Spider-bionic nested local resonance phononic crystal structure and band gap regulation method

Abstract

The application discloses a spider bionic nested local resonance phononic crystal structure and a band gap regulation method, and comprises at least one phononic crystal unit cell with radial-circumferential coupling force transmission paths, wherein the phononic crystal unit cell comprises an outer frame, an intermediate frame and an inner frame which are sequentially nested from outside to inside and constitute a circumferential force transmission path, an intermediate connecting beam connected between the outer frame and the intermediate frame, an internal connecting beam connected between the intermediate frame and the inner frame and constituting a radial force transmission path with the intermediate connecting beam, and a nested local resonance unit located between the outer frame and the intermediate frame and used for generating a low-frequency local resonance band gap. The combination of the circumferential force transmission path and the radial force transmission path makes the phononic crystal unit cell have a multi-path force transmission characteristic, and the multiple nested local resonance units and the spider bionic frame synergize to form multiple adjacent low-frequency flat bands, and the multiple adjacent low-frequency band gaps form a composite band gap, so that the application can consider both super-low frequency and wide frequency band.

Description

Technical Field

[0001] This invention belongs to the field of vibration control technology, and particularly relates to a spider-inspired nested local resonant phonon crystal structure and a bandgap modulation method. Background Technology

[0002] Phononic crystals and elastic metamaterials, due to their bandgap properties, can suppress the propagation of elastic waves and structural vibrations within a specific frequency range, and are often used in vibration reduction and noise reduction. Traditional phononic crystals based on the Bragg scattering mechanism usually require a lattice constant on the same order of magnitude as the target wavelength, making it easier to form a bandgap in the mid-to-high frequency range. However, achieving an effective bandgap in the low-frequency or even ultra-low-frequency range remains quite difficult.

[0003] To reduce the bandgap frequency, existing localized resonant phononic crystals introduce a mass block-flexible connection system into the matrix, enabling coupling between the localized resonant units and the matrix, thereby creating a bandgap in a range far below the Bragg frequency. However, existing localized resonant structures struggle to simultaneously achieve both ultra-low frequency and broadband vibration reduction. Summary of the Invention

[0004] Purpose of the invention: The first objective of this invention is to provide a spider-inspired nested local resonant phonon crystal structure that combines ultra-low frequency and broadband vibration reduction.

[0005] The second objective of this invention is to provide a method for bandgap modulation of a spider-inspired nested local resonant phonon crystal structure.

[0006] Technical Solution: The present invention discloses a spider-inspired nested local resonant phononic crystal structure, comprising at least one phononic crystal unit cell with a radial-circumferential coupled force transmission path. The phononic crystal unit cell includes an outer frame, a middle frame, and an inner frame nested from the outside to the inside to form a circumferential force transmission path, an intermediate connecting beam connecting the outer frame and the middle frame, an internal connecting beam connecting the middle frame and the inner frame and forming a radial force transmission path with the intermediate connecting beam, and a nested local resonant unit located between the outer frame and the middle frame for generating a low-frequency local resonant bandgap. One end of the nested local resonant unit is connected to the middle frame.

[0007] Furthermore, the outer frame is composed of multiple first connecting parts and multiple straight first protrusions spliced ​​together, and the first connecting parts and first protrusions are arranged alternately to form an annular closed frame structure, and the first connecting parts are set as an inwardly concave arc shape.

[0008] Furthermore, the outer frame, middle frame, and inner frame are concentrically arranged, with the middle frame and inner frame being formed by proportionally scaling down the outer frame at different scaling ratios.

[0009] Furthermore, multiple intermediate connecting beams are provided, and the multiple intermediate connecting beams are distributed in a circular array at the center point of the outer frame; the number of internal connecting beams is the same as the number of intermediate connecting beams, and the corresponding first boss, intermediate connecting beams and internal connecting beams are located on a straight line.

[0010] Furthermore, multiple nested local resonance units are provided, and the multiple nested local resonance units are distributed in a circular array at the center point of the outer frame, and the nested local resonance units are arranged alternately with the intermediate connecting beam.

[0011] Furthermore, the nested local resonant unit includes a resin shell with a receiving cavity at the top, a metal mass block inserted into the receiving cavity, and a resonant connecting beam connecting the resin shell and the intermediate frame.

