Thin-wall structure vibration control method based on inerter type nonlinear energy trap
By employing a vibration control method with an inertial capacitive nonlinear energy trap in aerospace thin-walled structures, the contradiction between lightweighting and vibration control is resolved, achieving adaptive vibration control over a wide frequency range and multiple operating conditions, and improving vibration suppression performance.
Patent Information
- Application Number
- CN202511703655.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-19
- Publication Date
- 2026-01-30
AI Technical Summary
Traditional vibration control methods present a contradiction between lightweighting and vibration control in aerospace thin-walled structures, making it difficult to adapt to wide-frequency vibrations and multi-condition environments, and unable to achieve effective adaptive vibration control.
A vibration control method based on inertial capacitive nonlinear energy traps is adopted. By establishing a coupled dynamic model, distributing inertial capacitive nonlinear energy trap units, and combining harmonic balance method and particle swarm optimization, adaptive frequency tracking and parameter adjustment are achieved, the parameters of inertial capacitive elements are optimized, and multi-condition adaptive vibration control is realized.
It achieves targeted energy transfer and vibration suppression of thin-walled structures under wide frequency and multiple operating conditions, reduces the added mass of vibration damping devices, and improves the system's adaptability and control effect.
Smart Images
Figure CN121432913A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of dynamics of thin-walled structures in civil aircraft, and in particular to a vibration control method for thin-walled structures based on an inertial capacitive nonlinear energy trap. Background Technology
[0002] In the aerospace field, to meet the demands for higher performance, lower energy consumption, and longer range of aircraft, thin-walled structures have been widely used in various aerospace equipment due to their significant lightweight advantages. However, the inherent low stiffness and low damping characteristics of thin-walled structures make them highly susceptible to interference from various vibration sources in complex service environments. These vibration problems bring many serious negative impacts to aerospace equipment. Vibration can cause fatigue damage to structural components, reduce the service life and reliability of structures, and even trigger catastrophic structural failures. Vibration transmitted to precision instruments and electronic equipment can affect their working accuracy and stability, leading to errors or malfunctions in critical systems such as navigation and communication. Vibration can also affect the comfort of astronauts, increasing fatigue and discomfort during long-term space missions and posing a potential threat to their physical and mental health.
[0003] Traditional vibration control methods, such as passive and semi-active control techniques like using vibration absorbers and dampers, are increasingly revealing their limitations when dealing with vibration problems in thin-walled structures. These methods often require significant space and weight, which contradicts the stringent lightweight requirements of the aerospace industry. Once installed, passive control devices have a fixed adjustable frequency range, making it difficult to dynamically adjust to real-time changes in the external environment and adapt to the complex and ever-changing aerospace service environment. When an aircraft encounters sudden airflow disturbances or changes in the orbital environment, passive control devices may fail to suppress vibrations effectively and in a timely manner, thus affecting the safe operation of the equipment. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention proposes a vibration control method for thin-walled structures based on an inertial capacitive nonlinear energy trap.
[0005] First, let's analyze the challenges of adaptive vibration control under multiple operating conditions for thin-walled structures:
[0006] (1) The complexity of broadband vibration characteristics. The vibration excitation faced by thin-walled structures in aerospace has obvious broadband characteristics, covering a wide frequency range from low frequency to high frequency. Thin-walled structures exhibit complex nonlinear characteristics at different frequencies, and the vibration affects the structure in different ways and to varying degrees, making it extremely difficult to establish an accurate broadband vibration model.
[0007] (2) The contradiction between lightweighting and vibration control. In the aerospace field, lightweighting has always been one of the important goals. However, lightweighting of structures often leads to a further reduction in their stiffness and damping, making them more sensitive to vibration and significantly increasing the difficulty of vibration control. It is necessary to seek effective vibration control methods while ensuring structural lightweighting.
[0008] (3) Multi-condition adaptability challenge. Aerospace equipment will experience a variety of different operating conditions throughout its service life. The environment and load conditions vary greatly, and the vibration characteristics and control requirements of thin-walled structures are also very different. It is necessary to propose an adaptive vibration control strategy to ensure good vibration control effect under various complex operating conditions.
