91 results about "Nonlinear stiffness" patented technology

The invention relates to the technical field of power grid stability analysis, in particular to a mechanical vibration micro-grid electromechanical coupling system stability analysis method, which comprises the following steps of: detecting a tooth surface contact radius, a relative speed and a Young modulus to generate a contact stiffness initial value, correcting nonlinear stiffness by interval difference, and calculating the stability of a micro-grid electromechanical coupling system. The method comprises the following steps: calculating a coupling response vector by combining rotor displacement and bearing clearance, inputting a Lyapunov exponent method to solve an exponent vector, constructing a model length ratio to detect derivative characteristics, extracting a multidimensional state vector in a positive value period and the coupling response vector to generate a compensation action, and constructing an FPGA simulation path injection disturbance execution error feedback back-transmission fuzzy control algorithm. According to the method, a contact stiffness dynamic correction and nonlinear difference method is introduced, six-degree-of-freedom displacement and bearing clearance parameters are combined, an electromechanical coupling model is established, a stability boundary is recognized through Lyapunov regression, a critical state is detected through derivative features, and multi-dimensional state vector fuzzy control compensation is fused. And the response and the immunity are optimized by combining FPGA simulation and a disturbance mechanism.

A method for rapidly solving transient dynamics of a crack-containing bearing structure of a bogie belongs to the technical field of bogie structure dynamic analysis, and comprises the following steps: acquiring a three-dimensional geometric model of the bearing structure, the geometric dimension of a crack and the position coordinate dimension of the crack; dividing the finite element model of the bearing structure, and carrying out grid division processing on the crack surface; selecting a main degree-of-freedom node of the finite element model on the surface of the bearing structure and the crack surface; performing substructure analysis on the finite element model of the bearing structure; obtaining a mass matrix, a damping matrix and a stiffness matrix of the finite element model of the bearing structure after the degree of freedom is reduced; carrying out constraint simulation on a crack surface node by adopting a one-way nonlinear rigidity unit; processing constraint boundary conditions; processing the excitation load; and solving a dynamic second-order differential equation set, and judging whether the crack surface is in contact or not. According to the method, the opening and closing effects of the crack can be considered, the transient dynamic response of the crack-containing bearing structure under the action of the external load is obtained, and the solving precision and efficiency are both considered.

The invention discloses a self-adaptive bearing weight quasi-zero stiffness vibration isolator and a control method thereof, and relates to the technical field of vibration isolation equipment. The device comprises a base, the tops of the two sides of the inner wall of the base are fixedly connected with horizontal guide rails, the horizontal guide rails are slidably connected with horizontal sliding blocks, the horizontal sliding blocks are fixedly provided with magnetic torsion negative stiffness mechanisms, the output ends of the magnetic torsion negative stiffness mechanisms are fixedly connected with connecting rods, and the other ends of the connecting rods are rotationally connected with a supporting table; the supporting table is located in the center of the base. The quasi-zero stiffness is formed by the negative stiffness of the magnetic torsion negative stiffness mechanism and the positive stiffness of the vertical spring so as to achieve low-frequency vibration isolation of equipment, quasi-zero stiffness matching of the vibration isolator to equipment with different weights can be achieved by adjusting the working length of the vertical spring, the optimal low-frequency vibration isolation effect is achieved, and the low-frequency vibration isolation efficiency is improved. And the non-linear stiffness of the quasi-zero stiffness vibration isolator for equipment with different weights is completely consistent, that is, the vibration isolator has the same dynamic characteristics under the equipment with different weights.