[0012] Furthermore, multiple phononic crystal unit cells are spliced ​​together in a two-dimensional periodic manner to form a plate-type phononic crystal vibration reduction structure.

[0013] Furthermore, the outer frame, middle frame, inner frame, middle connecting beam and internal connecting beam form a multi-level spider frame, and the multi-level spider frame and resonant connecting beam are all made of resin.

[0014] Furthermore, the metal mass block is made of a high-density material.

[0015] Based on the same inventive concept, this invention also discloses a method for bandgap modulation of a spider-inspired nested local resonant phonon crystal structure, wherein multiple nested local resonant units and a multi-level spider framework work together to form a composite bandgap. The ways to increase the starting and ending frequencies of the composite bandgap are: increasing the thickness of the resonant connecting beam or reducing the mass of the metal mass block; The ways to reduce the start and end frequencies of the composite bandgap are: to reduce the thickness of the resonant connecting beam or to increase the mass of the metal mass block.

[0016] Beneficial Effects: Compared with the prior art, the present invention has the following significant advantages: The outer frame, the intermediate connecting beam, and the intermediate frame constitute a circumferential force transmission path, and the intermediate connecting beams constitute a radial force transmission path. The combination of the circumferential and radial force transmission paths constitutes a spider web-inspired radial-circumferential hierarchical framework, enabling the phononic crystal unit cell to have multi-path force transmission characteristics, which is beneficial to improving the dispersion and control capability of vibration energy. The nested local resonant units of the present invention can form low-frequency local resonant band gaps. Multiple nested local resonant units and the spider-inspired framework work together to form multiple adjacent low-frequency flat bands. Multiple adjacent low-frequency band gaps form a composite band gap, enabling the present invention to take into account both ultra-low frequencies and wide bandwidths, and achieve ultra-low frequency broadband vibration reduction. Attached Figure Description

[0017] Figure 1This is a schematic diagram of the phononic crystal unit cell structure of the present invention; Figure 2 For the present invention Figure 1 Top view; Figure 3 For the present invention Figure 1 The main view; Figure 4 This is a schematic diagram of a plate-type phononic crystal vibration reduction structure constructed by splicing nine phononic crystal unit cells in a 3×3 manner in an embodiment of the present invention. Figure 5 This is a diagram of the composite bandgap band structure according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the first Brillouin zone according to an embodiment of the present invention; Figure 7 This is a diagram showing the effect of the connecting beam thickness on the composite bandgap performance according to an embodiment of the present invention. Figure 8 This is a diagram showing the effect of the outer frame thickness on the composite bandgap performance in an embodiment of the present invention. Figure 9 This is a diagram showing the effect of the height of the nested local resonant unit on the composite bandgap performance according to an embodiment of the present invention. Figure 10 This is a vibration transmission curve diagram of an embodiment of the present invention; Figure 11 This is a schematic diagram of the experimental testing apparatus according to an embodiment of the present invention; Figure 12 This is a comparison chart of the simulated and experimental vibration transmission curves of an embodiment of the present invention. Detailed Implementation

[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0019] Example 1 This invention discloses a spider-inspired nested localized resonant phononic crystal structure, comprising at least one phononic crystal unit cell 10 with a radial-circular coupled force transmission path. For example... Figures 1 to 3As shown, the phononic crystal unit cell 10 includes an outer frame 1, a middle connecting beam 2, a middle frame 3, an inner connecting beam 4, an inner frame 5, and nested local resonant units 9. The outer frame 1, middle frame 3, and inner frame 5 are nested sequentially from the outside to the inside. The middle connecting beam 2 connects the outer frame 1 and the middle frame 3, and the inner connecting beam 4 connects the middle frame 3 and the inner frame 5. The nested local resonant units 9 are located between the outer frame 1 and the middle frame 3. The nested local resonant units 9 are used to generate a low-frequency local resonant bandgap, and one end of the nested local resonant units 9 is connected to the middle frame 3. The outer frame 1, the middle connecting beam 2, and the middle frame 3 form a circumferential force transmission path, and the middle connecting beam 2 and the middle connecting beam 3 form a radial force transmission path. This invention combines the circumferential force transmission path, the radial force transmission path, and the low-frequency local resonant bandgap of the nested local resonant units 9, which is beneficial to improving the overall low-frequency vibration suppression effect.

