Programmable vibration suppression method and structure based on locally resonant metamaterial beams

Abstract

The present application belongs to the field of local resonance beam vibration isolation, and particularly relates to a programmable vibration suppression method and structure based on a local resonance metamaterial beam; the method is electrically connected with a piezoelectric sheet of the local resonance metamaterial beam, the metamaterial beam contains a combination curved beam resonator with four steady state combinations, and the code is composed of the steady state combinations; an elastic wave vibration signal at an excitation end is collected and preprocessed, a dominant frequency is extracted through fast Fourier transform, a control instruction is issued after matching a target code, and the steady state combination of the combination curved beam resonator driven by the piezoelectric sheet is switched to make the metamaterial beam form a band gap matching the dominant frequency. The present application realizes real-time on-demand vibration suppression of elastic waves, solves the problem that a traditional passive vibration isolation system cannot dynamically adjust the vibration isolation characteristics, and is suitable for a dynamically changing external excitation environment, with fast vibration isolation response speed and strong adaptability.

Description

Technical Field

[0001] This invention belongs to the field of vibration isolation of locally resonant beams, and relates to a programmable vibration suppression method and structure based on locally resonant metamaterial beams. Background Technology

[0002] Vibration propagates in various structures as elastic waves. In aerospace, marine engineering, and other fields, vibrations caused by extreme environments can easily interfere with precision equipment and devices, and even lead to safety accidents. Therefore, vibration isolation technology has become an important research direction in this field. Locally resonant metamaterial beams, leveraging their bandgap characteristics to suppress elastic waves, have become an important application of vibration isolation technology. Traditional locally resonant metamaterial beams are mostly passive vibration isolation systems. After structural design, their bandgap frequency range is fixed, and they can only suppress elastic waves of specific frequencies. In practical applications, the frequency of external excitation changes dynamically with the environment. Passive vibration isolation systems cannot adjust their isolation characteristics according to the real-time changes in the external excitation elastic wave frequency. They struggle to effectively suppress vibrations from elastic waves of non-preset frequencies. Even if bandgap characteristics are adjusted through physical reconstruction, the operation is complex and the response is lag-prone, making them unsuitable for dynamic working environments. Currently, there is a need for vibration isolation against dynamic external excitations.

[0003] Based on the above problems, there is an urgent need for a local resonant metamaterial beam vibration suppression technology that can quickly adjust the vibration isolation characteristics according to the real-time elastic wave frequency and realize on-demand vibration suppression of elastic waves, so as to solve the problem of insufficient adaptability of traditional passive vibration isolation systems. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies by proposing a programmable vibration suppression method based on a locally resonant metamaterial beam. The method is executed by a hardware control device electrically connected to a piezoelectric element on the locally resonant metamaterial beam. The locally resonant metamaterial beam includes a composite curved beam oscillator with four steady-state states. The encoding is composed of combinations of these steady-state states. The method involves: acquiring elastic wave vibration signals from the excitation end of the locally resonant metamaterial beam; preprocessing the elastic wave vibration signals; performing a fast Fourier transform on the preprocessed elastic wave vibration signals to extract the dominant frequency; retrieving a pre-established code transfer characteristic mapping database, which stores the correspondence between codes and bandgap frequencies; matching the target code corresponding to the dominant frequency; generating a control command corresponding to the target code; and sending the control command to a piezoelectric element driving circuit. The piezoelectric element driving circuit regulates the working state of the piezoelectric element, which drives the composite curved beam oscillator to switch to the steady-state combination corresponding to the target code, thereby enabling the locally resonant metamaterial beam to form a bandgap matching the dominant frequency.

[0005] Preferably, the processor on the data acquisition card performs the preprocessing operation on the elastic wave vibration signal. The preprocessing operation includes, in sequence, removing the DC component from the elastic wave vibration signal, performing low-pass digital filtering on the elastic wave vibration signal after removing the DC component, performing maximum and minimum value normalization on the elastic wave vibration signal after low-pass digital filtering, and sending the preprocessed elastic wave vibration signal to the main control unit of the hardware control device through a wired data transmission link.

[0006] More preferably, the microprocessor of the hardware control device executes the operation of performing a fast Fourier transform on the preprocessed elastic wave vibration signal to extract the dominant frequency. The operation includes performing frame segmentation processing on the preprocessed elastic wave vibration signal, with 1024 sampling points in each frame of the preprocessed elastic wave vibration signal, applying a Hanning window to the framed elastic wave vibration signal, performing a fast Fourier transform on the windowed elastic wave vibration signal to obtain frequency domain data, and extracting the frequency value with the largest amplitude from the frequency domain data as the dominant frequency.

[0007] More preferably, the industrial control computer of the hardware control device executes the operation of retrieving the pre-established code transfer characteristic mapping database and matching the target code corresponding to the dominant frequency. The establishment process of the code transfer characteristic mapping database includes testing the bandgap frequency range of the local resonant metamaterial beam corresponding to different codes, recording the one-to-one correspondence between the code and the bandgap frequency range, and storing the correspondence in the storage unit of the industrial control computer. The matching operation includes calculating the numerical intersection of the dominant frequency and each bandgap frequency range, selecting the code whose numerical intersection is the dominant frequency as the target code, and selecting the code whose bandgap frequency range contains the dominant frequency as the target code when no such code exists.

