Band gap adjustable phononic crystal and band gap adjusting method

Abstract

The application discloses a kind of phononic crystals with adjustable band gap and band gap adjusting method, the phononic crystal includes the single cell of two-dimensional periodic array arrangement, each single cell contains elastic / super-elastic base, local resonance oscillator, lift adjustment mechanism and prestress applying mechanism.The application decouples geometric reconstruction mechanism and mechanical prestress mechanism, includes two dimensions of control steps of coarse tuning and fine tuning: the vertical suspension height of oscillator is changed by lift adjustment mechanism, and the wide-range coarse tuning of equivalent geometric inertia and frequency is realized;At any height, by the stress stiffening effect of super-elastic material, high-resolution boundary fine tuning of environmental disturbance resistance is realized by prestress applying mechanism.The application overcomes the defect of traditional phononic crystal frequency band fixation, while maintaining the high bearing stiffness of structure, realizes the wide frequency, decoupling type precision self-adaptive regulation and control of low-frequency elastic wave and middle-high frequency coupled wave.

Description

Technical Field

[0001] This invention relates to the field of elastic wave metamaterials and structural dynamics control technology, specifically to a bandgap-tunable phononic crystal and a bandgap adjustment method, particularly a dual-tuning framework based on geometric reconstruction and mechanical prestressing of rigid columnar elastic metamaterials and its broadband vibration reduction application. Background Technology

[0002] Phononic crystals, as artificial structural materials that manipulate elastic wave propagation through engineered periodic structures, have attracted widespread attention in recent years in fields such as vibration isolation, noise suppression, earthquake protection, and elastic wave energy harvesting. Their core characteristic lies in their ability to generate specific band gaps—within which elastic wave propagation is strictly prohibited. Since Liu Zhengyou et al. first proposed phononic crystals based on local resonance mechanisms, inducing negative equivalent dynamic mass density through near-resonant anti-phase motion between internal resonators and the main structure has provided a feasible path to break the mass law at subwavelength scales.

[0003] However, traditional passive localized resonant phonon crystals suffer from a severe inherent limitation—spectral rigidity. Since their bandgap frequency is entirely determined by the geometric and material parameters during the design phase, their dynamic characteristics are fixed once fabricated. This lack of adaptability makes such passive structures unable to cope with complex service environments where the excitation spectrum changes over time or exhibits frequency drift, such as rotating machinery with varying rotational speeds, broadband vibration conditions, or seismic events with evolving dominant frequencies. To address this issue, researchers have explored active tuning strategies such as piezoelectric shunt circuits, magnetorheological modulation, and thermally induced stiffness variations. However, these methods generally suffer from practical engineering bottlenecks such as weak electromechanical coupling, narrow tunable bandwidth, excessive material damping, severe nonlinear hysteresis, and poor long-term reliability. Furthermore, many mechanically reconfigurable metamaterials reported in recent years rely excessively on soft, hyperelastic substrates or origami-inspired folding mechanisms. While these designs exhibit tunability at low frequencies, they completely lose the stiffness and stability necessary for a load-bearing structure. Introducing controllable and repeatable mechanical prestress into rigid structures to utilize the "stress stiffening effect" for bandgap control has been proven effective in theoretical numerical studies. However, achieving experimental verification and physical implementation in rigid columnar phonon crystal systems remains a key unresolved technical challenge. Summary of the Invention

[0004] The purpose of this invention is to provide a phononic crystal with adjustable bandgap and a method for adjusting the bandgap, which aims to overcome the defects of fixed frequency band in traditional passive phononic crystals and solve the problems of insufficient load-bearing stiffness, excessive material damping, and low control precision in existing active metamaterials.

[0005] The technical solution adopted in this invention is as follows: a phononic crystal with adjustable bandgap, which is composed of multiple phononic crystal unit cells arranged in a two-dimensional periodic array, each of the phononic crystal unit cells including: a hyperelastic substrate, a local resonant oscillator, a lifting adjustment mechanism and a prestressing application mechanism;

[0006] The lifting and adjusting mechanism includes a housing, a top cover, and a threaded knob; the housing is fixed to the top of the superelastic base, and the top cover and the threaded knob are located on the top of the housing;

[0007] The local resonant oscillator has a threaded through hole at its center (the size of which is recommended not to exceed the height of the outer casing). The bottom end of the threaded knob has a lead screw that meshes with the threaded through hole, and the two work together to form a helical transmission pair. The side wall of the outer casing has an anti-rotation groove, and the side wall of the local resonant oscillator has an anti-rotation key that slides with the anti-rotation groove, so as to convert the rotational motion of the threaded knob into the pure vertical translational motion of the local resonant oscillator.

