Parameter optimization method based on Ren-type grounded variable mass dynamic vibration absorber

Abstract

The present invention relates to the technical field of dynamic vibration absorbers, and in particular to a parameter optimization method based on a Ren-type grounded variable-mass dynamic vibration absorber, comprising the following steps: step one: adjusting the mass of the Ren-type grounded variable-mass dynamic vibration absorber to achieve a target tuning state; step two: designing a frequency response function L1 of a main system; step three: determining the relationship between the damping ratio #imgabs0# of the Ren-type grounded variable-mass dynamic vibration absorber and the frequency response of the main system; step four: determining the relationship between the mass ratio #imgabs1# of the Ren-type grounded variable-mass dynamic vibration absorber and the frequency response of the main system; step five: performing simulation analysis of the Ren-type grounded variable-mass dynamic vibration absorber; step six: optimizing the parameters of the Ren-type grounded variable-mass dynamic vibration absorber, adjusting the key parameters of the Ren-type grounded variable-mass dynamic vibration absorber, successfully reducing the frequency response peak of the vibration absorber, and significantly improving its vibration reduction performance.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic vibration absorbers, and in particular to a parameter optimization method based on a Ren-type ground-connected variable-mass dynamic vibration absorber. Background Art

[0002] Vibration is very common in nature, from microscopic particles to the macroscopic world, vibration is everywhere. In the actual process of transporting large flows of natural gas on offshore platforms, natural gas needs to be pressurized by a compressor after demercuration and desulfurization. Because the natural gas flow is too large, the problem of compressor vibration has existed for a long time. The traditional passive dynamic vibration absorber can be simplified as a single-degree-of-freedom "mass-spring-damper" system. Due to its simple structure and low cost, it is widely used in the field of industrial life. However, its structural parameters will not change under working conditions, so its effective working frequency band is narrow, so it is only used under conditions of a single excitation frequency. The traditional dynamic vibration absorber parameter optimization method mainly relies on the fixed point theory (PQTheory), such as a dynamic vibration absorber optimization design method based on negative stiffness and inertia disclosed in the publication number CN114880805A. The fixed point theory is based on the frequency ratio between the main system and the vibration absorber, thereby deriving the optimal parameters of the vibration absorber, such as the mass ratio, natural frequency ratio and damping ratio. This method is applicable to main systems with no damping or low damping, and can determine the optimal frequency ratio and damping ratio of the vibration absorber to achieve the best vibration reduction effect. However, this method has disadvantages. The fixed point theory is mainly applicable to narrow-band vibration reduction, and the vibration reduction effect for broadband excitation is not ideal. When there is large damping in the main system, the fixed point theory may no longer hold, and other methods are needed to optimize the parameters. Although the fixed point theory provides a basic design framework, in practical applications, it is still challenging to achieve accurate parameter optimization due to the uncertainty of system parameters and the complexity of external excitations. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a parameter optimization method based on a Ren-type ground-connected variable mass dynamic vibration absorber.

[0004] The technical solution adopted by the present application to solve the technical problem is: a parameter optimization method based on a Ren-type ground-type variable mass dynamic vibration absorber comprises the following steps:

[0005] Step 1: Adjust the mass of the Humanoid grounded variable mass dynamic vibration absorber to reach the target tuning state;

[0006] Step 2: Design the frequency response function L of the main system 1 ;

[0007] Step 3: Determine the damping ratio of the Ren-type grounded variable mass dynamic vibration absorber Relationship with the main system frequency response;

[0008] Step 4: Determine the mass ratio of the Humanoid grounded variable mass dynamic vibration absorber Relationship with the main system frequency response;

[0009] Step 5: Conduct simulation analysis of the Ren-type grounded variable mass dynamic vibration absorber;

[0010] Step 6: Parameter optimization of the Ren-type grounded variable mass dynamic vibration absorber.

[0011] The Ren-type grounded variable mass dynamic vibration absorber comprises a main system, a displacement sensor is arranged on the main system, the main system is connected to a liquid tank and the ground through springs, the liquid tank is connected to a water pump and a liquid storage tank in turn, a flow meter is arranged between the liquid tank and the liquid storage tank, the water pump, the flow meter and the displacement sensor are all connected to a control system, and the main system and the liquid tank are grounded through damping;

[0012] remember are the mass, stiffness, damping and displacement of the main system respectively, is the mass of liquid in the liquid tank, is the mass of the liquid tank; is the total mass of the humanoid grounded variable mass dynamic vibration absorber, , are the stiffness, damping and displacement of the Ren-type grounded variable mass dynamic vibration absorber, F is the external excitation force, is the angular frequency of the exciting force.