[0009] Therefore, this invention proposes a vibration control method for thin-walled structures based on an inertial capacitive nonlinear energy trap, comprising the following steps:
[0010] Step (1) Broadband vibration control based on distributed capacitive nonlinear energy trap: Establish a coupled dynamic model of thin-walled main structure and capacitive nonlinear energy trap, discretize the thin-walled structure into several degrees of freedom and determine the displacement vector, distribute several capacitive nonlinear energy trap elements on the surface of the structure, clarify the parallel or series coupling mode of each element with the main structure, and write the coupled dynamic equation including the inertial effect of capacitive element, linear damping, linear stiffness and cubic nonlinear stiffness; according to the resonance frequency of each order of the main structure, set the linear stiffness matching the target frequency for each capacitive nonlinear energy trap element, and set the nonlinear stiffness and linear damping to avoid over-damping according to the broadband control requirements, and determine the connection mode of capacitive element and main structure, and output the initial parameterized coupling model;
[0011] Step (2) Adaptive frequency tracking and parameter adjustment of vibration response of thin-walled structure: Based on the initial parameterized coupling model, the steady-state response of the main structure and the inertial capacitive nonlinear energy trap is assumed to be in simple harmonic form by using the harmonic balance method and substituted into the coupling equation. The algebraic equation system is obtained by separating the real part and the imaginary part, and the steady-state amplitude of the main structure and each energy trap unit is obtained by solving it. The real-time frequency is extracted by performing short-time Fourier transform on the measured vibration response. The center frequency of the bandpass filter is adjusted online by using the subspace identification results. The control parameters are updated with the minimum mean square algorithm with the goal of minimizing the response. The adaptively updated nonlinear stiffness and damping parameters are output.
[0012] Step (3) Consider the optimization of key design parameters of the inertial capacitive nonlinear energy trap for multi-condition adaptive operation: take the adaptive update parameters output in step (2) as the initial value, take the minimum integral of the power spectral density of the main structure frequency domain response as the optimization objective, use particle swarm optimization to perform global optimization of the inertial mass, nonlinear stiffness and linear damping of the inertial capacitive element, and use model predictive control to roll the parameter increment in the prediction time domain, obtain the optimal parameter combination under the constraints of parameter physical boundary and rate of change, output the optimal parameters for multi-condition adaptive operation, and realize multi-condition adaptive vibration control of thin-walled structure.
[0013] The technical solution provided by this invention brings at least the following beneficial effects:
[0014] This invention employs a nonlinear energy trap to ensure targeted energy transfer, effectively transferring the energy of the main structure to the nonlinear energy trap, thereby achieving targeted suppression of vibration control in thin-walled systems. The inertial capacitive type nonlinear energy trap provides an effective method to significantly reduce the additional mass required for vibration reduction devices. Time-frequency analysis is performed through short-time Fourier transform to track changes in the frequency of external excitation signals. A frequency identification-based control strategy is applied to the inertial capacitive type nonlinear energy trap vibration reduction system. By dynamically adjusting the nonlinear stiffness through the control unit, the optimal operating frequency of the system is made consistent with the excitation frequency, achieving multi-condition adaptive vibration control. Attached Figure Description
[0015] Figure 1 This is a flowchart of the present invention. Detailed Implementation
[0016] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.
[0017] like Figure 1 As shown, this invention provides a vibration control method for thin-walled structures based on an inertial capacitive nonlinear energy trap, comprising the following steps:
[0018] Step (1) Broadband vibration control based on distributed capacitive nonlinear energy trap: Establish a coupled dynamic model of thin-walled main structure and capacitive nonlinear energy trap, discretize the thin-walled structure into several degrees of freedom and determine the displacement vector, distribute several capacitive nonlinear energy trap elements on the surface of the structure, clarify the parallel or series coupling mode of each element with the main structure, and write the coupled dynamic equation including the inertial effect of capacitive element, linear damping, linear stiffness and cubic nonlinear stiffness; according to the resonance frequency of each order of the main structure, set the linear stiffness matching the target frequency for each capacitive nonlinear energy trap element, and set the nonlinear stiffness and linear damping to avoid over-damping according to the broadband control requirements, and determine the connection mode of capacitive element and main structure, and output the initial parameterized coupling model;
[0019] Step (2) Adaptive frequency tracking and parameter adjustment of vibration response of thin-walled structure: Based on the initial parameterized coupling model, the steady-state response of the main structure and the inertial capacitive nonlinear energy trap is assumed to be in simple harmonic form by using the harmonic balance method and substituted into the coupling equation. The algebraic equation system is obtained by separating the real part and the imaginary part, and the steady-state amplitude of the main structure and each energy trap unit is obtained by solving it. The real-time frequency is extracted by performing short-time Fourier transform on the measured vibration response. The center frequency of the bandpass filter is adjusted online by using the subspace identification results. The control parameters are updated with the minimum mean square algorithm with the goal of minimizing the response. The adaptively updated nonlinear stiffness and damping parameters are output.
