it works normally in the 100-8000Hz frequency range. However, considering the influence of the plate wall reflection on the experiment below 800Hz, the frequency range of 800-7000Hz was determined as the signal stability area of ​​the microphone, signal amplifier, and oscilloscope, and this was used as the bandwidth range of the experiment.

[0099] (2) Experimental procedures:

[0100] Unstructured amplitude data is denoted as A0, and structured amplitude data, i.e., amplitude data with an oscillator, is denoted as A. By comparing the structured and unstructured data of the internal cavity of the Galton plate at the same frequency, the rate of change of amplitude data (denoted as K value) is obtained.

[0101]

[0102] The value of K is plotted as a rate of change curve. The relationship between the value of K and 1 reflects the rise and fall of sound intensity energy. If the value of K is less than 1, the sound wave energy is weakened after passing through the oscillator structure; if the value of K is greater than 1, the sound wave energy is strengthened after passing through the oscillator structure.

[0103] Data measurement:

[0104] (a) Bragg scattering type

[0105] To discuss the Bragg scattering mechanism in detail, we set the transverse oscillator region to be 60 cm and the longitudinal oscillator region to be 30 cm. The transverse spacing (first preset length) of the lattice units formed by the oscillator is 5 cm, and the longitudinal spacing (second preset length) of the lattice units is 5 cm. The K-values ​​of oscillators with different arrangements and shapes are measured below.

[0106] like Figure 5A The oscillators are arranged in a triangular array, and each oscillator is a solid, round wooden rod. For example... Figure 5B As shown, a typical bandgap is clearly present under a triangular array, such as... Figure 5B In the mid-gray regions BG1 and BG2, the band gaps under the triangular structure are located in the ranges of [1.2, 2.0] kHz and [3.6, 4.5] kHz, respectively.

[0107] like Figure 6A The aforementioned pre-set length oscillators are arranged in a square array with T-shaped oscillators. Figure 6B It can be seen that typical band gaps are clearly present, such as Figure 6B The gray area shows that the band gaps of this structure are located in the ranges of [1.4, 3.1] kHz and [3.7, 5.7] kHz, respectively.

[0108] (ii) Local resonance type

[0109] like Figure 7A As shown, using the same preset length square array pattern as described above, a rubber tube with a diameter of 2.0 cm was designed, and 4 mm diameter alumina beads were filled inside as oscillators to explore the band gap characteristics of the local resonant phonon crystal.

[0110] like Figure 7B As shown in the figure, the typical band gaps caused by Bragg scattering still exist. In the gray area of ​​the figure, the band gaps of the composite rubber cylinder oscillator are located in the ranges of [1.5, 2.0] kHz and [3.5, 5.7] kHz, respectively.

[0111] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A phonon crystal simulation device, characterized in that, This includes a signal source, power amplifier, speaker, Galton board, microphone, signal amplifier, and oscilloscope; The signal source is used to generate signals; The power amplifier is connected to the signal source, performs power amplification on the signal, and sends the amplified signal to the speaker. The loudspeaker is disposed at the notch of the Galton plate and is connected to the power amplifier; under the action of the amplified signal, the loudspeaker emits sound waves of a specific frequency into the Galton plate; The Galton plate is used to simulate a phononic crystal; The microphone is used to detect sound waves inside the Galton plate; The signal amplifier amplifies the sound wave signal detected by the microphone and sends the amplified sound wave signal to the oscilloscope. The oscilloscope is connected to the signal amplifier and is used to detect the amplitude-frequency characteristics of the amplified acoustic signal and generate an amplitude-frequency characteristic diagram; wherein the amplitude-frequency characteristic diagram is used to determine the bandgap characteristics of the phononic crystal.

2. The apparatus according to claim 1, characterized in that, The Galton plate includes a vibrator, a plate wall, and a cover plate; wherein the vibrator is disposed on the bottom plate within the cavity formed by the plate wall and the cover plate; both the plate wall and the cover plate are provided with sound-absorbing inner walls.

3. The apparatus according to claim 2, characterized in that, The oscillator is arranged according to a periodic structure; the periodic structure includes a square structure and a triangular structure; the horizontal spacing of the lattice units formed by the oscillator is a first preset length, and the vertical spacing of the lattice units formed by the oscillator is a second preset length.

4. The apparatus according to claim 2, characterized in that, The oscillator includes a Bragg scattering type oscillator or a local resonance type oscillator; The Bragg scattering oscillator includes a columnar body, made of materials including PVC and wood; the columnar body includes a cylindrical, T-shaped, or cross-shaped columnar body; The resonant oscillator includes a resonant body; the resonant body includes an empty rubber tube or a resonant column filled with particles.

5. The apparatus according to claim 1, characterized in that, The signal amplifier includes: a first resistor, a second resistor, a third resistor, a fourth resistor, a first capacitor, a second capacitor, and an operational amplifier; One end of the microphone is grounded, and the other end is connected to one end of the first resistor and the first capacitor. The other end of the first resistor is connected to the power supply. The other end of the first capacitor is connected to one end of the second resistor. The other end of the second resistor is connected to one end of the third resistor and the inverting input of the operational amplifier. The other end of the third resistor is connected to the output of the operational amplifier. One end of the second capacitor is connected to the non-inverting input of the operational amplifier, and the other end of the second capacitor is grounded. One end of the fourth resistor is connected to the non-inverting input of the operational amplifier, and the other end of the fourth resistor is grounded. The output of the operational amplifier is connected to the oscilloscope.

6. The apparatus according to claim 1, characterized in that, The frequency range of the microphone, signal amplifier, and oscilloscope is 200–7000 Hz.

7. A phonon crystal simulation method, applied to the phonon crystal simulation apparatus according to any one of claims 1 to 6, characterized in that, include: A signal is generated using the signal source and sent to the power amplifier; The power amplifier receives the signal sent by the signal source, performs power amplification on the signal, and sends the amplified signal to the speaker. The loudspeaker, under the influence of the amplified signal, emits sound waves of a specific frequency into the Galton plate; the Galton plate is used to simulate a phonon crystal. The microphone is used to detect sound waves inside the Galton plate; The signal amplifier is used to amplify the sound wave signal detected by the microphone, and the amplified sound wave signal is sent to the oscilloscope. The amplitude-frequency characteristics of the amplified acoustic signal are detected using the oscilloscope, and an amplitude-frequency characteristic diagram is generated; wherein, the bandgap characteristics of the phononic crystal can be determined by the change between the amplitude-frequency characteristic diagram corresponding to the Galton plate including the oscillator and the amplitude-frequency characteristic diagram corresponding to the Galton plate excluding the oscillator.

8. A method for detecting phonon crystals, characterized in that, include: Using the phonon crystal simulation method of claim 7, a first amplitude-frequency characteristic diagram of the signal is determined, and the first amplitude characteristic of the signal is determined using the first amplitude-frequency characteristic diagram; The oscillator in the Galton plate is removed, and the second amplitude-frequency characteristic diagram of the signal is determined using the phonon crystal simulation method of claim 7, and the second amplitude characteristic of the signal is determined using the second amplitude-frequency characteristic diagram; The bandgap characteristics of the phononic crystal are determined using the first amplitude characteristic and the second amplitude characteristic.

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