[0008] More preferably, the control command is a graded voltage drive signal with a voltage amplitude of ±100V. The graded voltage drive signal is sent to the independent drive channel of each piezoelectric element via a CAN bus. Each independent drive channel synchronously receives the graded voltage drive signal and drives the corresponding piezoelectric element. The piezoelectric element synchronously drives all combined curved beam oscillators on the local resonant metamaterial beam to switch to a steady state. After the combined curved beam oscillators complete the steady state switch, the elastic wave vibration signal at the response end of the local resonant metamaterial beam is collected, and the amplitude attenuation ratio of the elastic wave vibration signal at the excitation end and the response end is calculated. The amplitude attenuation ratio is the ratio of the amplitude at the response end to the amplitude at the excitation end. When the ratio is less than 0.1, it is determined that the steady state switch is complete. When the ratio is greater than or equal to 0.1, the extraction of the dominant frequency and subsequent steps are re-executed.

[0009] A programmable vibration damping structure based on a locally resonant metamaterial beam, applied to any of the programmable vibration damping methods based on locally resonant metamaterial beams described above, includes a locally resonant metamaterial beam body, a sensing module, a programming module, and a driving module. The sensing module, programming module, and driving module are electrically connected sequentially. The driving module is electrically connected to the locally resonant metamaterial beam body. The locally resonant metamaterial beam body includes an upper cantilever beam, a lower cantilever beam, and a combined curved beam oscillator. The combined curved beam oscillator is periodically bonded between the upper cantilever beam and the lower cantilever beam at fixed intervals. The combined curved beam oscillator consists of two single... The composite curved beam oscillator is composed of reverse-bonded curved beams. The height-to-thickness ratio of the single curved beam oscillator is greater than 2.31 and its second-order mode is restricted. The single curved beam oscillator has two steady-state states, and the composite curved beam oscillator has four steady-state states. A piezoelectric sheet is attached to the curved beam surface of the composite curved beam oscillator. The piezoelectric sheet is electrically connected to the drive module. The sensing module is used to collect elastic wave vibration signals and transmit the elastic wave vibration signals to the programming module. The programming module is used to generate control commands and output the control commands to the drive module. The drive module is used to adjust the working state of the piezoelectric sheet according to the control commands.

[0010] More preferably, the single-curved beam oscillator includes a mass block, a curved beam, and a base. The mass block is disposed at the end of the curved beam. The curved beam and the base are an integrally formed structure manufactured by fused deposition modeling. The longitudinal projection length of the curved beam is 80 mm, the midpoint height of the curved beam is 2.5 mm, the cross-sectional thickness of the curved beam is 1 mm, and the cross-sectional width of the curved beam is 10 mm. The base is used to fix the single-curved beam oscillator to other structures. The mass block is made of lead, and the curved beam and the base are made of polylactic acid.

[0011] More preferably, the piezoelectric sheet is a square curved piezoelectric sheet with external dimensions of 21mm × 7.8mm × 0.7mm, a capacitance of 220nF, a resonant frequency of 730Hz, and eight piezoelectric sheets. The eight piezoelectric sheets are respectively attached to the upper and lower curved beam surfaces of the combined curved beam oscillator. Each piezoelectric sheet is equipped with an independent driving channel, which is electrically connected to the output terminal of the driving module. The independent driving channel is used to independently output a driving signal to the corresponding piezoelectric sheet.

[0012] More preferably, the number of the combined curved beam oscillators is eight, the fixed interval between two adjacent combined curved beam oscillators is 100mm, the upper cantilever beam and the lower cantilever beam are both formed by computer numerical control machining, the material of the upper cantilever beam and the lower cantilever beam is white polyethylene plastic, the density of the white polyethylene plastic is 980.8kg / m³, the elastic modulus is 2100MPa, and the Poisson's ratio is 0.3, the density of the polylactic acid is 1200kg / m³, the elastic modulus is 2750MPa, and the Poisson's ratio is 0.3, and the combined curved beam oscillators are bonded and fixed to the upper cantilever beam and the lower cantilever beam with epoxy resin adhesive.

[0013] Further preferably, the sensing module includes a piezoelectric accelerometer and a data acquisition card. The piezoelectric accelerometer is used to collect elastic wave vibration signals, and the data acquisition card is used to convert the analog signals of the elastic wave vibration signals into digital signals. The programming module includes a host computer and a slave computer. The host computer is an Advantech IPC series industrial control computer equipped with a solid-state drive (SSD). The SSD is used to store a code transfer characteristic mapping database and elastic wave vibration signal logs. The slave computer is an STM32H743IIK6 microprocessor and is externally connected to a W25Q256 FLASH memory. The FLASH memory is used to store an encoding frequency mapping table and piezoelectric element driving parameters. The driving module includes an instruction decoding circuit and a power supply module. The instruction decoding circuit includes a TJA1050 CAN bus receiver and a level conversion circuit. The power supply module is a Mornsun LM100-20B05 power supply module, which provides high-voltage power to the piezoelectric element and low-voltage DC power to the sensing module and the programming module.

[0014] Technical effects: The core inventive technology of this invention is to design the composite curved beam oscillator with four steady-state states. The encoding is composed of combinations of steady-state states and establishes a correspondence with the bandgap frequency. A hardware control device acquires elastic wave signals in real time and matches them with the target encoding, driving piezoelectric elements to regulate the steady-state combinations of the composite curved beam oscillator. This technology precisely solves the core problem of traditional passive vibration isolation systems being unable to adjust vibration isolation characteristics according to dynamic external excitation. It allows for rapid adjustment of the bandgap frequency of the metamaterial beam without physical reconstruction, achieving real-time, on-demand vibration suppression of elastic waves, adapting to various dynamically changing vibration environments. Furthermore, the oscillator state switching responsiveness is excellent, and the controllability and accuracy of the vibration suppression process are significantly improved. Attached Figure Description

[0015] Figure 1 This application presents a programmable vibration suppression method for locally resonant metamaterial beams. Figure 2 This is a front view of the single-curved beam oscillator of the present invention; Figure 3 This is a side view of the single-curved beam oscillator of the present invention; Figure 4 This is a top view of the single-curved beam oscillator of the present invention; Figure 5 This is an axonometric view of the single-curved beam oscillator of the present invention; Figure 6 This is a front view of the combined curved beam oscillator of the present invention; Figure 7 This is a side view of the combined curved beam oscillator of the present invention; Figure 8 This is a top view of the combined curved beam oscillator of the present invention; Figure 9 This is an axonometric view of the combined curved beam oscillator of the present invention; Figure 10 This is a 3D diagram of the local resonant beam of the present invention; Figure 11 This is a schematic diagram illustrating the global vibration suppression principle and structure of the present invention; Figure 12 This is a schematic diagram illustrating the coded bandgap reconstruction mechanism and comparison of the present invention; Figure 13 This is a flowchart of the intelligent adaptive vibration suppression control process and system architecture of the present invention.