[0020] Step (3) Consider the optimization of key design parameters of the inertial capacitive nonlinear energy trap for multi-condition adaptive operation: take the adaptive update parameters output in step (2) as the initial value, take the minimum integral of the power spectral density of the main structure frequency domain response as the optimization objective, use particle swarm optimization to perform global optimization of the inertial mass, nonlinear stiffness and linear damping of the inertial capacitive element, and use model predictive control to roll the parameter increment in the prediction time domain, obtain the optimal parameter combination under the constraints of parameter physical boundary and rate of change, output the optimal parameters for multi-condition adaptive operation, and realize multi-condition adaptive vibration control of thin-walled structure.
[0021] Step (1) Broadband vibration control based on distributed inertial capacitive nonlinear energy trap includes:
[0022] To address the complexity of broadband vibration characteristics, a distributed capacitive nonlinear energy trap system is proposed. A coupled dynamic model of the thin-walled main structure and the capacitive nonlinear energy trap is established, considering parallel or series coupling between the nonlinear energy trap and the thin-walled main structure. A dynamic model of the interaction between the nonlinear energy trap and the thin-walled main structure is also established.
[0023] Thin-walled main structure-inertial capacitive nonlinear energy trap coupled dynamic model: Assuming the thin-walled structure is discretized into n degrees of freedom, the displacement vector is... A capacitive nonlinear energy trap system contains m elements (distributed arrangement), and the relative displacement of the i-th capacitive nonlinear energy trap is... This inertial capacitive nonlinear energy trap is connected in parallel or in series with the thin-walled main structure. When connected in parallel , When the identity matrix is concatenated,
[0024] The coupled dynamic equations are then:
[0025] ;
[0026] Where M, C, and K are the mass matrix, linear damping matrix, and linear stiffness matrix of the thin-walled main structure, respectively; Let be the inertial mass of the inertial capacitive element of the i-th inertial capacitive nonlinear energy trap; , , These represent the linear damping, linear stiffness, and cubic nonlinear stiffness of the i-th inertial capacitive nonlinear energy trap, respectively. This is the external excitation vector.
[0027] The linear damping, linear stiffness, and cubic nonlinear stiffness of the nonlinear energy trap were initially determined.
[0028] Linear stiffness matching: based on the j-th order resonance frequency of the main structure (Based on the j-th order stiffness K of the main structure) j Quality M j calculate, ),set up This ensures that the inertial capacitive nonlinear energy trap is compatible with the resonant frequency of the main structure.
[0029] Nonlinear stiffness coefficient: ,in Adjust the nonlinear stiffness according to the wideband control requirements;
[0030] Linear damping: ,in To avoid excessive damping that reduces broadband response.
[0031] To enhance the vibration control capability of the system, an inertial capacitive element is designed. The connection method between the inertial capacitive element and the thin-walled main structure is determined. A coupled dynamic model of thin-walled structure-inertial capacitive nonlinear energy trap is established. The vibration information at different positions on the structural surface is fully utilized to achieve fine control of broadband vibration.