[0013] The step 1 includes the following sub-steps:

[0014] 1-1: Calculate the natural frequency of the Ren-type grounded variable mass dynamic vibration absorber The maximum value of and minimum value , the calculation formula is:

[0015] (1)

[0016] (2)

[0017] In the formula, is the stiffness of the humanoid grounded variable mass dynamic absorber;

[0018] 1-2: The control system receives the signal from the displacement sensor and controls the amount of liquid sent into or out of the liquid tank through the water pump. When the excitation force frequency range is When the water pump is controlled to stop.

[0019] The step 2 includes the following sub-steps:

[0020] 2-1: The dynamic analysis of the Ren-type grounded variable mass dynamic vibration absorber model is carried out, and the system dynamic differential equation is:

[0021] (3)

[0022] (4)

[0023] The matrix form is:

[0024] (5)

[0025] In the formula, are the displacement, velocity and acceleration of main system 1, are the displacement, velocity and acceleration of the Ren-type grounded variable mass dynamic vibration absorber, F 0 is the amplitude of the excitation force;

[0026] 2-2: Use the complex number method to solve equation (5) express , let the solution of the differential equation be of the form , , then the amplitude expression of the main system (1) and the Ren-type grounded variable mass dynamic absorber is:

[0027] Main system (1) Amplitude expression X 1 :

[0028] (6)

[0029] Amplitude expression of Ren-type grounded variable mass dynamic vibration absorber 2 :

[0030] (7)

[0031] In the formula, ; ; ; , represents the imaginary unit, i.e. .

[0032] The steady-state amplitudes of the main system (1) and the Human-type grounded variable mass dynamic absorber are shown in equations (8) and (9):

[0033] (8)

[0034] (9)

[0035] In the formula, ; ;

[0036] 2-3: Introducing the intermediate variable main system damping ratio 、Human-type grounded variable mass dynamic vibration absorber damping ratio , quality ratio , natural frequency ratio and forced vibration frequency ratio After performing intermediate variable substitution calculation, the expression of the amplitude magnification factor of the main system is:

[0037] (10)

[0038] In the formula, ; ; ; ;

[0039] - static deformation of the system;

[0040] ——mass ratio;

[0041] ——natural frequency of main system;

[0042] ——Natural frequency of human-type grounded variable mass dynamic vibration absorber;

[0043] ——natural frequency ratio;

[0044] ——Forced vibration frequency ratio, expressed as the multiple relationship between the exciting force frequency and the main system resonant frequency;

[0045] ——damping ratio of the main system;

[0046] ——Damping ratio of humanoid grounded variable mass dynamic vibration absorber;

[0047] 2-4: Frequency response function L of the main system 1 for:

[0048] (11)

[0049] In the formula, ; ; ; .

[0050] The damping ratio of the Ren-type grounded variable mass dynamic vibration absorber in step 3 is The relationship with the main system frequency response is as follows: As the damping ratio of the Ren-type grounded variable mass dynamic vibration absorber As the frequency increases, the effect at the best vibration absorption frequency becomes worse and the peak value of the main system frequency response decreases.

[0051] The mass ratio of the humanoid ground-type variable mass dynamic vibration absorber in step 4 is The relationship with the main system frequency response is: as the mass ratio With the increase of , when the human-type grounded variable mass dynamic vibration absorber is at the optimal working frequency, the frequency response value of the main system decreases and the vibration absorption effect becomes better.

[0052] In the step five, a visualization model is established based on Simulink, and the model is solved using the Runge-Kutta method in the Simulink environment. By changing the step size and frequency, analytical solutions and approximate analytical solutions under different parameters are obtained to realize the simulation analysis of the Ren-type grounded variable mass dynamic vibration absorber.

[0053] In step six, the snake algorithm + Levy flight strategy is used to improve the snake optimization algorithm.

[0054] The parameter optimization function corresponding to minimizing the maximum value of the main system frequency response function in step 6 is: , where the constraints are: , , , Hz, is the excitation force frequency.