[0020] like Figure 2 As shown, the outer frame 1, the middle frame 3, and the inner frame 5 are concentrically arranged, and the middle frame 3 and the inner frame 5 are formed by proportionally scaling down the outer frame 1 at different scaling ratios. The outer frame 1 is composed of multiple first connecting parts 11 and multiple straight first protrusions 12, arranged alternately to form a closed annular frame structure. The middle frame 3 is composed of multiple second connecting parts 13 and multiple straight second protrusions 14, arranged alternately to form a closed annular frame structure. The inner frame 5 is composed of multiple third connecting parts 15 and multiple straight third protrusions 16, arranged alternately to form a closed annular frame structure. The first connecting parts 11, second connecting parts 13, and third connecting parts 15 are configured as inwardly concave arc shapes. The number of first connecting parts 11, second connecting parts 13, and third connecting parts 15 is the same, and the corresponding first boss 12, second boss 14, and third boss 16 are located on a straight line. The outer frame 1, middle frame 3, inner frame 5, middle connecting beam 2, and internal connecting beam 4 form a multi-level spider frame.

[0021] like Figure 1 and Figure 2 As shown, multiple intermediate connecting beams 2 are arranged in a circular array with the center point of the outer frame 1 as the center. The number of internal connecting beams 4 is the same as the number of intermediate connecting beams 2. The first boss 12, intermediate connecting beams 2, second boss 14, internal connecting beams 4, and third boss 16 are located on a straight line. Multiple nested local resonance units 9 are arranged in a circular array with the center point of the outer frame 1 as the center, and the nested local resonance units 9 are arranged alternately with the intermediate connecting beams 2.

[0022] The nested local resonance unit 9 includes a resonant connecting beam 6, a resin shell 7, and a metal mass block 8. The top of the resin shell 7 has a receiving cavity, and the metal mass block 8 is inserted into the receiving cavity of the resin shell 7. The two ends of the resonant connecting beam 6 are connected to the resin shell 7 and the intermediate frame 3, respectively. In practical applications, the resin shell 7 can also completely enclose the exterior of the metal mass block 8, or the metal mass block 8 can be bonded to the top of the resin shell 7. The metal mass block 8 provides the inertial force required for local resonance, while the resin shell 7 and the resonant connecting beam 6 provide flexible support and coupling connection. When external vibrations are transmitted to the phonon crystal unit cell 10, relative vibrations occur between the metal mass block 8, the resin shell 7, and the multi-level spider frame, thereby generating a local resonance effect.

[0023] The outer frame 1, the intermediate connecting beam 2, and the intermediate frame 3 form a circumferential force transmission path, while the intermediate connecting beam 2 forms a radial force transmission path. The combination of the circumferential and radial force transmission paths constitutes a spiderweb-inspired radial-circumferential hierarchical framework, giving the phononic crystal unit cell 10 multi-path force transmission characteristics and improving the dispersion and control of vibration energy. This invention uses a resonant connecting beam 6, a resin shell 7, and a metal mass block 8 to form nested local resonant units 9, and utilizes the resonant connecting beam 6 to form flexible coupling, enabling the phononic crystal unit cell 10 to form local resonant bandgap in a range far below the traditional Bragg scattering frequency. The multiple nested local resonant units and the multi-level spiderweb framework work synergistically to form multiple adjacent low-frequency flat bandgap, and these multiple adjacent low-frequency bandgap forms a composite bandgap, allowing this invention to address both ultra-low frequencies and wideband, achieving ultra-low frequency broadband vibration reduction. Under different characteristic modes, the amplitude, vibration direction, and phase relationship of each nested local resonant unit 9 are different. For example, the structure composed of the resin shell 7 and the metal mass block 8 is denoted as an oscillator. Some modes exhibit the same phase motion of multiple oscillators, some exhibit the opposite phase motion of adjacent oscillators, and some involve only a portion of the oscillators. Even with identical geometric connections, these different modal combinations will cause varying degrees of bending, stretching, or torsional deformation in the radial beams and circumferential members of the spider web, thus forming different modal characteristic frequencies. This can be summarized as follows: multiple geometrically identical nested local resonant units 9 within a single cell are connected to a multi-level spider web frame through radial and circumferential members. Due to the dynamic coupling between the nested local resonant units 9 and between the nested local resonant units 9 and the multi-level spider web frame, the vibration amplitude, vibration direction, and phase relationship of each oscillator differ under different characteristic modes, thus forming multiple adjacent local vibrations and oscillator-frame coupled modes, i.e., forming multiple adjacent low-frequency flat bandgap modes.