The invention belongs to the technical field of automobiles, and particularly relates to an electronic mechanical braking system self-adaptive clamping force control method considering friction hindrance. Comprising the steps that 1, a proportional-integral theory is adopted to design a clamping force closed-loop controller and a fuzzy self-adaptive control parameter adjusting method of the electronic mechanical braking system, and proportional parameters and integral parameters of the clamping force closed-loop built-in controller are dynamically adjusted; secondly, feedforward compensation control based on friction estimation is designed through a third-order expansion state observer, and dynamic estimation is conducted on nonlinear friction obstruction of the electronic mechanical braking system; and step 3, the permanent magnet synchronous motor servo control comprehensively applies excitation axis zero control setting, double-axis compensation constraint and a proportional-integral algorithm to realize position closed-loop and current closed-loop controller design. According to the invention, the problems of remarkable nonlinear stiffness characteristic, nonlinear friction obstruction, electromagnetic coupling of the excitation shaft and the torque shaft of the permanent magnet synchronous motor and the like in the working process of an electronic mechanical braking system are effectively solved.

Anti-vibration units are provided for vibration suppression in multiple directions. The anti-vibration units may have an X-shaped structure as part of its support structure. The anti-vibration units can work for ultra-low frequency vibration isolation in three directions in a passive manner. The anti-vibration units can achieve a flexible nonlinear stiffness, which contains zero or quasi-zero stiffness, negative stiffness and positive stiffness. A smooth multi-equilibria state is also achievable. Compared with traditional spring-mass-damper (SMD) and typical QZS systems, the provided anti-vibration units can have an enhanced QZS range of larger stroke with guaranteed loading capacity, and can also achieve a lower resonant frequency with a lower resonant peak. At least some embodiments of the anti-vibration units may include a new and innovative arrangement of components that enables a more compact design than typical anti-vibration systems.

The invention provides a gap nonlinear control surface flutter wind tunnel test system and method based on steering engine excitation. The system comprises a wind tunnel test section, a test object and a parameter-adjustable excitation mechanism outside a wind tunnel field, wherein the parameter-adjustable excitation mechanism is composed of a transverse clamping mechanism, a longitudinal supporting mechanism, an excitation system and an angle sensor. The excitation system comprises a steering engine, a steering engine rocker arm and a connecting rod, one end of a spring rod is fixed to the longitudinal supporting mechanism, and the other end is in clearance fit with the connecting rod. By adjusting the effective length of the spring rod, the fit clearance and the excitation of the steering engine, the clearance nonlinear rigidity applied to the test control surface can be changed. In a wind tunnel test, an angle sensor is used for collecting rudder shaft rotation angular displacement response in real time, excitation-response characteristic testing before and after flutter occurs is achieved, and the influence rule of gap nonlinear parameters on rudder surface dynamic characteristics is effectively studied. The test principle is simple, and a new way is provided for excitation-response characteristic measurement of the full-motion control surface under different gap nonlinear rigidities.

The application discloses an adjustable nonlinear dynamic vibration absorber and system, and has the technical scheme that a tuning mass block is slidably connected to the surface of a support plate, and first scissor structures are rotatably connected between the tuning mass block and the two ends of the support plate; the first scissor structures are provided with second scissor structures and dampers, the second scissor structures and the dampers can drive the first scissor structures to stretch and contract through elastic belts, the second scissor structures are provided with elastic elements for driving the second scissor structures to stretch and contract; the stretching direction of the elastic elements is parallel to the sliding direction of the tuning mass block, and is perpendicular to the damping direction of the dampers, so that the first scissor structures and the second scissor structures can realize vibration absorption through geometric nonlinearity when moving. The stiffness and damping characteristics of the application can be adjusted, and the linear elements can be used to realize nonlinear stiffness, damping and super-low natural frequency, and the problem of Duffing system instability that cannot be eliminated by traditional nonlinear vibration absorbers is solved.

The invention provides a nonlinear dynamic modeling, solving and control method of a linear motor, and belongs to the field of structural dynamics, and the method comprises the steps: 1) simplifying an LRA into a two-degree-of-freedom mass-spring-damping nonlinear system, and obtaining the linear stiffness and cubic nonlinear stiffness of a beam spring; (2) nBgleff discrete data points of different relative displacements of the motor vibrator and the shell are obtained through simulation, an nBgleff fitting curve is obtained, and then electromagnetic force is obtained; 3) identifying system damping parameters by combining measured data; according to the method, the goodness of fit Rnl of the model to the LRA vibration response is larger than 0.95, vibration characteristics can be accurately predicted, the LRA vibration consistency is effectively improved through the control strategy, and the tactile feedback experience is improved.