[0055] Compared with the prior art, the present invention has the following beneficial effects: the human-shaped grounded variable-mass dynamic vibration absorber used in the present application can effectively suppress the vibration response of the main system; the human-shaped grounded variable-mass dynamic vibration absorber used in the present application adjusts its natural frequency by changing the mass of the vibration absorber, so that it can track the external excitation frequency, and can reduce the vibration of the main system in a wider frequency range compared to traditional vibration absorbers. With the change of mass, the human-shaped grounded variable-mass dynamic vibration absorber designed in the present invention can obtain a larger effective bandwidth;

[0056] This application improves the snake algorithm based on Levy flight. By simulating the randomness and disorder of Levy flight, the optimization algorithm can better search for the optimal solution in the solution space. This method improves the global search ability of the algorithm, which helps to jump out of the local optimal solution and find the global optimal solution.

[0057] The introduction of the snake algorithm of Levy flight increases the randomness of the algorithm and helps to avoid falling into the local optimal solution. The Levy distribution has a long tail characteristic, which can increase the long-distance jumps of particles, thereby improving the exploration ability of the algorithm and increasing the diversity of the population. The improved snake algorithm has a higher convergence speed and better solution quality when solving single-objective optimization problems. Compared with the traditional snake optimizer, the present application can find the global optimal solution faster and can find a solution closer to the global optimal solution. Based on this, the key parameters of the Ren-type grounded variable mass dynamic vibration absorber are adjusted, and the frequency response peak of the vibration absorber is successfully reduced, significantly improving its vibration reduction performance. The displacement response amplitude of the optimized vibration absorber at the key frequency point is effectively controlled, reducing the structural vibration, which is crucial to improving the stability of the structure and extending its service life. The results of parameter optimization not only confirm the effectiveness of the algorithm, but also demonstrate the potential of the vibration absorber to suppress vibration in practical applications, laying a solid foundation for further engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is the structural diagram of the Ren-type grounded variable mass dynamic vibration absorber;

[0059] Figure 2 This is the analysis diagram of the Ren-type grounded variable mass dynamic vibration absorber model;

[0060] Figure 3 The frequency response diagram of the main system corresponding to the Ren-type grounded variable mass dynamic vibration absorber with different damping ratios;

[0061] Figure 4 The frequency response diagram of the main system corresponding to the Ren-type grounded variable mass dynamic vibration absorber with different mass ratios;

[0062] Figure 5 This is a simulation model diagram of a Ren-type grounded variable mass dynamic vibration absorber;

[0063] Figure 6 The displacement frequency response function diagram of the main system;

[0064] Figure 7 It is the time domain diagram of the main system vibration;

[0065] Figure 8 is the relationship between the average fitness and the number of iterations;

[0066] Fig. 9 It is the relationship between the best fitness and the number of iterations.

[0067] In the figure: 1. Main system; 2. Liquid tank; 3. Water pump; 4. Liquid storage tank; 5. Flow meter; 6. Displacement sensor; 7. Control system. DETAILED DESCRIPTION

[0068] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0069] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0070] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0071] Example 1

[0072] Reference Figure 1 The Ren-type grounded variable mass dynamic vibration absorber includes a main system 1, on which a linear displacement sensor 6 is arranged. The main system 1 is connected to a liquid tank 2 and the ground through springs respectively. The liquid tank 2 is connected to a water pump 3 and a liquid storage tank 4 in sequence through a lightweight hose. A flow meter 5 is arranged on the lightweight hose between the liquid tank 2 and the liquid storage tank 4. The water pump 3, the flow meter 5 and the displacement sensor 6 are all connected to a control system 7. The main system 1 and the liquid tank 2 are grounded through damping.

[0073] The variable mass part of the Ren-type grounded variable mass dynamic vibration absorber is the mass of the liquid in the liquid tank 2. The upper part of the liquid tank 2 is sealed and a piston is installed inside. When the mass of the liquid changes, the piston can slide up and down, and the liquid tank 4 and the water pump 3 and the water pump 3 and the liquid tank 2 can flow in both directions. When the mass is too small, the water pump 3 rotates forward to inject the liquid into the liquid tank 2. When the mass is too large, the water pump 3 rotates reversely to pump the liquid out of the liquid tank 2.

[0074] The entire control part consists of a control system, a flow meter, a displacement sensor, and a water pump. A linear displacement sensor is installed on the mass block of the main system 1 to collect the displacement signal of the mass block. The information on the amount of liquid flowing out of the light hose or into the additional liquid tank during the mass change is monitored by the flow meter 5.