[0024] The outer frame 1, middle frame 3, inner frame 5, middle connecting beam 2, internal connecting beam 4, and resonant connecting beam 6 are all made of resin, preferably a high-molecular-weight material such as photosensitive resin, epoxy resin, or nylon resin. The metal mass block 8 is made of a high-density material such as tungsten or lead. Except for the metal mass block 8, the phonon crystal unit cell 10 is made of resin. The combination of the metal mass block 8 and resin not only ensures the lightweight structure and ease of manufacturing of the phonon crystal unit cell 10, but also creates a significant mass-stiffness difference, which is beneficial for generating a low-frequency local resonant bandgap. The multi-level spider frame of this invention can be manufactured in an integrated manner, resulting in good continuity, convenient manufacturing, and simple assembly of the phonon crystal unit cell 10, making it suitable for engineering applications. In summary, the phonon crystal unit cell 10 of this invention can balance structural continuity, manufacturability, and ultra-low frequency broadband vibration reduction capabilities. This invention can be applied to scenarios with high requirements for low-frequency vibration control, such as ships, underwater equipment, offshore platforms, precision instruments, and mechanical equipment.

[0025] like Figure 2As shown, L1 represents the length of the first boss 12, L2 represents the length of the intermediate connecting beam 2, L3 represents the length of the internal connecting beam 4, L4 represents the length of the resonant connecting beam 6, L5 represents the side length of the metal mass block 8 projected onto the horizontal plane, L6 represents the width of the intermediate connecting beam 2, and L7 represents the width of the internal connecting beam 4. By adjusting the aforementioned geometric parameters, the equivalent mass, equivalent stiffness, and coupling strength between the nested local resonant unit 9 and the multi-level spider frame in the phononic crystal unit cell 10 can be changed, thereby controlling the start frequency, end frequency, and bandgap width of the composite bandgap. The thickness of the resonant connecting beam 6 mainly adjusts the position of the composite bandgap by changing the equivalent connection stiffness between the nested local resonant unit 9 and the multi-level spider frame. As the thickness of the resonant connecting beam 6 increases, the start frequency and end frequency of the composite bandgap move synchronously towards higher frequencies. The thickness of the outer frame 1 primarily affects the constraint effect of the multi-level spider frame, having a relatively small impact on the starting frequency of the composite bandgap. Instead, it adjusts the ending frequency and bandgap width of the composite bandgap by changing the coupling state on the high-frequency side. The "high-frequency side" refers to the vibration mode region near and above the ending frequency of the composite bandgap. Within the frequency range of the composite bandgap's ending frequency and above, vibration is no longer primarily confined to the nested local resonant unit 9, but rather more energy is transferred to the multi-level spider frame and the outer frame 1. Therefore, the deformation and constraint effect of the outer frame 1 have a more significant impact on the ending frequency of the composite bandgap. As the thickness of the outer frame 1 increases, the starting frequency of the composite bandgap changes less, the ending frequency generally decreases, the absolute bandgap width decreases accordingly, and the relative bandwidth of the composite bandgap exhibits a non-monotonic change, first increasing and then decreasing. Appropriately increasing the thickness of the outer frame 1 can improve the deformation coordination of the multi-level spider frame and the outer frame 1, as well as the coupling between the nested local resonant units 9, thus increasing the relative bandwidth of the composite bandgap. However, excessively thick outer frame 1 will significantly enhance the overall constraint, limiting the deformation of the multi-level spider frame near the high-frequency boundary (termination frequency) of the bandgap, causing the termination frequency to decrease and the bandgap to narrow. In this embodiment, the relative bandwidth increases from approximately 69.8% to 72.7% with the change in the thickness of the outer frame 1, and then decreases to 59.6%. There is an optimal intermediate range for the thickness of the outer frame 1, rather than the principle that thicker is always better. The height of the local resonant unit 9 is mainly adjusted by changing the mass and inertial characteristics of the local resonant unit 9 to regulate the low-frequency local resonant bandgap. As the height of the local resonant unit 9 increases, that is, as the mass of the metal mass block 8 increases, the composite bandgap moves towards the lower frequency direction while maintaining a relatively stable relative bandwidth. In practical applications, the starting frequency, termination frequency, and bandgap width of the composite bandgap can be directionally set by coordinating the adjustment of three types of geometric parameters: the stiffness of the connecting beam, the constraint of the outer frame, and the inertia of the oscillator.