The invention discloses a nonlinear acoustic transducer control method and system based on an Aubry-Mather set, and belongs to the technical field of acoustic transducers. The method comprises the following steps: firstly, based on an Aubry-Mather set theory, constructing a nonlinear vibration model used for describing nonlinear vibration of a transducer diaphragm; secondly, based on a nonlinear vibration model, regional piezoelectric driving and dynamic phase regulation are carried out to simulate a quasi-periodic fluctuation mode; then, on the basis of fluctuation characteristics disclosed by the nonlinear vibration model, a multi-diaphragm collaborative vibration system is constructed, and quasi-periodic superposition of sound waves is realized by optimizing diaphragm space layout; and finally, based on stiffness parameters in the nonlinear vibration model, integrating a micro electro mechanical system (MEMS) process and a nonlinear material, and realizing equivalent nonlinear stiffness on a physical device through gradient polarization design. The dynamic adaptability, the energy transfer efficiency and the high-frequency output performance of the transducer in a broadband range are effectively improved, and the transducer is particularly suitable for ultrasonic imaging and other high-frequency acoustic application scenes.

The invention discloses a high-Q-value resonator based on boundary stiffness modulation, and belongs to the technical field of micro electro mechanical systems, the high-Q-value resonator comprises a resonator, a first stiffness adjusting mechanism and a second stiffness adjusting mechanism, the first stiffness adjusting mechanism and the second stiffness adjusting mechanism are connected with the two ends of the resonator, and the stiffness adjusting mechanisms achieve initial stiffness adjustment of bending, torsion and stretching through structural design and electrostatic trimming; fine rigidity trimming is achieved through static electricity; the rigidity adjusting mechanism changes the boundary clamping condition of the resonator, so that the Q value, the inherent frequency, the static pull-in voltage and the nonlinearity of the resonator can be adjusted; the frequency stability, the sensitivity and the non-linear rigidity of the resonator can be effectively adjusted, and the resonator has the advantages of being large in adjusting range and controllable in adjusting parameter.

The present application belongs to the technical field of bridge wind tunnel test device, and provides a kind of wind tunnel test device simulating nonlinear vibration of bridge structure, including rigid model, rigid rod, rigid circular arc suspension arm, linear tensile spring, nonlinear elastic element and light high-strength fine rope.Nonlinear elastic element can adopt cable structure, membrane structure, nonlinear tensile spring, mechanical super material or superstructure.By designing the nonlinear stiffness characteristics of nonlinear elastic element, the layout mode and the combination mode of linear tensile spring, various target nonlinear stiffness modes can be realized to carry out large amplitude vertical torsional coupled flutter test of bridge structure under nonlinear stiffness.In the process of large amplitude vibration of model, the center hanging point of nonlinear elastic element and linear tensile spring can always maintain vertical displacement and deformation, and the device can ensure stable stiffness, damping, mass and mass moment characteristics.

A multi-stage nonlinear stiffness hourglass spring comprises a conical rubber body with a central hollow vibration damping zone, and a support plate and a mounting plate arranged in parallel. The conical rubber body is vulcanized and connected between the support plate and the mounting plate. The conical rubber body has a rubber stopper in the central hollow vibration damping zone, a first vibration damping gap is formed between the side surface of the rubber stopper and the inner side surface of the conical rubber body, and a second vibration damping gap is formed between the top surface of the rubber stopper and the mounting surface where the mounting plate is located. The hourglass spring provided by the present invention has a rubber stopper provided in the central hollow vibration damping zone of the rubber body. When the hourglass spring is subjected to a large load, the inner side surface of the rubber body can contact the rubber stopper to form a section of nonlinear variable stiffness. After the rubber stopper contacts the metal part of the mounting surface where the mounting plate is located, another section of nonlinear variable stiffness can be provided, and the nonlinear stiffness variation range is large.