[0016] In the diagram: 1. First mass block; 2. Second mass block; 3. First curved beam; 4. Second curved beam; 13. First base; 14. First base; 3. Upper curved beam; 4. Lower curved beam; 5-12. Piezoelectric sheet; 17. Combined curved beam vibrator; 14. Upper cantilever beam; 15. Lower cantilever beam. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0018] Traditional local resonant metamaterial beams are passive vibration isolation systems. Their bandgap frequency is fixed and cannot be dynamically adjusted according to the frequency of externally excited elastic waves. Furthermore, they lack a complete method to collect vibration signals in real time, match corresponding vibration isolation codes, and drive structural adjustments. Therefore, they are difficult to effectively suppress vibrations in the face of dynamically changing vibration environments.

[0019] Based on this, please refer to Figures 1-13In the integrated scheme of the local resonant beam, the operation and structural features for installing the curved beam oscillator assembly are described as follows: The single curved beam oscillator consists of a first mass block 1, a second mass block 2, a first curved beam 3, and a second curved beam 4 as its basic structure, and is fixed by a first base 13 and a first base 14. The combined curved beam oscillator is composed of two single curved beam oscillators bonded together in reverse using epoxy resin. The longitudinal projection length of the curved beam is 80mm; the height at the middle of the curved beam is 2.5mm; the cross-sectional thickness of the curved beam is 1mm; and the cross-sectional width of the curved beam is 10mm. The mass blocks are replaced by lead blocks; the curved beam and the base are generated by fused deposition modeling (FDM) 3D printing using polylactic acid (PLA) with a density of 1200kg / m³. 3 Its elastic modulus is 2750 MPa, and its Poisson's ratio is 0.3. Secondly, as... Figure 8 As shown, to achieve rapid and efficient switching between two steady states (operating states) for a single oscillator, piezoelectric sheets 5-12 are attached to both sides of the upper curved beam 3 and the lower curved beam 4, thereby actively controlling the mechanical characteristics of each combined curved beam oscillator (a total of four states). The piezoelectric sheets used are square curved sheets of model CMBP01. Their dimensions (mm) are: 21 × 7.8 × 0.7, driving voltage: ±100V, capacitance: 2 × 110nF, and resonant frequency: 730Hz. Finally, as... Figure 9 As shown, eight composite curved beam oscillators 17 are periodically bonded and fixed (using epoxy resin adhesive) at 100mm intervals between the upper cantilever beam 14 and the lower cantilever beam 15 to form a localized resonant beam, thereby generating band gaps at different frequency bands and achieving efficient vibration suppression. The upper and lower cantilever beams are formed using computer numerical control (CNC) machining, and the material is white polyethylene plastic with a density of 980.8 kg / m³. 3 Its elastic modulus is 2100 MPa and its Poisson's ratio is 0.3.

[0020] This invention provides a programmable vibration suppression method based on a locally resonant metamaterial beam. A hardware control device executes the method, electrically connected to a piezoelectric element on the locally resonant metamaterial beam. The beam includes a composite curved beam oscillator with four steady-state states. An encoding is formed by combining these steady-state states. Elastic wave vibration signals from the excitation end of the beam are acquired, preprocessed, and subjected to a Fast Fourier Transform to extract the dominant frequency. A pre-established code transfer characteristic mapping database is retrieved, storing the correspondence between encodings and bandgap frequencies. A target encoding corresponding to the dominant frequency is matched, generating a control command corresponding to the target encoding. This control command is sent to a piezoelectric element driving circuit, which regulates the piezoelectric element's operating state. The piezoelectric element drives the composite curved beam oscillator to switch to the steady-state combination corresponding to the target encoding, thus forming a bandgap in the locally resonant metamaterial beam that matches the dominant frequency.

[0021] The core of this method is to construct a complete closed loop from vibration signal acquisition to oscillator state control based on a hardware control device. The four steady-state states of the composite curved beam oscillator are the foundation for bandgap adjustment. Different combinations of steady-state states correspond to different structural stiffness characteristics, thus forming bandgap frequencies. Encoding is the carrier that associates the steady-state combinations with the bandgap frequencies, and the code transmission characteristic mapping database provides data support for frequency and code matching. The hardware control device, as the execution entity, is crucial for connecting signal processing and structural control. Its electrical connection with the piezoelectric element ensures the effective transmission of control commands. The piezoelectric element, as the execution element, converts electrical signals into mechanical actions, driving the composite curved beam oscillator to complete the switching of steady-state states.

[0022] The method proceeds sequentially through signal acquisition, signal processing, encoding and matching, command issuance, and structural control. First, the elastic wave vibration signal from the excitation end is acquired. This signal directly reflects the external excitation frequency. After preprocessing to remove interference, the accuracy of subsequent frequency extraction is ensured. Then, a Fast Fourier Transform (FFT) is used to convert the time-domain vibration signal into frequency-domain data, extracting the dominant frequency as the core frequency feature of the external excitation. Subsequently, a database matching process is used to obtain the target code that forms the corresponding bandgap. The generated control command is transmitted to the piezoelectric element via the drive circuit, ultimately achieving state switching and precise bandgap matching for the composite curved beam oscillator. This method, through coded oscillator state control, enables rapid adjustment of the metamaterial beam bandgap frequency without requiring physical structural reconstruction, adapting to dynamically changing external excitation environments.