[0032] Step (2) Adaptive frequency tracking and parameter adjustment method for vibration response of thin-walled structures, including:
[0033] The steady-state response of the coupled dynamic model of the thin-walled main structure-inertial capacitive nonlinear energy trap is solved using the harmonic balance method. The dynamic response of the thin-walled system under white noise excitation and random load excitation is analyzed. Specifically, the steady-state response of the coupled dynamic model of the thin-walled main structure-inertial capacitive nonlinear energy trap is solved using the harmonic balance method as follows:
[0034] Assume the steady-state response of the thin-walled main structure-inertial capacitive nonlinear energy trap coupled system is in simple harmonic form:
[0035] , ;
[0036] Main structure amplitude column vector, The amplitude of the inertial capacitive nonlinear energy trap is given by ω, the external excitation frequency is given by φ, and the phase of the main structure is given by φ. For the phase of the amplitude of the inertial capacitive nonlinear energy trap, after substituting it into the coupled dynamic equations and separating the real and imaginary parts, we obtain a system of algebraic equations:
[0037] ;
[0038] Given the harmonic excitation amplitude vector, solving this system of equations yields the steady-state amplitude X. ;
[0039] Time-frequency analysis using short-time Fourier transform includes:
[0040] Short-time Fourier transform time-frequency analysis: Perform a short-time Fourier transform on the vibration response to extract the real-time frequency.
[0041] ;
[0042] in, Use the Hanning window function (the window length is selected based on the rate of change of the response, such as 0.1~0.5s). Centered on the time window.
[0043] It retains the important dynamic characteristics of the system, uses the subspace identification principle to estimate the response frequency, adjusts the center frequency of the bandpass filter in real time according to the estimated frequency to achieve tracking filtering of the vibration response frequency, and constructs an adaptive controller based on the least mean square algorithm. The adaptive controller realizes parameter updates and adjusts the control parameters in real time to cope with uncertainties in multiple working conditions and external disturbances, so as to achieve adaptive vibration control of thin-walled structures.
[0044] Adaptive controller parameter updates include: aiming at "minimizing the response".
[0045] Error signal:
[0046] in, To achieve a zero response, For the actual measurement of the main structure displacement response
[0047] weight vector (Control parameter mapping) Update formula: ;
[0048] in, The step size (to balance convergence speed and stability). The reference signal is the frequency feature extracted by the short-time Fourier transform.
[0049] Step (3) considers the optimization of key design parameters for the multi-condition adaptive inertial capacitive nonlinear energy trap, including:
[0050] The parameters of the inertial capacitive nonlinear energy trap, such as inertial mass, nonlinear stiffness, and damping, are analyzed. Minimizing the system response is determined as the optimization objective. The particle swarm optimization method is used to optimize the parameters of the nonlinear energy trap and inertial capacitive elements.
[0051] Particle Swarm Optimization (PSO) Objectives and Update Rules:
[0052] 1) Optimize the objective function (minimize the frequency domain response):
[0053] ;
[0054] in, In response to the power spectral density, by random excitation With system frequency response calculate:
[0055] ;
[0056] 2) PSO parameter update formula (optimization variable):
[0057] ;
[0058] ;
[0059] in, For the particle position, For particle velocity, For inertial weights, As a learning factor, It is a random number. For the best in particle history, It is optimal for the group.
[0060] Analyze the energy flow of a thin-walled system during vibration to determine the energy transfer and dissipation between different parts of the system.
[0061] The system's total energy expression (including the contribution of the inertial capacitance-nonlinear energy trap):
[0062] ;
[0063] Energy dissipation rate:
[0064] ;
[0065] By comparing with traditional nonlinear energy traps, the impact of nonlinear energy traps and inertial capacitance elements on energy flow is evaluated. The vibration reduction effects of different vibration control parameter configurations are compared and analyzed from both time and frequency domain perspectives. The vibration reduction effect comparison index (compared to traditional nonlinear energy traps, traditional nonlinear energy traps have no inertial capacitance) is also analyzed. ):
[0066] ;
[0067] Where A0 is the amplitude of the main structure of a traditional nonlinear energy trap. The amplitude of the main structure is controlled by an inertial capacitive nonlinear energy trap.
[0068] Develop a multi-condition adaptive control algorithm based on model prediction and intelligent optimization. Based on the real-time status of the current operating condition and the predicted operating condition in the future, calculate the optimal multi-condition adaptive model prediction control algorithm in advance and automatically optimize the control parameters in real time to adapt to the dynamic changes in the operating condition.
[0069] Multi-condition adaptive model predictive control algorithm: Based on model predictive control, parameters are optimized in advance to predict the response. Time domain N, control time domain M, optimization objective:
[0070] ;
[0071] Constraints (Physical boundary parameters) (Parameter change rate limit), where, To predict the response at time t+k for time t, For parameter increments, To predict the parameter increment at time t+k at time t. For smoothing weights.