The application discloses a bearing stress state measurement method based on a resonance attenuation method and related devices, and the bearing-main shaft system is loaded in the mode of electromagnetic loading. The resonance attenuation method in the nonlinear parameter identification method is used to obtain an attenuation response curve, and the instantaneous frequency and envelope amplitude are obtained based on a transient time-frequency signal analysis method, and then the main curve is identified from the measured bearing-main shaft system. A quasi-static model of the bearing is established to obtain the mapping relationship between the bearing stress state and the nonlinear non-time-varying stiffness, and the external loading state of the bearing is effectively and accurately detected through multiple tests on the nonlinear stiffness of the bearing system in the actual operation process. The application is suitable for multiple types of assembled angular contact ball bearings and is suitable for accurate measurement of the bearing stress state.

The invention belongs to the technical field of robot milling dynamic characteristic analysis, and discloses a robot milling stability prediction method and device considering nonlinear rigidity, and the method comprises the steps: (1) employing a cubic polynomial to represent the nonlinear characteristic of the joint rigidity of a robot, and constructing a nonlinear kinetic equation of the robot; (2) solving the nonlinear kinetic equation based on an incremental harmonic balance method to obtain a nonlinear frequency response function of the robot; and (3) obtaining a stability lobe graph based on the nonlinear frequency response function and a milling stability frequency domain model constructed by adopting a milling vibration stability analysis zero-order method, and then completing prediction of the milling stability of the robot based on the obtained stability lobe graph. According to the method, the influence of the nonlinear rigidity of the joint is effectively considered, and the accuracy of prediction of the milling stable area of the robot is improved.

A headrest can include a first headrest structure and a second headrest structure. A vibration isolator can be operatively positioned between the first headrest structure and the second headrest structure. The vibration isolator can be configured to exhibit a non-linear stiffness profile. The non-linear stiffness profile includes a region of quasi-zero stiffness.

The present application relates to a kind of pipeline vibration absorber with linear-nonlinear characteristics and its design method, wherein, pipeline vibration absorber includes: shell and resonance component;The side surface of shell is the circular arc surface that is attached to the surface of pipeline, and circular arc mounting cavity coaxial with circular arc surface is arranged in shell;Resonance component is installed in circular arc mounting cavity, for presenting linear stiffness or equivalent nonlinear stiffness in vibration state;Resonance component includes: vibrator unit and damping element;Vibrator unit is arranged in circular arc mounting cavity with shell connection, and vibrator unit presents linear stiffness of resonance component with linear characteristics in vibration state based on the connecting structure between shell;Damping element is covered on vibrator unit, and when vibrator unit is in vibration state, damping element is used to present as nonlinear characteristics when physical coupling occurs between vibrator unit and shell, and the equivalent nonlinear stiffness of resonance component is obtained.

The invention relates to the technical field of new energy automobiles, in particular to an electric vehicle suspension key working point displacement checking method and device.According to the method, through parametric modeling and accurate working condition definition, the torque transient response characteristic of an electric vehicle motor is fully considered, and the displacement prediction precision is improved; by adopting a nonlinear rigidity segmented mapping technology, errors caused by linearization hypothesis are avoided, and accurate prediction and one-time qualified design of the suspension performance are realized through displacement check and optimization adjustment; the NVH performance of the electric vehicle is effectively improved, the acceleration of the motor under the Tip-in working condition is greatly reduced, and noise in the vehicle is reduced.

This invention discloses a method and apparatus for designing the stiffness curve of a powertrain mounting system. The design method includes: acquiring vehicle state parameters and stiffness curve data for each mounting; establishing a dynamic model of the powertrain mounting system based on the vehicle state parameters and stiffness curve data, and determining the vibration data for each mounting; comparing the nonlinear stiffness curve data and vibration data of each mounting with preset data conditions, and correcting the stiffness curve data based on the comparison results to obtain a corrected dynamic model; wherein the stiffness curve data includes nonlinear stiffness curve data; and determining the first limit dimension of the mounting based on the comparison results, according to the vehicle state parameters and preset limit rules. The technical solution of this invention, combined with the design of stiffness curve data under actual vehicle conditions, improves the reliability of noise and vibration transmission reduction in mountings, and effectively improves vehicle ride comfort.