[0008] The prestressing application mechanism includes at least two prestressing tendons that run longitudinally through the hyperelastic substrate. The prestressing tendons are distributed on the inner sides of the two edges of the hyperelastic substrate. The outer sides of both ends of the hyperelastic substrate are respectively attached to a bearing plate. The two ends of the prestressing tendons pass through the bearing plate and are anchored by fasteners, which is used to convert tensile tension into a static compressive load that is uniformly distributed in the hyperelastic substrate.

[0009] Preferably, the material of the local resonant oscillator is a high-density material (either metal or non-metal), and the materials of the housing, lead screw, and prestressing application mechanism of the lifting adjustment mechanism are all high-strength materials.

[0010] Preferably, the top cover is a split-type assembly structure, with the internal parts connected by pins and the external parts fixed to the top of the outer shell by at least four high-strength pins; the surface of the top cover is provided with a circular keyway (the keyway direction range is (0, 360°)) for inserting locking pins to fix the rotation angle of the threaded knob.

[0011] Preferably, the outer shell can be cylindrical, square, or other geometric shapes, and 2 to 8 anti-rotation grooves are provided on the side wall of the outer shell.

[0012] Preferably, the plane of the hyperelastic substrate is also regularly arranged with multiple elliptical perforations (the ratio of the major and minor axes can be freely given, ranging from (0, +∞)). Other types of holes (circular, square, star-shaped, etc.) can also be used to reduce the local bending flexibility of the hyperelastic substrate and reduce the total self-weight of the structure, thereby reducing the starting frequency of the local resonant bandgap.

[0013] The above-mentioned bandgap adjustment method for a phononic crystal with adjustable bandgap decouples the geometric reconstruction mechanism from the mechanical prestress mechanism and includes a coarse tuning step and a fine tuning step.

[0014] The coarse tuning step includes: continuously changing the vertical suspension height of the local resonant oscillator relative to the hyperelastic substrate by rotating the lifting adjustment mechanism. (The range can be 1 / 8 to 1 / 4 of the height of the outer shell column), thereby adjusting the equivalent geometric inertia to achieve a wide range of low-frequency shifts in the low-frequency bandgap of the phononic crystal local resonance.

[0015] The fine-tuning step includes: tensioning the prestressing tendons through the prestressing application mechanism to apply a controlled external tensile force to the hyperelastic substrate, converting it into a precompressive stress P (not exceeding the yield stress of the substrate material). By utilizing the stress stiffening effect of a hyperelastic base under large deformation kinematics to change the global geometric stiffness matrix, precise subhertz-level fine-tuning of the bandgap boundary can be achieved without altering the physical geometry.

[0016] Preferably, in the coarse tuning step, for the first local resonant bandgap at low frequencies, the local resonant oscillator and the hyperelastic substrate are equivalent to a cantilever beam structure, with the vertical suspension height... With the increase of , the equivalent cantilever length changes, and its equivalent lateral bending stiffness satisfies the following relationship: Where E is the elastic modulus of the hyperelastic matrix. Let the moment of inertia of the cross section be... The initial effective bending length; the increase in height drives the bandgap initiation frequency to shift significantly to lower frequencies.

[0017] Preferably, in the fine-tuning step, the applied pre-compression stress P introduces a negative geometric stiffness. This reduces the system's tangent recovery capability when Much smaller than the critical buckling stress of the hyperelastic substrate At that time, the modulated local resonant frequency Satisfies the analytic relation: This enables high-resolution frequency shifting that is resistant to environmental micro-disturbances.

[0018] Preferably, for the coupling dispersive bandgap, the vertical suspension height is adjusted accordingly. The increase in the local resonant oscillator's spatial distance from the elastic dynamic pivot of the hyperelastic substrate increases, thus increasing the equivalent dynamic mass rotational inertia tensor of the unit cell. Polarization occurs; when the excitation frequency approaches the torsional pole frequency, When the value is negative, the system generates strong bending-torsional coupling vibration and mode hybridization, thereby cutting off the transmission path of high-frequency stress waves and forming a broadband gap.