Claims
1. A method for vibration control of thin-walled structures based on inerter-type nonlinear energy sink, characterized by, The method comprises the following steps: Step (1) wideband vibration control based on distributed inerter type nonlinear energy sink: a coupled dynamic model of a thin-walled main structure and an inerter type nonlinear energy sink is established, the thin-walled structure is discretized into several degrees of freedom and a displacement vector is determined, a plurality of inerter type nonlinear energy sink units are distributed on the surface of the structure, the parallel or series coupling mode of each unit with the main structure is determined, and a coupled dynamic equation including the inertia effect, linear damping, linear stiffness and cubic nonlinear stiffness of the inerter element is written; according to the resonance frequencies of each order of the main structure, the linear stiffness of each inerter type nonlinear energy sink unit is set to match the target frequency, the nonlinear stiffness and the linear damping to avoid excessive damping are set according to the wideband control requirement, and the connection mode of the inerter element and the main structure is determined, and an initial parameterized coupled model is output; Step (2) adaptive frequency tracking and parameter adjustment of the vibration response of the thin-walled structure: based on the initial parameterized coupled model, the steady-state response of the main structure and the inerter type nonlinear energy sink is assumed to be a simple harmonic form by using the harmonic balance method and substituted into the coupled equation, and an algebraic equation set is obtained by separating the real part and the imaginary part, and the steady-state amplitude of the main structure and each energy sink unit is obtained by solving; the real-time frequency is extracted by performing short-time Fourier transform on the measured vibration response, the center frequency of the band-pass filter is adjusted online by using the subspace identification result, and the control parameters are updated by using the least mean square algorithm to minimize the response, and the adaptively updated nonlinear stiffness and damping parameters are output; Step (3) optimization of key design parameters of the inerter type nonlinear energy sink considering multi-working condition adaptivity: taking the adaptively updated parameters output in step (2) as initial values, taking the integral minimum of the frequency domain response power spectral density of the main structure as the optimization objective, and using particle swarm optimization to globally optimize the inertia mass, nonlinear stiffness and linear damping of the inerter element, and obtaining the optimal parameter combination under the constraints of the physical boundaries and the change rate of the parameters, and outputting the multi-working condition adaptive optimal parameters, and realizing the multi-working condition adaptive vibration control of the thin-walled structure.
2. The method of claim 1, wherein, In step (1), the distributed arrangement refers to dispersing the inerter type nonlinear energy sink units on the surface of the thin-walled structure according to the modal shape peak value area, to ensure that each unit is independently connected to the degrees of freedom of the main structure.
3. The method of claim 1, wherein, In step (1), the selection of the coupling mode is based on: parallel connection when the inertia effect needs to be added to the main structure with the same displacement, and series connection when the relative displacement needs to be amplified.
4. The method of claim 1, wherein, In step (1), the linear damping is set to be not higher than a preset proportion of the critical damping of the corresponding mode of the main structure as an upper limit, to retain the wideband response capability.
5. The method of claim 1, wherein, In step (2), the short-time Fourier transform uses the Hanning window, and the window length is dynamically adjusted according to the response change rate, to ensure the accuracy of the real-time frequency extraction.
6. The method of claim 1, wherein, In step (2), the least mean square algorithm takes the difference between the expected zero response and the actual response as the error signal, and takes the extracted frequency characteristics as the reference signal, and the step size considers both the convergence speed and the stability.
7. The method of claim 1, wherein, In step (2), further comprising: writing back the adaptively updated nonlinear stiffness and damping parameters to the coupled dynamic equation in real time to form a closed-loop parameter refresh.
8. The method of claim 1, wherein, In step (3), the particle swarm optimization uses an inertial weight reduction strategy to balance global exploration and local development, and the learning factor is fixed as a preset constant.
9. The method of claim 1, wherein, In step (3), the model predictive control uses parameter increments as control variables, implements only the first increment at each sampling time and updates it on a rolling basis to adapt to dynamic changes in operating conditions.
10. The method of claim 1, wherein, Step (3) further includes: calculating the percentage decrease in amplitude as an evaluation index of vibration reduction effect.