The invention belongs to the technical field of bridge wind tunnel test devices, and provides a wind tunnel test device for simulating nonlinear vibration of a bridge structure, which comprises a rigid model, a rigid rod, a rigid arc suspension arm, a linear extension spring, a nonlinear elastic element and a light high-strength string. The nonlinear elastic element can adopt a cable structure, a membrane structure, a nonlinear extension spring, a mechanical metamaterial or a superstructure. Various target nonlinear rigidity modes can be realized by designing the nonlinear rigidity characteristics and the arrangement mode of the nonlinear elastic elements and the combination mode of the nonlinear elastic elements and the linear extension springs, so that a large-amplitude vertical torsion coupling flutter test under the nonlinear rigidity of a bridge structure can be carried out. In the large-amplitude vibration process of the model, the central lifting point of the nonlinear elastic element and the linear extension spring can always keep vertical displacement and deformation, and the device can ensure stable rigidity, damping, mass and mass moment characteristics.

The present application belongs to the technical field of nonlinear stiffness identification of vibration excitation device, and particularly relates to a low-frequency vibration table spring piece return mechanism nonlinear stiffness dynamic measurement system and method. The system comprises a program-controlled signal generator, a power amplifier, a low-frequency vibration table installed with a spring piece return mechanism, an eddy current displacement sensor, a data acquisition card, a computer and a software analysis module. The output vibration displacement signals and input standard sinusoidal voltage signals are subjected to FFT analysis by the data processing unit to obtain corresponding signal amplitudes and phases, and then the transfer function of the low-frequency vibration table first-order inertia link form corresponding to the selected amplitude output vibration displacement signals in the working frequency range is calculated by the transfer function calculation unit. Finally, the power series fitting unit is used for power series fitting to obtain the power series expression representing the nonlinear stiffness, thereby completing the dynamic measurement of the low-frequency vibration table spring piece return mechanism nonlinear stiffness. Overall, the measurement system has simple structure, simple measurement method operation process and wide application range, and can realize accurate dynamic measurement of the low-frequency vibration table spring piece return mechanism nonlinear stiffness.

The invention belongs to the technical field of structural vibration control, and discloses a nonlinear energy trap device for vertical vibration control of a large-span bridge, which comprises a vertical spring and a cam-roller-horizontal spring combination, the vertical spring and the cam-roller-horizontal spring are combined and connected in parallel to provide overall rigidity. The non-linear energy sink device may ideally exhibit a predetermined non-linear stiffness characteristic near the static equilibrium location of the NES device. According to the invention, NES with any continuous stiffness can be realized, including cubic stiffness NES, negative stiffness NES, polynomial stiffness NES, piecewise linear stiffness NES and the like. The required mounting space is small, and the requirement for the mounting space can be met according to the characteristic that the clear height in a girder box of a large-span bridge is generally within the range of 3-5 m.

The application relates to a self-resetting torsional energy dissipation support component with nonlinear stiffness, belonging to the technical field of energy dissipation and shock absorption, which comprises an outer sleeve and an inner sleeve which are mutually sleeved, a plurality of torsional steel pipes are arranged in the inner sleeve cavity, rotating discs are fixed at the two ends of the torsional steel pipes, upper and lower core plates which are slidably connected and are used in cooperation with the rotating discs are arranged on the inner sleeve body, support connecting pieces are fixed at the ends of the upper and lower core plates away from the inner sleeve, a plurality of self-resetting spring assemblies are symmetrically arranged in the inner sleeve cavity away from the two ends of the torsional steel pipes, a pair of curve grooves are symmetrically arranged in the center of the rotating discs, struts which are used in cooperation with the curve grooves are arranged on the upper and lower core plates, during work, the upper and lower core plates move towards or away from each other, the rotating discs rotate, the rotating directions of the rotating discs on the two sides of the inner sleeve are opposite during work, the torsional steel pipes are twisted, the metal of the torsional steel pipes is deformed to dissipate energy, meanwhile, the self-resetting spring assemblies are stretched to provide nonlinear restoring force.