[0026] In this embodiment, the phononic crystal unit cell 10 forms a composite bandgap in the low-frequency range, as shown below. Figure 5As shown. In this embodiment, the phononic crystal unit cell 10 consists of three adjacent low-frequency local resonant band gaps, namely 14.5–16.5 Hz (band gap 1), 16.5–26.6 Hz (band gap 2), and 26.6–28.5 Hz (band gap 3). The composite band gap formed by these three adjacent low-frequency local resonant band gaps is 14.5–28.5 Hz. This composite band gap is not formed by a single mode, but by the interaction of multiple low-frequency local resonant modes. Among them, the metal mass block 8 mainly provides inertial force, while the resonant connecting beam 6 and the resin shell 7 mainly provide elastic support. When the phononic crystal unit cell 10 is excited to vibrate in the low-frequency range, relative vibration occurs between the metal mass block 8, the resin shell 7, and the multi-level spider frame. The multiple low-frequency local resonant modes are distributed adjacently in frequency, so that multiple band gap segments are connected to each other, thereby forming a continuous low-frequency composite band gap.

[0027] like Figure 6 As shown, in this embodiment, the first Brillouin zone adopts the Brillouin zone corresponding to a square lattice, and the band structure calculation path can be performed along the Γ-XM-Γ direction. Through this path, the band structure of the phononic crystal unit cell 10 under periodic boundary conditions can be obtained, and the existence of a band gap in the low-frequency range can be determined accordingly.

[0028] Example 2 This invention discloses a spider-inspired nested local resonant phonon crystal structure, in which multiple phonon crystal unit cells 10 are arranged in a two-dimensional periodic manner.

[0029] Multiple phonon crystal unit cells 10 are spliced ​​together in a two-dimensional periodic manner to form a plate-type phonon crystal vibration damping structure. The first bosses 12 of adjacent phonon crystal unit cells 10 are interconnected. The plate-type phonon crystal vibration damping structure can be installed on the surface of the equipment to be damped, or it can be embedded in equipment support plates, sandwich plates, mechanical mounting bases, ship frame structures, underwater equipment hulls, or offshore platform support structures. In practical applications, the number of phonon crystal unit cells 10 is set according to the size of the equipment to be damped, the installation space, and the target damping frequency. The plate-type phonon crystal vibration damping structure composed of multiple phonon crystal unit cells 10 is installed on the area to be damped, such as in a 2×2, 3×3, 4×4, or 5×5 arrangement; for example... Figure 4 As shown, nine phonon crystal units 10 are spliced ​​together in a 3×3 manner to form a plate-type phonon crystal vibration reduction structure.

[0030] When vibration waves propagate in the plate-type phononic crystal vibration damping structure, the nested local resonant units 9 in each phononic crystal unit cell 10 will vibrate locally within the low-frequency local resonant bandgap range, hindering the continued propagation of vibration energy. Due to the periodic arrangement of multiple phononic crystal unit cells 10, the local resonance effect of the nested local resonant units 9 is coupled with the wave propagation characteristics of the periodically arranged structure, thereby forming a low-frequency bandgap or a composite bandgap, thus suppressing the propagation of vibration within the target frequency range.

[0031] Example 3 This invention discloses a method for bandgap control of a spider-inspired nested local resonant phonon crystal structure. The frame structure composed of an outer frame 1, a middle frame 3, an inner frame 5, a middle connecting beam 2, and an internal connecting beam 4 is referred to as a multi-level spider frame. Multiple nested local resonant units 9 and the multi-level spider frame work together to form multiple adjacent low-frequency bandgap, and multiple adjacent low-frequency bandgap forms a composite bandgap.

[0032] The method to increase the bandgap width, starting frequency, and ending frequency of the composite bandgap is to increase the thickness of the resonant connecting beam 6. The method to decrease the bandgap width, starting frequency, and ending frequency of the composite bandgap is to decrease the thickness of the resonant connecting beam 6.