[0023] Traditional vibration signal preprocessing lacks standardized execution entities and specific operating procedures, which easily leads to inconsistent processing methods and poor signal processing effects, resulting in large errors in subsequent frequency extraction and affecting the overall accuracy of vibration suppression.

[0024] Based on this, the processor on the data acquisition card performs the preprocessing operation on the elastic wave vibration signal. The preprocessing operation, in sequence, includes removing the DC component from the elastic wave vibration signal, performing low-pass digital filtering on the DC-removed elastic wave vibration signal, and performing maximum-minimum normalization on the low-pass digitally filtered elastic wave vibration signal. The preprocessed elastic wave vibration signal is then sent to the main control unit of the hardware control device via a wired data transmission link. This scheme explicitly uses the processor on the data acquisition card as the main execution body for the preprocessing operation, utilizing the hardware characteristics of the data acquisition card to ensure the real-time performance and stability of signal processing. The preprocessing operation is performed in a fixed sequence. DC component removal eliminates DC offset interference in the signal, avoiding the influence of DC components on subsequent frequency domain analysis. Low-pass digital filtering filters out high-frequency noise in the signal, retaining the effective frequency components of the elastic wave vibration signal. Maximum-minimum normalization maps the signal amplitude to a fixed range, unifying the signal scale and facilitating subsequent frequency calculation and analysis.

[0025] The preprocessed signal is transmitted to the main control unit via a wired data transmission link. Wired transmission ensures signal stability, avoids signal attenuation and interference associated with wireless transmission, and guarantees that the main control unit receives a high-quality, effective signal. This solution improves the effectiveness and consistency of vibration signal preprocessing by clearly defining the execution entity and standardizing processing steps, laying a data foundation for the accurate extraction of the dominant frequency and effectively reducing frequency extraction errors caused by signal interference.

[0026] Traditional elastic wave vibration signal frequency extraction operations lack specific execution hardware and standardized operating procedures. Inadequate signal processing before Fourier transform can easily lead to low frequency extraction accuracy and failure to accurately reflect the dominant frequency of external excitation, resulting in coding matching errors.

[0027] Based on this, the microprocessor of the hardware control device executes the operation of extracting the dominant frequency by performing a Fast Fourier Transform (FFT) on the preprocessed elastic wave vibration signal. This operation includes frame segmentation of the preprocessed elastic wave vibration signal, with each frame containing 1024 sampling points. A Hanning window is then applied to the framed elastic wave vibration signal. A FFT is then performed on the windowed elastic wave vibration signal to obtain frequency domain data. The frequency value with the largest amplitude is extracted from the frequency domain data as the dominant frequency. This scheme designates the microprocessor of the hardware control device as the main body for frequency extraction. The high-speed computing power of the microprocessor ensures the real-time performance of frequency extraction. Frame segmentation divides the continuous vibration signal into fixed-length frames. The 1024 sampling points per frame balance computational efficiency and frequency extraction accuracy, avoiding insufficient accuracy due to too few sampling points and computational delay caused by too many sampling points. The Hanning window is used in the windowing process, which effectively suppresses spectral leakage during the Fourier transform process, reduces errors in frequency analysis, and allows the frequency domain data to more accurately reflect the frequency characteristics of the signal.

[0028] The Fast Fourier Transform (FFT) converts the time-domain frame signal into frequency-domain data. The frequency value with the largest amplitude in the frequency-domain data is the dominant frequency of the external excitation. This extraction method can accurately capture the core frequency that causes vibration. By clearly defining the hardware execution entity and standardizing step-by-step operations, this scheme effectively improves the accuracy and efficiency of dominant frequency extraction, reduces spectral leakage and errors caused by signal processing, and provides a reliable frequency basis for accurate matching in subsequent encoding.

[0029] Traditional encoding matching operations lack specific execution hardware and standardized database establishment and frequency matching procedures. The correspondence between encoding and bandgap frequency is unclear, which can easily lead to inaccurate matching results and the inability to quickly find the corresponding target encoding, affecting the accuracy and response speed of bandgap adjustment.

[0030] Based on this, the industrial control computer of the hardware control device executes the operation of retrieving the pre-established code transfer characteristic mapping database and matching the target code corresponding to the dominant frequency. The establishment process of the code transfer characteristic mapping database includes testing the bandgap frequency range of the local resonant metamaterial beam corresponding to different codes, recording the one-to-one correspondence between the code and the bandgap frequency range, and storing the correspondence in the storage unit of the industrial control computer. The matching operation includes calculating the numerical intersection of the dominant frequency and each bandgap frequency range, selecting the code whose numerical intersection is the dominant frequency as the target code, and selecting the code whose bandgap frequency range contains the dominant frequency as the target code when there is no such code.

[0031] This solution utilizes an industrial control computer as the primary execution unit for code matching and database management. Leveraging its large-capacity storage and high-speed computing capabilities, it achieves efficient database storage and rapid code matching. The database was established through actual testing, ensuring the authenticity and accuracy of the correspondence between codes and bandgap frequency ranges, providing a reliable data foundation for subsequent matching. The matching operation employs a numerical intersection calculation method. First, codes that perfectly match the dominant frequency are selected; if no perfectly matching code exists, codes containing that frequency are selected. This matching rule balances accuracy and adaptability, enabling the rapid identification of the optimal target code. By clearly defining the execution hardware, standardizing the database establishment process, and establishing clear matching rules, this solution improves the accuracy and speed of code matching, ensuring the rapid identification of the corresponding target code based on the dominant frequency, thus providing a guarantee for the rapid adjustment of the oscillator state.