This invention discloses a three-dimensional vibration damping structure and device with nonlinear stiffness. The three-dimensional vibration damping structure includes an upper end face, a lower end face, and a damping structure. The upper end face and the lower end face are coaxially arranged. The damping structure includes multiple elastic bending rods arranged circumferentially along the line connecting the axes of the upper end face and the lower end face. The cross-section of each elastic bending rod is crescent-shaped. When the three-dimensional vibration damping structure is compressed, nonlinear geometric stiffness is generated. The nonlinear stiffness can be flexibly adjusted through various structural parameters of the rods, thereby allowing for the design of the three-dimensional vibration damping structure according to vibration requirements. Benefiting from the nonlinear stiffness characteristics, the vibration damping performance of the structure is effectively improved. This invention also discloses a damping device that overcomes the shortcomings of existing nonlinear stiffness damping devices, opening up a new direction for the design, analysis, and application of nonlinear stiffness damping devices.

The embodiment of the invention provides a foundation pit rigidity analysis method based on performance design and related equipment, and belongs to the technical field of building design. The method comprises the steps that a nonlinear soil pressure displacement function model corresponding to foundation pit supporting is constructed according to the nonlinear relation between supporting structure displacement and soil pressure; deriving the nonlinear soil pressure displacement function model to obtain a nonlinear rigidity model of the foundation soil; the method comprises the following steps: dispersing a foundation pit supporting structure into beam units, and simplifying a surrounding foundation soil body into a distributed spring system coupled with beam unit nodes so as to construct a spring generalized finite element model; and calculating updated soil pressure distribution according to the node displacement and the nonlinear soil pressure displacement function model, and outputting final supporting structure internal force, deformation and soil pressure distribution results. According to the embodiment of the invention, more accurate and more reliable design of the supporting performance of the foundation pit can be realized, and key technical support is provided for safety evaluation of the supporting performance of the foundation pit.

In the field of medical wearable devices, the present invention provides a wearable device for suppressing arm tremors, comprising a flexible wristband and a nonlinear vibration suppression component. Four nonlinear vibration suppression components are evenly distributed around the outer wall of the flexible wristband. The nonlinear vibration suppression components are detachably mounted on the flexible wristband. The nonlinear vibration suppression components capture and consume vibration energy through a targeted energy transfer mechanism. The nonlinear vibration suppression components utilize their own strong nonlinear stiffness to form a resonant capture behavior with the natural frequency of the main vibration system, transferring the energy of the main vibration system to the NES through targeted energy transfer and dissipating it through damping. Most of the energy does not return from the NES to the main vibration system, achieving one-way energy transfer, thereby preventing arm tremors.

The invention relates to a decoupling device (50) for oscillatory systems, the decoupling device comprising: at least one nonlinear stiffness element having a negative stiffness knl(u) and comprising at least one first spring element (27); and at least one linear stiffness element which has a positive stiffness kl,stat, is connected in parallel with the at least one nonlinear stiffness element, and comprises at least one second spring element (28). The at least one nonlinear stiffness element having a negative stiffness knl(u) is connected in series with at least one further stiffness element having a linear stiffness Kl and comprising at least one third spring element (29), and this series connection is connected in parallel with the at least one linear stiffness element having a positive stiffness kl,stat, wherein a quasi-zero-stiffness isolator is formed with an increased magnitude of the negative stiffness knl,ser,tot(u).