[0075] Example 2

[0076] On the basis of Example 1, the Ren-type grounded variable mass dynamic vibration absorber in this application is to ground the damping element of the Voigt-type dynamic vibration absorber, and the rest of the parts remain unchanged, so the vibration reduction performance of the system changes. The model of the damped Ren-type grounded variable mass dynamic vibration absorber is as follows: Figure 2 shown.

[0077] remember are the mass, stiffness, damping and displacement of the main system 1, is the mass of liquid in liquid tank 2 (i.e. variable mass), is the mass of the liquid tank 2 (i.e. fixed mass); is the total mass of the humanoid grounded variable mass dynamic vibration absorber, , are the stiffness, damping and displacement of the Ren-type grounded variable mass dynamic vibration absorber, and F is the external excitation force. is the angular frequency of the exciting force.

[0078] The parameter optimization method based on the Ren-type grounded variable mass dynamic vibration absorber includes the following steps:

[0079] Step 1: Adjust the mass of the Humanoid grounded variable mass dynamic vibration absorber to reach the target tuning state;

[0080] If you want to achieve a good vibration reduction effect, you must adjust the mass of the humanoid grounded variable mass dynamic vibration absorber to make its natural frequency and the angular frequency of the exciting force Equal. Step 1 includes the following sub-steps:

[0081] 1-1: Calculate the natural frequency of the Ren-type grounded variable mass dynamic vibration absorber The maximum value of and minimum value , the calculation formula is:

[0082] (1)

[0083] (2)

[0084] In the formula, It is the stiffness of the humanoid grounded variable mass dynamic vibration absorber.

[0085] 1-2: The control system 7 receives the signal from the displacement sensor 6 and controls the amount of liquid sent into or pumped out of the liquid tank 2 through the water pump 3. When the excitation force frequency ranges within Specifically, when the frequency of the external excitation force received by the displacement sensor 6 is lower than the minimum value of the natural frequency In order to reduce the natural frequency of the human-shaped grounded variable mass dynamic vibration absorber to match the excitation force frequency, the mass of the human-shaped grounded variable mass dynamic vibration absorber needs to be increased. On the contrary, when the external excitation force frequency received by the sensor is higher than the maximum value of the natural frequency In order to increase the natural frequency of the Ren-type grounded variable mass dynamic vibration absorber to match the excitation force frequency, the mass of the Ren-type grounded variable mass dynamic vibration absorber needs to be reduced. Therefore, the amount of liquid sent into or pumped out of the liquid tank 2 is controlled by the water pump 3 to increase or decrease the mass of the Ren-type grounded variable mass dynamic vibration absorber. When the excitation force frequency is within the range of When , water pump 3 is controlled to stop.

[0086] When the Ren-type grounded variable mass dynamic vibration absorber is in operation, the frequency of the excitation force applied to the main system 1 changes, and there is a deviation between the target resonant frequency of the vibration absorber and the excitation force frequency. The vibration reduction effect of the vibration absorber is reduced, and the vibration of the main system 1 intensifies. At this time, the displacement sensor 6 transmits the signal to the control system, and the external excitation force frequency received by the displacement sensor 6 and the maximum natural frequency of the Ren-type grounded variable mass dynamic vibration absorber are analyzed. and minimum value The control system 7 can automatically and continuously monitor the amount of liquid delivered into or drawn out of the liquid tank 2 by the water pump 3 in real time by using the flow meter 5 provided at the hose.

[0087] When the mass of the humanoid grounded variable mass dynamic vibration absorber reaches the target tuning state, the control system 7 will instruct the water pump motor to stop. , can be changed by the change of the mass of water in the liquid tank 2, to achieve The frequency of the excitation force within the range is tracked to achieve a tuned state, thereby significantly reducing the vibration response of the main system 1.