[0032] Traditional control command issuance and oscillator state switching operations lack specific command formats, transmission methods, and state verification standards, which can easily lead to problems such as command transmission delays, poor oscillator synchronization switching, and inability to determine whether effective bandgap adjustment has been achieved, thus affecting the overall vibration suppression effect.

[0033] Based on this, the control command is a graded voltage drive signal with a voltage amplitude of ±100V. The graded voltage drive signal is sent to the independent drive channel of each piezoelectric element via the CAN bus. Each independent drive channel synchronously receives the graded voltage drive signal and drives the corresponding piezoelectric element. The piezoelectric element synchronously drives all the combined curved beam oscillators on the local resonant metamaterial beam to switch to a steady state. After the combined curved beam oscillators complete the steady state switch, the elastic wave vibration signal at the response end of the local resonant metamaterial beam is collected, and the amplitude attenuation ratio of the elastic wave vibration signal at the excitation end and the response end is calculated. The amplitude attenuation ratio is the ratio of the amplitude at the response end to the amplitude at the excitation end. When the ratio is less than 0.1, it is determined that the steady state switch is complete. When the ratio is greater than or equal to 0.1, the extraction of the dominant frequency and subsequent steps are re-executed.

[0034] This scheme sets the control commands to ±100V graded voltage drive signals, which are compatible with the driving characteristics of the piezoelectric elements and can effectively drive them to produce mechanical movements. Commands are transmitted via a CAN bus, utilizing its multi-node synchronous transmission characteristics to ensure that the independent drive channels of each piezoelectric element can receive commands synchronously, achieving synchronous state switching of all composite curved beam oscillators and avoiding abnormal bandgap characteristics caused by asynchronous switching. Each piezoelectric element is equipped with an independent drive channel, ensuring the driving accuracy of each element and guaranteeing the accuracy of oscillator state switching. A clear state verification standard is also established. The bandgap adjustment effect is judged by calculating the amplitude attenuation ratio between the excitation and response ends. A ratio less than 0.1 indicates effective vibration suppression; otherwise, the relevant steps are repeated, forming a closed-loop verification and adjustment mechanism. This scheme, through its clear command format, synchronous transmission and drive method, and quantified state verification standard, improves the synchronicity and accuracy of oscillator state switching, ensuring that the metamaterial beam can form an effective bandgap to achieve vibration suppression.

[0035] Traditional local resonant metamaterial beam vibration isolation structures lack a core structural design that enables dynamic bandgap adjustment. The oscillator lacks multi-steady-state characteristics and has not established a sensing, programming, and driving module system adapted to the structure, thus failing to achieve the function of adjusting the structure's vibration isolation characteristics based on vibration signals.

[0036] Based on this, this embodiment provides a programmable vibration damping structure based on a locally resonant metamaterial beam, including a locally resonant metamaterial beam body, a sensing module, a programming module, and a driving module. The sensing module, programming module, and driving module are electrically connected in sequence. The driving module is electrically connected to the locally resonant metamaterial beam body. The locally resonant metamaterial beam body includes an upper cantilever beam, a lower cantilever beam, and a combined curved beam oscillator. The combined curved beam oscillator is periodically bonded between the upper cantilever beam and the lower cantilever beam at fixed intervals. The combined curved beam oscillator is composed of two single curved beam oscillators bonded in opposite directions. The single-curved beam oscillator has a height-to-thickness ratio greater than 2.31 and its second-order mode is restricted. The single-curved beam oscillator has two steady-state states, while the combined curved beam oscillator has four steady-state states. A piezoelectric element is mounted on the curved beam surface of the combined curved beam oscillator, and the piezoelectric element is electrically connected to the drive module. The sensing module collects elastic wave vibration signals and transmits them to the programming module. The programming module generates control commands and outputs these commands to the drive module. The drive module adjusts the working state of the piezoelectric element according to the control commands. The core innovation of this structure lies in the multi-stable-state design of the combined curved beam oscillator. The single-curved beam oscillator achieves bistable characteristics through a structural design with a height-to-thickness ratio greater than 2.31 and restricted second-order modes. Two single-curved beam oscillators are bonded in opposite directions to form a combined curved beam oscillator with four steady-state states. Different combinations of steady-state states correspond to different structural stiffnesses, providing a structural basis for bandgap frequency adjustment. The composite curved beam oscillator is periodically bonded between the upper and lower cantilever beams to ensure the overall periodic characteristics of the metamaterial beam, which meets the structural requirements for local resonance.

[0037] The single-curved beam oscillator of this invention effectively restricts the second-order modes through a high-thickness-ratio directional design. The specific design mechanism, parameter basis, and verification results are as follows: The high-thickness-ratio of the single-curved beam oscillator is defined as the ratio of the height at the center of the curved beam to the thickness of the cross-section. In this invention, the height at the center of the curved beam is 2.5 mm and the cross-section thickness is 1 mm, resulting in a calculated high-thickness-ratio of 2.5, which is greater than the critical threshold of 2.31, satisfying the structural conditions for second-order mode restriction. When the high-thickness-ratio is greater than 2.31, the stiffness distribution and natural frequency of the curved beam are directionally controlled, and the second-order natural mode frequency is raised to outside the vibration suppression operating frequency band. External elastic wave excitation cannot induce second-order mode vibration; only the fundamental frequency mode participates in local resonance and bistable switching, structurally eliminating mode interference, resonance shift, and bistable failure caused by the second-order mode. Finite element modal simulation and shaking table experiments have verified that the single-curved beam oscillator with this high thickness ratio design exhibits only a single-mode response in the working frequency band, with no excitation or coupling of the second-order mode. This ensures the stability of the oscillator's bistable characteristics, thereby guaranteeing accurate switching between the four steady states and reliable bandgap control of the combined curved beam oscillator.