[0033] like Figure 7 As shown, with the increase in the thickness of the resonant connecting beam 6, the equivalent bending stiffness of the resonant connecting beam 6 and the coupling stiffness between the nested local resonant unit 9 and the multi-level spider frame increase, causing the overall starting frequency (lower boundary) and ending frequency (upper boundary) of the composite bandgap to shift towards higher frequencies. A smaller thickness of the resonant connecting beam 6 is beneficial for reducing the starting frequency of the composite bandgap; with an appropriate increase in the thickness of the resonant connecting beam 6, the absolute bandwidth of the composite bandgap increases slightly, but because the upward shift of the center frequency of the composite bandgap is more significant, the relative bandwidth of the composite bandgap exhibits a non-monotonic change of first increasing slightly and then decreasing. Therefore, the thickness of the resonant connecting beam 6 is mainly used to adjust the position (upper and lower boundaries) of the composite bandgap and to balance the starting frequency and bandgap width of the composite bandgap.

[0034] The thickness of the outer frame 1 also affects the composite bandgap. When the thickness of the outer frame 1 increases, the overall boundary support stiffness of the phononic crystal unit cell 10 increases, and the constraint between the nested local resonant unit 9 and the outer frame 1 strengthens, causing a shift in the low-frequency local resonant bandgap. For example... Figure 8 As shown in (a), when the thickness of the outer frame 1 is 6mm to 8mm, the starting frequency (lower boundary) of the composite bandgap in this embodiment shifts towards lower frequencies as the thickness of the outer frame 1 increases; when the thickness of the outer frame 1 is greater than 8mm, the starting frequency (lower boundary) of the composite bandgap in this embodiment shifts towards higher frequencies as the thickness of the outer frame 1 increases; the ending frequency (upper boundary) of the composite bandgap in this embodiment shifts towards lower frequencies as the thickness of the outer frame 1 increases. Figure 8 As shown in (b), when the thickness of the outer frame 1 is 6mm to 8mm, the relative width (bandgap width) of the composite bandgap in this embodiment increases with the increase of the thickness of the outer frame 1; when the thickness of the outer frame 1 is greater than 8mm, the relative width (bandgap width) of the composite bandgap in this embodiment decreases with the increase of the thickness of the outer frame 1. Within a small thickness range of the outer frame 1, as the thickness increases, the starting frequency of the composite bandgap shifts towards lower frequencies, and the relative width increases with the increase of the thickness; when the thickness of the outer frame 1 increases to the peak inflection point, as the thickness increases, the starting frequency of the composite bandgap shifts towards higher frequencies, and the bandgap width decreases with the increase of the thickness. The ending frequency of the composite bandgap shifts towards higher frequencies with the increase of the thickness of the outer frame 1. In practical applications, by reasonably selecting the thickness of the outermost outer frame 1, a balance can be achieved between structural strength and low-frequency bandgap performance.

[0035] The method to increase the onset frequency and termination frequency of the composite bandgap is to decrease the thickness of the nested local resonant unit 9. The method to decrease the onset frequency and termination frequency of the composite bandgap is to increase the thickness of the nested local resonant unit 9.

[0036] When the thickness of the nested local resonant unit 9 increases, the equivalent mass and moment of inertia of the metal mass block 8 increase, the low-frequency local resonant bandgap decreases, and thus the composite bandgap shifts to an even lower frequency range. For example... Figure 9 As shown in (a), the start and end frequencies of the composite bandgap in this embodiment shift to lower frequencies as the thickness of the nested local resonant unit 9 increases; as Figure 9 As shown in (b), the bandgap width of the composite bandgap in this embodiment increases with the increase of the thickness of the nested local resonant unit 9. Under the condition that other material and geometric parameters remain unchanged, Figure 9 This reflects the influence of the thickness of the nested local resonant unit 9 on the composite bandgap performance in this embodiment. As the thickness of the nested local resonant unit 9 increases (essentially changing the mass of the metal mass block 8), the equivalent mass and moment of inertia of the metal mass block 8 increase, reducing the low-frequency local resonant bandgap. Consequently, the starting and ending frequencies of the composite bandgap shift towards lower frequencies. Within the parameter range examined in this embodiment, the absolute bandwidth of the composite bandgap also shows an increasing trend. It should be noted that increasing the mass of the metal mass block 8 generally helps to reduce the low-frequency local resonant bandgap, but the specific changes in the bandgap ending frequency and bandwidth are also related to the connection stiffness, the main frame mode, and the oscillator-frame coupling state. Therefore, the above bandwidth variation law mainly applies to this embodiment and structures with similar dynamic configurations. Therefore, increasing the thickness of the nested local resonant unit 9 helps to reduce the starting frequency of the composite bandgap, achieving vibration suppression in lower frequency bands. The thickness of the nested local resonant unit 9 mainly adjusts the position of the composite bandgap by changing the inertial characteristics of the nested local resonant unit 9.