[0088] Step 2: Design the frequency response function L of the main system 1 1 ;

[0089] Step 2 includes the following sub-steps:

[0090] 2-1: The dynamic analysis of the Ren-type grounded variable mass dynamic vibration absorber model is carried out, and the system dynamic differential equation is:

[0091] (3)

[0092] (4)

[0093] The matrix form is:

[0094] (5)

[0095] In the formula, are the displacement, velocity and acceleration of main system 1, are the displacement, velocity and acceleration of the Ren-type grounded variable mass dynamic vibration absorber, F 0 is the amplitude of the excitation force;

[0096] 2-2: Use the complex number method to solve equation (5) express , let the solution of the differential equation be of the form , , then the amplitude expression of the main system 1 and the Ren-type grounded variable mass dynamic vibration absorber is:

[0097] Main system 1 amplitude expression X 1 :

[0098] (6)

[0099] Amplitude expression of Ren-type grounded variable mass dynamic vibration absorber 2 :

[0100] (7)

[0101] In the formula, ; ; ; , represents the imaginary unit, i.e. .

[0102] Therefore, the steady-state amplitudes of the main system 1 and the Human-type grounded variable mass dynamic absorber are shown in equations (8) and (9):

[0103] (8)

[0104] (9)

[0105] In the formula, ; .

[0106] 2-3: Introducing the intermediate variable main system damping ratio 、Human-type grounded variable mass dynamic vibration absorber damping ratio , quality ratio , natural frequency ratio and forced vibration frequency ratio The intermediate variable substitution calculation is performed. From this, the amplitude magnification coefficient expression of the main system 1 can be deduced as:

[0107] (10)

[0108] In the formula, ; ; ; ;

[0109] ——static deformation of the system, unit: m;

[0110] ——mass ratio, dimensionless;

[0111] ——Natural frequency of main system 1, unit: rad;

[0112] ——Natural frequency of the Ren-type grounded variable mass dynamic vibration absorber, unit: rad;

[0113] ——natural frequency ratio, dimensionless;

[0114] ——Forced vibration frequency ratio, expressed as the multiple relationship between the exciting force frequency and the resonant frequency of the main system 1, dimensionless;

[0115] ——Main system damping ratio, dimensionless.

[0116] ——Damping ratio of a humanoid grounded variable-mass dynamic vibration absorber, dimensionless.

[0117] 2-4: Frequency response function L of the main system 1 for:

[0118] (11)

[0119] In the formula, ; ; ; .

[0120] Can be ordered According to formula (10), the frequency response of the Ren-type grounded variable mass dynamic vibration absorber is studied.

[0121] Step 3: Determine the damping ratio of the Ren-type grounded variable mass dynamic vibration absorber Frequency response relationship with main system 1;

[0122] There are many influencing parameters in the frequency response function of the main system 1, but after the substitution and discussion of the intermediate variables, there are two variables that mainly affect the frequency response function, namely the damping ratio and the mass ratio. The effect of changing the damping ratio of the Ren-type grounded variable mass dynamic vibration absorber on the frequency response characteristics of the main system is analyzed. According to formula (10), the different The frequency response function curve of the matched main system is as follows: Figure 3 shown.

[0123] from Figure 3 It can be seen that when the damping is relatively small ( ), when the human-type grounded variable mass dynamic vibration absorber is at the best working frequency (the resonance frequency of the vibration absorber is the same as the external excitation frequency), the vibration absorption effect is the best, and the amplitude of the main system 1 is suppressed to the maximum, but the vibration reduction bandwidth of the human-type grounded variable mass dynamic vibration absorber is very narrow. When the excitation frequency changes, the amplitude of the main system is likely to increase. Therefore, the damping ratio of the human-type grounded variable mass dynamic vibration absorber is The relationship with the frequency response of the main system 1 is as follows: As the damping ratio of the Ren-type grounded variable mass dynamic vibration absorber As the value increases, the effect at the best vibration absorption frequency becomes worse, and the peak value of the frequency response of the main system 1 decreases.

[0124] Step 4: Determine the mass ratio of the Humanoid grounded variable mass dynamic vibration absorber Relationship with the main system frequency response;

[0125] According to formula (10), different mass ratios of the human-shaped grounded variable mass dynamic vibration absorber are obtained. Corresponding main system frequency response function diagram, quality ratio Increase from 0.02 to 0.5, such as Figure 4 shown.

[0126] like Figure 4 As shown, the mass ratio of the Ren type grounded variable mass dynamic vibration absorber is The relationship with the main system frequency response is: as the mass ratio With the increase of the mass of the human-shaped grounded variable-mass dynamic vibration absorber, the frequency response value of the main system (1) decreases when the human-shaped grounded variable-mass dynamic vibration absorber is at the optimal working frequency, and the vibration absorption effect is significantly improved. In addition, the second resonance peak of the frequency response curve of the main system 1 moves to the right, and the highest peak of the first resonance rises accordingly. Increasing the mass of the human-shaped grounded variable-mass dynamic vibration absorber can obtain a better vibration reduction effect, but in combination with engineering practice, the mass of the human-shaped grounded variable-mass dynamic vibration absorber in actual application should not be too large.