[0038] Piezoelectric elements are mounted on the surface of the curved beam, serving as the actuators for structural adjustment and electrically connected to the drive module to receive drive signals. A modular system is also constructed, with sensing, programming, and drive modules sequentially connected electrically. The sensing module acquires vibration signals, the programming module processes signals and generates control commands, and the drive module converts the commands into drive signals for the piezoelectric elements. These three modules work collaboratively with the metamaterial beam body to construct a complete hardware system from signal acquisition to structural control. Through the design of a multi-stable oscillator and the accompanying modular system, this structure achieves programmability for vibration isolation structures, providing hardware support for dynamically adjusting the bandgap frequency and breaking the fixed bandgap limitation of traditional passive structures.

[0039] Traditional single-curved beam oscillators lack specific structural components, dimensional parameters, and material design, making it impossible to guarantee the realization of their bistable characteristics. Furthermore, the structural forming method is unclear, which can easily lead to problems such as insufficient structural strength and unsmooth transitions between steady states, thus affecting the overall performance of the composite curved beam oscillator.

[0040] Based on this, the single-curved beam oscillator includes a mass block, a curved beam, and a base. The mass block is located at the end of the curved beam. The curved beam and the base are an integrally formed structure manufactured by fused deposition modeling (FDM). The longitudinal projection length of the curved beam is 80 mm, the mid-section height is 2.5 mm, the cross-sectional thickness is 1 mm, and the cross-sectional width is 10 mm. The base is used to fix the single-curved beam oscillator to other structures. The mass block is made of lead, and the curved beam and the base are made of polylactic acid (PLA). This design clarifies that the single-curved beam oscillator consists of a mass block, a curved beam, and a base. The mass block, located at the end of the curved beam, provides inertial characteristics to the oscillator and is a crucial part for achieving local resonance. The lead material of the mass block ensures the inertial effect and enhances the resonance suppression capability. The curved beam has specific dimensional parameters: a longitudinal projection length of 80 mm, a mid-section height of 2.5 mm, a cross-sectional thickness of 1 mm, and a cross-sectional width of 10 mm. Combined with a height-to-thickness ratio greater than 2.31, this ensures the realization of its bistable characteristics. The curved beam and base are integrally molded using fused deposition modeling (FDM) additive manufacturing, enhancing the overall strength and stability of the structure, avoiding structural gaps caused by splicing, and ensuring smooth switching of the oscillator's states. The curved beam and base, made of polylactic acid (PLA), possess suitable elastic modulus and stiffness to meet the steady-state switching requirements of the oscillator. The base provides a fixed connection for the oscillator, ensuring its stable installation between the cantilever beams of the metamaterial beam. This solution, through specific structural composition, quantified dimensional parameters, suitable material selection, and an integrated molding method, ensures the stable realization of the bistable characteristics of the single curved beam oscillator, improves structural strength and performance, and lays the foundation for the multi-stable characteristics of composite curved beam oscillators.

[0041] Traditional piezoelectric elements lack specific model parameters, mounting methods, and drive configurations, resulting in poor compatibility with composite curved beam oscillators. This can lead to issues such as poor driving performance and inability to accurately drive the oscillator to switch steady-state states, thus affecting the accuracy of bandgap adjustment.

[0042] Based on this, the piezoelectric element is a square curved piezoelectric element with dimensions of 21mm × 7.8mm × 0.7mm, a capacitance of 220nF, and a resonant frequency of 730Hz. Eight piezoelectric elements are used, each mounted on one of the upper and lower curved beam surfaces of the combined curved beam oscillator. Each piezoelectric element has an independent drive channel electrically connected to the output of the drive module, used to independently output a drive signal to the corresponding piezoelectric element. This design specifies that the piezoelectric element is a square curved piezoelectric element, whose dimensions, capacitance, and resonant frequency are compatible with the structure and drive requirements of the combined curved beam oscillator. This effectively converts electrical signals into mechanical bending motion, driving the curved beam to achieve steady-state switching. The eight piezoelectric elements mounted on the upper and lower curved beam surfaces ensure uniform drive of the curved beam, guaranteeing the smoothness and accuracy of oscillator state switching and avoiding uneven structural stress caused by unilateral drive. Each piezoelectric element is equipped with an independent drive channel, electrically connected to the drive module, enabling precise and independent control of each piezoelectric element. It outputs a matching drive signal based on control commands, ensuring that the drive action of the piezoelectric element matches the oscillator state corresponding to the target code. This solution improves the compatibility and driving accuracy between the piezoelectric elements and the composite curved beam oscillator through specific piezoelectric element parameters, a reasonable mounting method, and independent drive configuration, ensuring accurate driving of the oscillator to complete steady-state switching.

[0043] Traditional local resonant metamaterial beams lack requirements on the number and spacing of composite curved beam oscillators, the processing technology and material parameters of cantilever beams are unclear, and there are no specific regulations on structural connection methods. This can easily lead to problems such as poor periodic characteristics of metamaterial beams, insufficient overall structural strength, and unstable bandgap characteristics.