[0019] Beneficial effects: This invention constructs a dual-tuning framework that integrates macroscopic geometric reconstruction and microscopic mechanical prestressing, achieving decoupled, wide-bandwidth, high-resolution precise control of low-frequency elastic waves and mid-to-high-frequency coupled waves, while maintaining the excellent stiffness and load-bearing integrity of the structure as an engineering vibration reduction base. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall three-dimensional structure of a phononic crystal unit cell after assembly, provided by the present invention.

[0021] Figure 2 yes Figure 1 A schematic diagram of the three-dimensional split structure of a medium phonon crystal unit cell.

[0022] Figure 3 yes Figure 1 A schematic diagram of the cross-sectional structure of a unit cell of a medium phonon crystal along line II.

[0023] Figure 4 This is a top view and a schematic diagram of the localized explosion structure at the top of the phononic crystal unit cell of the present invention.

[0024] Figure 5 This is a three-dimensional structural diagram of the local resonant oscillator (main cylindrical body) in this invention.

[0025] Figure 6 This is a schematic diagram of the local assembly of the mounting holes and pins of the phononic crystal unit cell shell of the present invention.

[0026] Figure 7 This is a three-dimensional structural diagram of the pressure plate in this invention.

[0027] Figure 8 This is a schematic diagram of the overall assembly structure of the array formed by the arrangement of phononic crystal unit cells of the present invention.

[0028] Figure 9 This is the coarse-tuned state of the bandgap tunable phonon crystal of the present invention. The band gap curve for increasing height.

[0029] Figure 10 This is the coarse-tuned state of the bandgap tunable phonon crystal of the present invention. The band gap curve for increasing height.

[0030] Figure 11 This is the coarse-tuned state of the bandgap tunable phonon crystal of the present invention. Bandgap curve of increased height

[0031] Figure 12 This is the coarse-tuned state of the bandgap tunable phonon crystal of the present invention. The band gap curve for increasing height.

[0032] Reference numerals in the attached diagram: 1. Anti-rotation side key; 2. Local resonance oscillator; 3. Threaded knob; 4. Top cover; 5. Prestressed through hole; 6. Pin; 7. Side key mounting hole; 8. Pressure plate. Detailed Implementation

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

[0034] like Figure 1-8 As shown, a bandgap adjustable phononic crystal is composed of multiple phononic crystal unit cells arranged in a two-dimensional periodic array. Each phononic crystal unit cell includes: a hyperelastic substrate, a local resonant oscillator 2, a lifting adjustment mechanism, and a prestressing application mechanism.

[0035] The lifting and adjusting mechanism includes a housing, a top cover 4, and a threaded knob 3; the housing is fixed to the top of the superelastic base, and the top cover 4 and the threaded knob 3 are disposed on the top of the housing;

[0036] The local resonant oscillator 2 has a threaded through hole at its center, and the bottom end of the threaded knob 3 has a lead screw that meshes with the threaded through hole. The two work together to form a helical transmission pair. The side wall of the outer shell has an anti-rotation groove, and the side wall of the local resonant oscillator 2 has an anti-rotation side key 1 that slides with the anti-rotation groove, so as to convert the rotational motion of the threaded knob 3 into the pure vertical translational motion of the local resonant oscillator 2.

[0037] The prestressing application mechanism includes at least two prestressing tendons that run longitudinally through the hyperelastic substrate. The prestressing tendons are distributed on the inner sides of the two edges of the hyperelastic substrate. The outer sides of both ends of the hyperelastic substrate are respectively attached to a bearing plate 8. The two ends of the prestressing tendons pass through the bearing plate 8 and are anchored by fasteners, which is used to convert tensile tension into a static compressive load that is uniformly distributed in the hyperelastic substrate.

[0038] The local resonant oscillator 2 is made of high-density material (either metal or non-metal). The housing, lead screw, and prestressing application mechanism of the lifting adjustment mechanism are all made of high-strength material. The top cover 4 is a split-type assembly structure, internally connected by pins 6, and externally fixed to the top of the housing by at least four high-strength pins. The surface of the top cover 4 has a circular keyway (the keyway direction range is (0, 360°)) for inserting locking pins to fix the rotation angle of the threaded knob. The housing can be cylindrical, square, or other geometric shapes, and 2 to 8 anti-rotation straight grooves are opened on the side wall of the housing. The plane of the hyperelastic substrate also has multiple elliptical perforations (the ratio of the major and minor axes can be freely given, ranging from (0, +∞)) or other types of holes (circular, square, star-shaped, etc.) arranged regularly to reduce the local bending flexibility of the hyperelastic substrate and reduce the overall self-weight of the structure, thereby reducing the starting frequency of the local resonant bandgap.