[0127] Step 5: Conduct simulation analysis of the Ren-type grounded variable mass dynamic vibration absorber;

[0128] This application uses MATLAB software to build a visual model based on Simulink. In the Simulink environment, it is critical to choose an appropriate algorithm. The simulation algorithm is one of the solutions to ordinary differential equations, state equations, and transfer function numerical calculation methods. In order to ensure computational efficiency, it must be reasonably simplified to better simulate the actual situation. This application uses the Runge-Kutta method.

[0129] As a high-precision single-step algorithm, the Runge-Kutta method is widely used in the numerical solution of differential equations. In order to ensure the computational efficiency, it must be reasonably simplified so as to better simulate the actual situation. Since this algorithm has high accuracy and suppresses errors, it is relatively complex. This method is used when the derivative and initial value of the equation are known, and the complex differential equation solution is simplified through computer simulation.

[0130] The Runge-Kutta method indirectly chooses the Taylor series expansion method in its specific approach. After predicting the slopes of several points in the integral interval, it calculates the weighted average, which is regarded as the basis for calculating the next point, and then constructs a more accurate numerical integral calculation formula. The Runge-Kutta method is one of the most important iterative specific methods for simulating the implicit or explicit product of the solution of partial differential equations. The fourth-order Runge-Kutta method, also known as "RK4" or simply "Runge-Kutta method".

[0131] In the Simulink environment, the fourth-order Runge-Kutta method is used to solve the model. By changing the step size and frequency, analytical solutions and approximate analytical solutions under different parameters can be obtained.

[0132] The dynamic differential equations of the Ren-type grounded variable mass dynamic vibration absorber system are shown in equations (3) and (4). The Simulink model structure is established as follows: Figure 5 shown.

[0133] The parameters of the main system (1) and the related parameters of the Ren-type grounded variable mass dynamic vibration absorber are shown in Table 1.

[0134] Table 1 Parameters of the main system and the Ren type grounded variable mass dynamic vibration absorber

[0135]

[0136] The initial displacement, velocity, and acceleration of the main system 1 are all set to zero. Then a sinusoidal excitation force of 10 N is applied to the main system 1. In order to ensure that the main system 1 reaches a steady-state vibration state, the simulation time is set to 3000 s. is the frequency of the external excitation force, in radians per second. According to the calculation formula of the natural frequency, the first-order resonant frequency of the entire vibration system is around 1 rad / s, and the second-order resonant frequency of the system is around 2.2 rad / s, so the excitation force is set to the range of 0 rad / s-2.5 rad / s in the software. Set the simulation algorithm to the fixed-step "Rung-Kutta" algorithm, with a fixed time step of 0.001 seconds and an absolute accuracy of 10 -3 .

[0137] Figure 6 In the figure, the green, red and blue curves correspond to the displacement frequency response function curves of the main system 1 when the mass of the human-shaped grounded variable mass dynamic vibration absorber becomes the maximum value, the minimum value and the human-shaped grounded variable mass dynamic vibration absorber is not installed. Figure 6 It can be clearly seen that when the Ren-type grounded variable mass dynamic vibration absorber is not set in the main system 1, the main system 1 reaches a resonance state of about 2 rad / s, which is also called the natural frequency of the main system 1. When the mass of the Ren-type grounded variable mass dynamic vibration absorber reaches the maximum value, the vibration response of the main system 1 at 1 rad / s is reduced by 33.264 dB (from 2.5 dB to -30.764 dB), and the first and second resonance peaks appear at 0.929 rad / s and 2.153 rad / s, respectively. When the mass of the Ren-type grounded variable mass dynamic vibration absorber is the minimum value, the frequency response function of the main system 1 at 1.581 rad / s is reduced by 40.351 dB (from 8.516 dB to -31.835 dB), and the first and second resonance peaks appear at 1.414 rad / s and 2.236 rad / s, respectively.