[0044] Based on this, the number of composite curved beam oscillators is eight, with a fixed interval of 100mm between adjacent composite curved beam oscillators. Both the upper and lower cantilever beams are formed using computer numerical control (CNC) machining. The upper and lower cantilever beams are made of white polyethylene plastic with a density of 980.8 kg / m³, an elastic modulus of 2100 MPa, and a Poisson's ratio of 0.3. The polylactic acid (PLA) has a density of 1200 kg / m³, an elastic modulus of 2750 MPa, and a Poisson's ratio of 0.3. The composite curved beam oscillators are bonded to the upper and lower cantilever beams using epoxy resin adhesive. This scheme clearly defines the periodic arrangement of the eight composite curved beam oscillators at a fixed interval of 100mm, ensuring the periodic structural characteristics of the metamaterial beam, meeting the structural design requirements of local resonance, and forming stable bandgap characteristics. The upper and lower cantilever beams are formed using computer numerical control (CNC) machining, ensuring dimensional accuracy and structural consistency, and providing a foundation for the stable installation of the composite curved beam oscillator. The white polyethylene plastic cantilever beam and the polylactic acid curved beam base are compatible in terms of density, elastic modulus, and Poisson's ratio, ensuring the overall mechanical properties of the metamaterial beam and meeting the requirements for vibration propagation and suppression. The composite curved beam oscillator is bonded to the cantilever beam with epoxy resin adhesive, ensuring a strong connection and structural integrity, preventing structural loosening during vibration, and guaranteeing the stability of the bandgap characteristics. This solution, through clear oscillator arrangement requirements, quantified material parameters, precise machining processes, and reliable connection methods, improves the structural stability and periodic characteristics of the metamaterial beam, ensuring stable bandgap characteristics and providing a reliable structural foundation for dynamic vibration suppression.

[0045] Traditional sensing, programming, and driving modules lack specific hardware components, model parameters, and functional divisions. The compatibility of each module is poor, which can easily lead to problems such as inaccurate signal acquisition, low data processing efficiency, and untimely command driving, making it impossible to achieve collaborative work with the metamaterial beam body.

[0046] Based on this, the sensing module includes a piezoelectric accelerometer and a data acquisition card. The piezoelectric accelerometer is used to collect elastic wave vibration signals, and the data acquisition card is used to convert the analog signals of the elastic wave vibration signals into digital signals. The programming module includes a host computer and a slave computer. The host computer is an Advantech IPC series industrial control computer equipped with a solid-state drive (SSD). The SSD is used to store a code transfer characteristic mapping database and elastic wave vibration signal logs. The slave computer is an STM32H743IIK6 microprocessor and is externally connected to a W25Q256 FLASH memory. The FLASH memory is used to store an encoding frequency mapping table and piezoelectric element driving parameters. The driving module includes an instruction decoding circuit and a power supply module. The instruction decoding circuit includes a TJA1050 CAN bus receiver and a level conversion circuit. The power supply module is a Mornsun LM100-20B05 power supply module, which provides high-voltage power to the piezoelectric element and low-voltage DC power to the sensing module and the programming module. This solution features specific hardware configurations and functional divisions for three modules. The piezoelectric accelerometer in the sensing module accurately acquires elastic wave vibration signals, while the data acquisition card performs analog-to-digital conversion, transforming analog signals into easily processed digital signals. The programming module employs a host computer and slave computer architecture. An Advantech IPC series industrial control computer serves as the host computer, responsible for large-scale data storage and complex calculations, while an STM32H743IIK6 microprocessor acts as the slave computer, handling real-time data processing and instruction issuance. This combination balances storage capacity and real-time computation, with supporting storage hardware providing a reliable storage medium for various data and parameters. The instruction decoding circuit in the drive module converts instructions from the programming module into signals recognizable by the piezoelectric element. The power supply module provides a suitable power supply for the entire system; high voltage powers the piezoelectric element drive, while low voltage powers the sensing and programming modules, ensuring the normal operation of each module. The hardware models and parameters of each module are mutually compatible, with clear functional divisions, enabling efficient collaboration between signal acquisition, data processing, instruction generation, and drive execution. This provides a stable hardware control system for programmable vibration suppression of metamaterial beams.

[0047] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. The above descriptions are only preferred embodiments of this application. It should be noted that due to the limitations of written expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of this application, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of this application.

Claims

1. A programmable vibration suppression method based on a locally resonant metamaterial beam, characterized in that, include: S1: Collect the elastic wave vibration signal at the excitation end of the local resonant metamaterial beam, and preprocess the elastic wave vibration signal; S2: Perform a fast Fourier transform on the preprocessed elastic wave vibration signal to extract the dominant frequency; S3: Retrieve a pre-established code transfer characteristic mapping database, which stores the correspondence between codes and bandgap frequencies; S4: Match the target code corresponding to the dominant frequency, and generate the control command corresponding to the target code; S5: Send the control command to the piezoelectric element drive circuit, and regulate the working state of the piezoelectric element through the piezoelectric element drive circuit; S6: The piezoelectric element drives the combined curved beam oscillator to switch to the steady-state combination corresponding to the target code; S7: To form a bandgap in the local resonant metamaterial beam that matches the dominant frequency.

2. The programmable vibration suppression method based on a locally resonant metamaterial beam according to claim 1, characterized in that, The preprocessing of the elastic wave vibration signal includes: removing the DC component from the elastic wave vibration signal, performing low-pass digital filtering on the elastic wave vibration signal after removing the DC component, performing maximum and minimum value normalization on the elastic wave vibration signal after low-pass digital filtering, and sending the preprocessed elastic wave vibration signal to the main control unit of the hardware control device through a wired data transmission link.

3. The programmable vibration suppression method based on a locally resonant metamaterial beam according to claim 1, characterized in that, The step of performing Fast Fourier Transform (FFT) on the preprocessed elastic wave vibration signal to extract the dominant frequency includes performing frame segmentation on the preprocessed elastic wave vibration signal, with 1024 sampling points per frame, applying a Hanning window to the framed elastic wave vibration signal, performing FFT on the windowed elastic wave vibration signal to obtain frequency domain data, and extracting the frequency value with the largest amplitude from the frequency domain data as the dominant frequency.