[0039] The bandgap adjustable phononic crystal assembly process of this invention deeply integrates precision mechanical transmission and prestressing technology. Its detailed integrated assembly steps are as follows:

[0040] First, the unit cell transmission and resonance system is precisely assembled. The high-density lead core, serving as the core local resonant oscillator 2, is precisely and vertically placed into the outer shell above the superelastic substrate (with lightweight elliptical perforations on its surface). Figure 1 As shown in Figure 2. Ensure that the bottom of the lead core is perfectly aligned and fitted with the receiving groove in the center of the base, as shown in the cross-sectional view. Figure 3 As shown;

[0041] Using a purely vertical lifting mechanism, the anti-rotation side key 1 needs to be horizontally inserted through the pre-drilled side key mounting hole 7 on the side wall of the outer casing and deeply embedded into the side wall of the lead core, such as... Figure 4 As shown in Figures 5 and 6. The circumferential rotational freedom of the lead core is completely locked by the side key tail that engages with the anti-rotation groove inside the outer casing. Next, the lead screw with the adjustment knob is screwed vertically downwards into the internal threaded hole at the center of the lead core to engage it. The two halves of the split-type top cover 4 are then fastened together from the left and right sides to the top of the outer casing to tightly wrap and limit the lead screw. Finally, the pin 6 is used to firmly lock it in place, completing the encapsulation of a single phonon crystal unit cell (e.g., ...). Figure 1 As shown), the rotation drive of the knob can be effectively converted into the vertical translation of the lead core; after the assembly of the required unit cells is completed, the two-dimensional array construction and prestressing loading stage is entered, and all unit cells are neatly arranged according to the predetermined two-dimensional square lattice, strictly ensuring that the longitudinal prestressing through holes 5 reserved on both sides of each substrate are connected in a straight line; then, multiple prestressing tendons are sequentially passed through the above-mentioned aligned prestressing through holes 5, as shown. Figure 8 As shown, the bearing plates 8 are perpendicularly and tightly attached to both ends of the entire array (as shown). Figure 7(as shown); Finally, the ends of the prestressed tendons are made to penetrate the reserved holes in the bearing plate 8, nuts are screwed on both ends and gradually tightened, and the rigid pressure equalization effect of the bearing plate 8 pressing inward overcomes the bearing defects of the soft substrate, and a controlled and uniformly distributed mechanical pre-compression static load is applied to the entire relatively soft substrate array, and finally the construction of the elastic wave metamaterial system with dual bandgap adjustable characteristics is completed.

[0042] After the system is built, the elastic wave bandgap can be tuned in both broadband and low frequency modes using the "geometry-stress" dual-channel approach based on this physical model. The first step is the coarse adjustment of the geometric reconstruction: manually rotating the threaded knobs at the top of each unit cell to sequentially set the height increment of the internal lead core. The four stepped states (the number of states can be increased or decreased according to the actual situation). Frequency sweeping and data acquisition were performed using the instrument. Test results showed that when the lead core height increased to... In the limiting configuration, the lower boundary of the system bandgap drops significantly from the initial state, such as... Figure 9 As shown in Figures 10, 11, and 12. The second step is the fine-tuning of the stress softening effect: the lead cores of the entire array are uniformly configured at arbitrary heights, and then a digital torque wrench or an online digital tension controller is used to precisely control the screwing amount of the outer nuts of the cross supports, gradually generating a controlled equivalent static pressure load inside the soft substrate (this load must be strictly controlled within a range lower than the theoretical buckling load of the substrate material to maintain macroscopic structural stability). Dispersion spectrum and transmission loss tests confirm that this prestressed state weakens the tangential torsional stiffness of the substrate, causing the bandgap frequency to shift to lower frequencies.

[0043] It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this example can be implemented using existing technology.