[0138] According to the theoretical calculation formula of the natural frequency, when the mass of the Ren-type grounded variable mass dynamic vibration absorber is the minimum value of 0.4 kg, its natural frequency is 1.58 rad / s. The Simulink simulation results show that the frequency response function of the main system 1 is the minimum value at 1.581 rad / s, and the theoretical derivation is consistent with the simulation. Figure 7 It is the vibration response diagram of the main system 1 corresponding to the case where the excitation force frequency is equal to 1.581 rad / s, when the main system 1 has no Human-shaped grounded variable mass dynamic vibration absorber and when the main system 1 is installed with the Human-shaped grounded variable mass dynamic vibration absorber with the minimum mass.

[0139] Depend on Figure 7It can be seen that when the main system 1 is not installed with the Human-type grounded variable mass dynamic vibration absorber, the steady-state amplitude of the main system 1 is 3.332 m; when the mass of the Human-type grounded variable mass dynamic vibration absorber is the smallest, the steady-state amplitude of the main system 1 is reduced to 0.032 m. After the Human-type grounded variable mass dynamic vibration absorber is installed, the amplitude reduction reaches 99.04%. The simulation results show that installing the Human-type grounded variable mass dynamic vibration absorber can effectively suppress the vibration response of the main system 1.

[0140] Step 6: Parameter optimization of Ren-type grounded variable mass dynamic vibration absorber;

[0141] The purpose of optimizing the parameters of the Ren-type grounded variable mass dynamic vibration absorber in the present application is to significantly reduce the response peak at the resonance frequency of the main system frequency response function within the operating frequency band of the vibration absorber.

[0142] From the previous analysis, it can be seen that mass, stiffness and damping are all factors affecting the working performance of the human-type grounded variable mass dynamic vibration absorber. Based on the modal parameter identification at the installation position of the human-type grounded variable mass dynamic vibration absorber, the present invention uses an improved snake optimization algorithm (LSO) to optimize the parameters of the human-type grounded variable mass dynamic vibration absorber.

[0143] Specifically, the present application improves the snake optimization algorithm by adding the Levy flight strategy to the original snake algorithm.

[0144] Snake Optimization is a meta-heuristic optimization algorithm inspired by the mating behavior of snakes. If the temperature is low and food is available, the mating behavior of snakes occurs; otherwise, the snakes will only look for food or eat the existing food. Based on this, the search process of the snake optimization algorithm will be considered in two stages: exploration and exploitation. Exploration describes environmental factors, namely cold places and food. In this stage, there is no situation where the snake only looks for food in the environment around it.

[0145] The development includes many transition stages to improve the algorithm's search efficiency. If food is available but the temperature is high, the snakes will focus only on eating the available food. Finally, if food is available and the area is cold, the mating process occurs. There are several situations in the mating process, namely fighting mode or mating mode. In fighting mode, each male will fight to get the best female and each female will try to choose the best male. In mating mode, the occurrence of mating behavior for each pair of snakes depends on the amount of food availability. In the search space, if mating behavior occurs, the female has the possibility to lay eggs, which hatch into new snakes.

[0146] Levy flight refers to a random walk whose step length probability distribution is a heavy-tailed distribution, that is, there is a relatively high probability of large steps in the process of random walk, so that it will not stay in a certain position. Therefore, the introduction of Levy flight can avoid being attracted by the local optimal value. Levy flight is a non-Gaussian random process, and its step length obeys Levy distribution. Based on this, in the improved snake optimization algorithm:

[0147] The struggle mode formula is:

[0148]

[0149]

[0150]

[0151]

[0152] The mating mode formula is:

[0153]

[0154]

[0155]

[0156]

[0157] in, For the The position of the male snake, t is the current iteration number, is a constant with a value of 2. For the fighting ability of male snakes, is a random number between [0, 1], is the position of the best individual in the female population, For the The position of the female snake, For the fighting ability of female snakes, is the position of the best individual in the male population, is the fitness value of the best individual in the female population, is the fitness value of the best individual in the male population, is the fitness value of the individual. The mating ability of male snakes. is the mating ability of female snakes, Q is the amount of food, The male population The fitness value of the snake, The female population The fitness value of the snake.

[0158] The random search path formula for Levy flight (simulated using the Mantegna algorithm): ;

[0159] and are two normally distributed random numbers in the interval [0,1], and the value of β is generally 1<β<3. It can be calculated by the following formula:

[0160]

[0161] in, is the standard gamma function.