4. The programmable vibration suppression method based on a locally resonant metamaterial beam according to claim 1, characterized in that, The process of establishing the code transfer characteristic mapping database includes testing the bandgap frequency range of the local resonant metamaterial beam corresponding to different codes, recording the one-to-one correspondence between the codes and the bandgap frequency ranges, and storing the correspondence in the storage unit of the industrial control computer. The matching operation includes calculating the numerical intersection of the dominant frequency and each bandgap frequency range, selecting the code whose numerical intersection is the dominant frequency as the target code, and selecting the code whose bandgap frequency range contains the dominant frequency as the target code when there is no such code.

5. The programmable vibration suppression method for beams based on localized resonance metamaterials according to claim 1, characterized in that, The control command is a graded voltage drive signal with a voltage amplitude of ±100V. The graded voltage drive signal is sent to the independent drive channel of each piezoelectric element via the CAN bus. Each independent drive channel synchronously receives the graded voltage drive signal and drives the corresponding piezoelectric element. The piezoelectric element synchronously drives all the combined curved beam oscillators on the local resonant metamaterial beam to switch to a steady state. After the combined curved beam oscillators complete the steady state switch, the elastic wave vibration signal at the response end of the local resonant metamaterial beam is collected, and the amplitude attenuation ratio of the elastic wave vibration signal at the excitation end and the response end is calculated. The amplitude attenuation ratio is the ratio of the amplitude at the response end to the amplitude at the excitation end. When the ratio is less than 0.1, it is determined that the steady state switch is complete. When the ratio is greater than or equal to 0.1, the extraction of the dominant frequency and subsequent steps are re-executed.

6. A programmable vibration suppression structure based on a locally resonant metamaterial beam, applied to the programmable vibration suppression method based on a locally resonant metamaterial beam as described in any one of claims 1-5, comprising a locally resonant metamaterial beam body, a sensing module, a programming module, and a driving module, wherein the sensing module, programming module, and driving module are electrically connected in sequence, and the driving module is electrically connected to the locally resonant metamaterial beam body, characterized in that, The localized resonant metamaterial beam body includes an upper cantilever beam, a lower cantilever beam, and a combined curved beam oscillator. The combined curved beam oscillator is periodically bonded between the upper and lower cantilever beams at fixed intervals. The combined curved beam oscillator is composed of two single curved beam oscillators bonded in opposite directions. The height-to-thickness ratio of the single curved beam oscillator is greater than 2.31, and its second-order mode is restricted. The single curved beam oscillator has two steady-state states, and the combined curved beam oscillator has four steady-state states. A piezoelectric sheet is attached to the curved beam surface of the combined curved beam oscillator. The piezoelectric sheet is electrically connected to the driving module. The sensing module is used to collect elastic wave vibration signals and transmit the elastic wave vibration signals to the programming module. The programming module is used to generate control commands and output the control commands to the driving module. The driving module is used to adjust the working state of the piezoelectric sheet according to the control commands.

7. The programmable vibration damping structure based on a locally resonant metamaterial beam according to claim 6, characterized in that, The single-curved beam oscillator includes a mass block, a curved beam, and a base. The mass block is disposed at the end of the curved beam. The curved beam and the base are integrally formed structures by fused deposition modeling. The longitudinal projection length of the curved beam is 80 mm, the mid-section height of the curved beam is 2.5 mm, the cross-sectional thickness of the curved beam is 1 mm, and the cross-sectional width of the curved beam is 10 mm. The base is used to fix the single-curved beam oscillator to other structures. The mass block is made of lead, and the curved beam and the base are made of polylactic acid.

8. The programmable vibration damping structure based on a locally resonant metamaterial beam according to claim 6, characterized in that, The piezoelectric element is a square curved piezoelectric element with dimensions of 21mm × 7.8mm × 0.7mm, a capacitance of 220nF, and a resonant frequency of 730Hz. There are eight piezoelectric elements, which are respectively attached to the upper and lower curved beam surfaces of the combined curved beam oscillator. Each piezoelectric element is equipped with an independent drive channel, which is electrically connected to the output terminal of the drive module. The independent drive channel is used to independently output a drive signal to the corresponding piezoelectric element.

9. The programmable vibration damping structure based on a locally resonant metamaterial beam according to claim 7, characterized in that, The composite curved beam oscillator comprises eight elements, with a fixed interval of 100mm between adjacent composite curved beam oscillators. Both the upper and lower cantilever beams are formed using computer numerical control (CNC) machining. The upper and lower cantilever beams are made of white polyethylene plastic with a density of 980.8 kg / m³, an elastic modulus of 2100 MPa, and a Poisson's ratio of 0.

3. The polylactic acid has a density of 1200 kg / m³, an elastic modulus of 2750 MPa, and a Poisson's ratio of 0.

3. The composite curved beam oscillators are bonded to the upper and lower cantilever beams using epoxy resin adhesive.

10. The programmable vibration damping structure based on a locally resonant metamaterial beam according to claim 6, characterized in that, The sensing module includes a piezoelectric accelerometer and a data acquisition card. The piezoelectric accelerometer is used to collect elastic wave vibration signals, and the data acquisition card is used to convert the analog signals of the elastic wave vibration signals into digital signals. The programming module includes a host computer and a slave computer. The host computer is an Advantech IPC series industrial control computer equipped with a solid-state drive (SSD) for storing a code transfer characteristic mapping database and elastic wave vibration signal logs. The slave computer is an STM32 microprocessor with an external FLASH memory for storing an encoding frequency mapping table and piezoelectric element driving parameters. The driving module includes an instruction decoding circuit and a power supply module. The instruction decoding circuit includes a CAN bus receiver and a level conversion circuit. The power supply module provides high-voltage power to the piezoelectric element and low-voltage DC power to the sensing module and the programming module.

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