Claims

1. A phononic crystal with an adjustable bandgap, characterized in that: It is composed of multiple phononic crystal unit cells arranged in a two-dimensional periodic array. Each phononic crystal unit cell includes: a hyperelastic substrate, a local resonant oscillator, a lifting adjustment mechanism, and a prestressing application mechanism. The lifting and adjusting mechanism includes a housing, a top cover, and a threaded knob; the housing is fixed to the top of the superelastic base, and the top cover and threaded knob are located on the top of the housing; The local resonant oscillator has a threaded through hole at its center, and the bottom end of the threaded knob has a lead screw that meshes with the threaded through hole. The two work together to form a helical transmission pair. The side wall of the outer shell has an anti-rotation groove, and the side wall of the local resonant oscillator has an anti-rotation key that slides with the anti-rotation groove, so as to convert the rotational motion of the threaded knob into the pure vertical translational motion of the local resonant oscillator. The prestressing application mechanism includes at least two prestressing tendons that run longitudinally through the hyperelastic substrate. The prestressing tendons are distributed on the inner sides of the two edges of the hyperelastic substrate. The outer sides of both ends of the hyperelastic substrate are respectively attached to a bearing plate. The two ends of the prestressing tendons pass through the bearing plate and are anchored by fasteners, which is used to convert tensile tension into a static compressive load that is uniformly distributed in the hyperelastic substrate.

2. The phononic crystal with adjustable bandgap according to claim 1, characterized in that: The local resonant oscillator is made of high-density material, and the housing, lead screw, and prestressing application mechanism of the lifting adjustment mechanism are all made of high-strength material.

3. A phononic crystal with an adjustable bandgap according to claim 2, characterized in that: The top cover is a split-type assembly structure, with its internal parts connected by pins and its external parts fixed to the top of the outer shell by at least four high-strength pins; the surface of the top cover has a circular keyway for inserting locking pins to fix the rotation angle of the threaded knob.

4. A phononic crystal with an adjustable bandgap according to claim 3, characterized in that: The outer shell is cylindrical or square in shape, and 2 to 8 anti-rotation grooves are opened on the side wall of the outer shell.

5. A phononic crystal with an adjustable bandgap according to claim 4, characterized in that: The plane of the superelastic substrate also has multiple elliptical perforations arranged regularly.

6. A method for bandgap adjustment of a phononic crystal with adjustable bandgap according to claim 1, 2, 3, 4 or 5, characterized in that: The method decouples the geometric reconstruction mechanism from the mechanical prestressing mechanism and includes a coarse tuning step and a fine tuning step. The coarse tuning step includes: continuously changing the vertical suspension height of the local resonant oscillator relative to the hyperelastic substrate by rotating the lifting adjustment mechanism. The range is taken as 1 / 8 to 1 / 4 of the height of the outer shell column. The equivalent geometric inertia is adjusted accordingly to achieve a large range of low-frequency shift of the low-frequency bandgap of the phononic crystal local resonance. The fine-tuning step includes: tensioning the prestressing tendons through the prestressing application mechanism to apply a controlled external tensile force to the hyperelastic substrate, converting it into a precompressive stress P, which does not exceed the yield stress of the substrate material. By utilizing the stress stiffening effect of a hyperelastic base under large deformation kinematics to change the global geometric stiffness matrix, precise subhertz-level fine-tuning of the bandgap boundary can be achieved without altering the physical geometry.

7. The method for bandgap adjustment of a phononic crystal with adjustable bandgap according to claim 6, characterized in that: In the coarse tuning step, for the first local resonant bandgap at low frequencies, the local resonant oscillator and the hyperelastic substrate are equivalent to a cantilever beam structure, with the vertical suspension height... With the increase of , the equivalent cantilever length changes, and its equivalent lateral bending stiffness satisfies the following relationship: Where E is the elastic modulus of the hyperelastic matrix. Let the moment of inertia of the cross section be... The initial effective bending length; the increase in height drives the bandgap initiation frequency to shift significantly to lower frequencies.

8. The method for adjusting the bandgap of a phononic crystal with adjustable bandgap according to claim 6, characterized in that: In the fine-tuning step, the applied pre-compression stress P introduces negative geometric stiffness. This reduces the system's tangent recovery capability when Much smaller than the critical buckling stress of the hyperelastic substrate At that time, the modulated local resonant frequency Satisfies the analytic relation: This enables high-resolution frequency shifting that is resistant to environmental micro-disturbances.

9. The method for adjusting the bandgap of a phononic crystal with adjustable bandgap according to claim 6, characterized in that: Regarding the coupling dispersive bandgap, with the vertical suspension height The increase in the local resonant oscillator's spatial distance from the elastic dynamic pivot of the hyperelastic substrate increases, thus increasing the equivalent dynamic mass rotational inertia tensor of the unit cell. Polarization occurs; when the excitation frequency approaches the torsional pole frequency, When the value is negative, the system generates strong bending-torsional coupling vibration and mode hybridization, thereby cutting off the transmission path of high-frequency stress waves and forming a broadband gap.

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