[0037] In practical applications, the geometry of the phononic crystal unit cell 10 can be designed according to the target vibration reduction frequency in different engineering scenarios, so that it can form a composite bandgap in the required low frequency range.

[0038] Example 4 Verify the vibration transmission characteristics of a spider-inspired nested local resonant phonon crystal structure of the present invention.

[0039] Vibration transmission analysis was performed on a plate-type phononic crystal vibration reduction structure formed by splicing multiple phononic crystal unit cells (10 units) to obtain the following results: Figure 10 The vibration transmission curves are shown. When the external excitation frequency falls within the composite bandgap range, the vibration transmission of the phononic crystal damping structure decreases significantly, from... Figure 10 It can be seen that a clear attenuation range appears in the vibration transmission curve; this attenuation range is consistent with... Figure 5 The range of the composite bandgap shown corresponds to the low-frequency vibration suppression effect of the present invention, indicating that the low-frequency vibration suppression effect of the present invention originates from the low-frequency local resonance bandgap characteristics of the phononic crystal unit cell 10.

[0040] Within the composite bandgap range, vibrational energy is difficult to propagate further through the plate-type phononic crystal damping structure. The vibrational energy at the input end is mainly confined to a local region or absorbed and dissipated by the nested local resonant unit 9, thus significantly reducing the output response. Outside the composite bandgap range, propagable modes exist in the plate-type phononic crystal damping structure, allowing vibrational energy to continue propagating along the spiderweb-like bionic framework, resulting in a relatively enhanced output response.

[0041] Therefore, this invention, through the synergistic effect of the multi-level spider frame, nested local resonant units 9, resin shell 7, and metal mass block 8, forms a composite bandgap in the low-frequency range and exhibits a significant vibration transmission attenuation effect in the plate-type phonon crystal vibration reduction structure. This plate-type phonon crystal vibration reduction structure is suitable for ship equipment, underwater vehicles, offshore platform support structures, mechanical equipment foundations, precision instrument mounting platforms, and other engineering structures requiring low-frequency vibration reduction.

[0042] Example 5 Physical and simulation experiments were conducted on a spider-inspired nested local resonant phonon crystal structure disclosed in this invention.

[0043] In this embodiment, the outer frame 1, middle frame 3, inner frame 5, middle connecting beam 2, internal connecting beam 4 and resonant connecting beam 6 are all made of resin in an integral molding process, and multiple phonon crystal unit cells 10 are spliced ​​together to form a plate-type phonon crystal vibration reduction structure.

[0044] Physical experiments, such as Figure 11As shown, the plate-type phonon crystal vibration damping structure is suspended by an elastic rope to approximate free boundary conditions. An exciter is placed on one side of the plate-type phonon crystal vibration damping structure or at a designated excitation position to input sweep frequency excitation. Accelerometers are placed at the excitation and response points to collect vibration signals from the input and output ends. A force sensor is placed between the vibration exciter and the plate-type phonon crystal vibration damping structure to measure the excitation force applied to the structure in real time and use it as the vibration input signal. A power amplifier amplifies the sweep frequency electrical signal output from the signal generator or data acquisition system to drive the vibration exciter to generate harmonic excitation that meets the experimental requirements. Accelerometers are arranged at the excitation and response points to collect the acceleration response from the input and output ends. The data acquisition system synchronously acquires and processes the excitation force and acceleration signals to calculate the vibration transmission characteristics of the structure. Using a data acquisition system with existing mature technology, vibration signals are acquired and processed to obtain the vibration transmission curve of the plate-type phonon crystal vibration damping structure. The experimental vibration transmission curve is shown in the figure below. Figure 12 As shown in (b) of the diagram.

[0045] In the simulation experiment, a simulation model of the plate phonon crystal vibration reduction structure with parameters identical to those in the physical experiment was constructed within 3D simulation software. A sweep frequency excitation identical to that in the physical experiment was input into the simulation model, and vibration signals were acquired and processed to obtain the vibration transmission curve of the plate phonon crystal vibration reduction structure. The simulated vibration transmission curve is shown below. Figure 12 As shown in (a) of the diagram.