The invention discloses a non-linear rigidity automatic adjusting vibration isolation device and a control method. The device comprises a base, a supporting seat, a positive rigidity mechanism, a negative rigidity mechanism and a dynamic adjusting assembly. The negative stiffness mechanism adopts the design of three layers of uniformly distributed'connecting rod-tension spring 'transmission units, generates negative stiffness by converting vertical displacement of a supporting seat into horizontal movement of a tension spring, and is connected with positive stiffness provided by the positive stiffness mechanism in parallel to form a quasi-zero stiffness core mechanics framework. The dynamic adjusting assembly can accurately adjust the working height of the positive stiffness mechanism, and in combination with a feedback control system with an angle sensor as the core, self-adaptive adjustment of the balance position of the system under different loads and maintenance of the quasi-zero stiffness state are achieved. The positive stiffness mechanism is integrated with a magneto-rheological damper, and the damping force of the magneto-rheological damper can be subjected to real-time and intelligent adjustment through a feedforward-feedback composite control strategy based on multi-sensor information fusion so as to suppress resonance, impact and broadband vibration. The problems that in the prior art, the vibration isolation frequency band is narrow, load self-adaption cannot be achieved, damping adjustment is not intelligent and the like are solved, and high bearing, strong vibration reduction and full-working-condition self-adaption vibration isolation are achieved.

The invention relates to a nonlinear structure reduced-order model construction method based on sparse recognition and a mixed mode, belongs to the technical field of structural dynamics analysis and aeroelastic mechanics analysis, and solves the problem that complex motion caused by geometric nonlinearity under large deformation cannot be accurately described in the prior art. Comprising the following steps: S1, establishing a nonlinear finite element model of a target large flexible wing to obtain a training data set; s2, solving a mixed modal basis based on the displacement residual error and SVD (Singular Value Decomposition); s3, establishing a nonlinear stiffness coefficient solving problem model, introducing LASSO regression to establish an LASSO regression optimization objective function, and solving to obtain a sparse nonlinear stiffness coefficient; s4, based on the sparse nonlinear stiffness coefficient and the structural kinetic equation, establishing a nonlinear structure reduced-order model; and S5, applying the nonlinear structure reduced-order model to statics response solution and dynamics response solution of the large flexible wing to obtain statics response and dynamics response results.

The application discloses a magneto-rheological damper with frequency-variable damping and nonlinear stiffness characteristics, wherein a main cylinder assembly comprises a main cylinder body and a piston member, the piston member comprises a piston cylinder, a permanent magnet and a floating spring, the piston cylinder is coaxially and slidably arranged in the main cylinder body, the permanent magnet is slidably arranged in the piston cylinder, and the floating spring is arranged in the piston cylinder and exerts an elastic force on the permanent magnet in the axial direction; a secondary cylinder assembly comprises a secondary cylinder body and a plurality of stiffness springs, the secondary cylinder body is coaxially arranged with the main cylinder body, and the stiffness springs are arranged in the secondary cylinder body in a following mode. The damper provided by the application can respond to vibration excitations with different frequencies and amplitudes, can provide large damping and large stiffness when the vibration excitation is low frequency and large amplitude, and can provide small damping and small stiffness when the vibration excitation is high frequency and small amplitude, so that good damping stiffness matching characteristics can be obtained in a wide frequency range, and the overall damping performance of the system is significantly improved.

The present application belongs to the technical field of dynamics modeling, in order to solve the problem of existing balancer simulation complex, low efficiency, put forward based on the nonlinear parameterization equivalent design balancer simplification method and system, the effect of balancer in the direction of motion of the slider is equivalent to the combination model of nonlinear spring-damping and preload force;Among them, the nonlinear spring-damping and preload force combination model includes the nonlinear stiffness term related to the displacement of the slider, and the nonlinear damping term related to the velocity of the slider;The nonlinear spring-nonlinear damping and preload force combination model is used as a parameter identification model, according to the collected slider displacement, slider velocity and the force applied by the balancer to the slider, the parameters in the parameter identification model are identified, and the equivalent force model of the balancer is obtained according to the parameter result after identification. The present application improves the applicability and fitting accuracy of the equivalent force model of the balancer to the actual working process.