[0046] from Figure 12 It can be seen that in the low-frequency range corresponding to the composite bandgap, the output response of the plate phononic crystal damping structure is significantly reduced, and the vibration transmission curve shows a clear attenuation range. The vibration transmission trend obtained from the physical experiment and the simulation experiment are consistent, indicating that the spider-inspired nested local resonant phononic crystal structure disclosed in this invention can effectively suppress vibration propagation in the low-frequency range.

Claims

1. A spider-inspired nested localized resonant phonon crystal structure, characterized in that: The phononic crystal unit cell (10) includes at least one phononic crystal unit cell (10) with a radial-circular coupled force transmission path. The phononic crystal unit cell (10) includes an outer frame (1), a middle frame (3) and an inner frame (5) nested from the outside to the inside to form a circumferential force transmission path, an intermediate connecting beam (2) connecting the outer frame (1) and the middle frame (3), an inner connecting beam (4) connecting the middle frame (3) and the inner frame (5) and forming a radial force transmission path with the intermediate connecting beam (2), and a nested local resonance unit (9) located between the outer frame (1) and the middle frame (3) for generating a low-frequency local resonance bandgap. One end of the nested local resonance unit (9) is connected to the middle frame (3).

2. The spider-inspired nested localized resonant phonon crystal structure according to claim 1, characterized in that: The outer frame (1) is composed of multiple first connecting parts (11) and multiple straight first protrusions (12), and the first connecting parts (11) and the first protrusions (12) are arranged alternately to form an annular closed frame structure; the first connecting parts (11) are set as an inwardly concave arc shape.

3. The spider-inspired nested localized resonant phonon crystal structure according to claim 2, characterized in that: The outer frame (1), middle frame (3) and inner frame (5) are set concentrically, and the middle frame (3) and inner frame (5) are formed by scaling down the outer frame (1) proportionally with different scaling ratios.

4. The spider-inspired nested localized resonant phonon crystal structure according to claim 3, characterized in that: Multiple intermediate connecting beams (2) are provided, and the multiple intermediate connecting beams (2) are arranged in a ring array at the center point of the outer frame (1); the number of internal connecting beams (4) is the same as the number of intermediate connecting beams (2), and the corresponding first boss (12), intermediate connecting beams (2) and internal connecting beams (4) are located on a straight line.

5. The spider-inspired nested localized resonant phonon crystal structure according to claim 1, characterized in that: Multiple nested local resonance units (9) are provided. The multiple nested local resonance units (9) are arranged in a ring array at the center point of the outer frame (1), and the nested local resonance units (9) and the intermediate connecting beam (2) are arranged alternately.

6. The spider-inspired nested localized resonant phonon crystal structure according to claim 1, characterized in that: The nested local resonant unit (9) includes a resin shell (7) with a receiving cavity at the top, a metal mass block (8) inserted into the receiving cavity, and a resonant connecting beam (6) connecting the resin shell (7) and the intermediate frame (3).

7. The spider-inspired nested localized resonant phonon crystal structure according to claim 1, characterized in that: Multiple phononic crystal units (10) are spliced ​​together in a two-dimensional periodic manner to form a plate-type phononic crystal vibration reduction structure.

8. The spider-inspired nested localized resonant phonon crystal structure according to claim 1, characterized in that: The outer frame (1), middle frame (3), inner frame (5), middle connecting beam (2) and internal connecting beam (4) form a multi-level spider frame. The multi-level spider frame and the resonant connecting beam (6) are both made of resin.

9. The spider-inspired nested localized resonant phonon crystal structure according to claim 1, characterized in that: The metal mass block (8) is made of high-density material.

10. A method for bandgap modulation of a spider-inspired nested local resonant phonon crystal structure, characterized in that: Multiple nested local resonant units (9) work together with a multi-level spider framework to form a composite bandgap; The ways to increase the starting and ending frequencies of the composite bandgap are: increasing the thickness of the resonant connecting beam (6) or decreasing the mass of the metal mass block (8); The ways to reduce the starting and ending frequencies of the composite bandgap are: to reduce the thickness of the resonant connecting beam (6) or to increase the mass of the metal mass block (8).

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