[0162] The improved snake optimization algorithm (LSO) is based on the group, and moves individuals in the group to good areas according to their fitness to the environment. However, it does not use evolution operators for individuals, but instead regards each individual as a point without volume in the D-dimensional search space, searching for food in the search space at a certain speed, which is dynamically adjusted according to its own experience and the experience of its companions.

[0163] The resonant frequency of the Ren-type grounded variable mass dynamic vibration absorber The corresponding main system (1) frequency response function maximum value is minimized as the objective to establish the objective function, and its function expression is shown in formula (10). Therefore, the optimization goal is to minimize the maximum value of the main system frequency response function, that is, , where the constraints are: , , , Hz, is the excitation force frequency.

[0164] In this embodiment, the improved snake optimization algorithm (LSO) is used to optimize the parameters of the Human-type grounded variable mass dynamic vibration absorber. The population is set to 200, the number of iterations is 200, and the relationship between the average fitness value and the fitness value and the number of iterations is as follows: Figure 8 , Fig. 9 shown.

[0165] The parameters of the Ren-type ground-type variable mass dynamic vibration absorber before and after optimization are shown in Table 2.

[0166] Table 2 Parameters of Ren-type ground-type variable mass dynamic vibration absorber before and after optimization

[0167]

[0168] It can be seen from Table 2 that the mass, stiffness and damping of the vibration absorber after optimization are all increased compared with those before optimization. Based on this optimized design parameter, the Ren-type grounded variable mass dynamic vibration absorber has a lower frequency response peak and its displacement response amplitude at the original frequency is greatly suppressed, and the parameter optimization result is good.

[0169] The above descriptions are only optional embodiments of the present invention, and are not intended to limit the patent scope of the present invention. All equivalent structural changes made using the contents of the present invention specification under the concept of the present invention, or direct / indirect applications in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A parameter optimization method based on a Ren-type ground-type variable mass dynamic vibration absorber, characterized in that: The steps include: Step 1: Adjust the mass of the Humanoid grounded variable mass dynamic vibration absorber to reach the target tuning state; Step 2: Design the frequency response function L1 of the main system (1); Step 3: Determine the damping ratio of the Ren-type grounded variable mass dynamic vibration absorber Frequency response relationship with the main system (1); Step 4: Determine the mass ratio of the Humanoid grounded variable mass dynamic vibration absorber Relationship with the main system frequency response; Step 5: Conduct simulation analysis of the Ren-type grounded variable mass dynamic vibration absorber; Step 6: Parameter optimization of the human-shaped ground-type variable mass dynamic vibration absorber. The optimized human-shaped ground-type variable mass dynamic vibration absorber parameters include the total mass of the human-shaped ground-type variable mass dynamic vibration absorber. , the stiffness of the Ren-type grounded variable mass dynamic vibration absorber , the damping of the human-shaped grounded variable mass dynamic vibration absorber .

2. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 1 is characterized in that: The Ren-type grounded variable mass dynamic vibration absorber comprises a main system (1), a displacement sensor (6) is arranged on the main system (1), the main system (1) is connected to a liquid tank (2) and the ground via springs, the liquid tank (2) is connected to a water pump (3) and a liquid storage tank (4) in sequence, a flow meter (5) is arranged between the liquid tank (2) and the liquid storage tank (4), the water pump (3), the flow meter (5) and the displacement sensor (6) are all connected to a control system (7), and the main system (1) and the liquid tank (2) are grounded via damping; remember are the mass, stiffness, damping and displacement of the main system (1), is the mass of the liquid in the liquid tank (2), is the mass of the liquid tank (2); is the total mass of the humanoid grounded variable mass dynamic vibration absorber, , are the stiffness, damping and displacement of the Ren-type grounded variable mass dynamic vibration absorber, F is the external excitation force, is the angular frequency of the exciting force.

3. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 2 is characterized in that: The step 1 includes the following sub-steps: 1-1: Calculate the natural frequency of the Ren-type grounded variable mass dynamic vibration absorber The maximum value of and minimum value , the calculation formula is: （1） （2） In the formula, is the stiffness of the humanoid grounded variable mass dynamic absorber; 1-2: The control system (7) receives the signal from the displacement sensor (6) and controls the amount of liquid sent into or pumped out of the liquid tank (2) through the water pump (3). When the frequency of the excitation force is within the range of When the water pump (3) is controlled to stop.

4. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 3 is characterized in that: The step 2 includes the following sub-steps: 2-1: The dynamic analysis of the Ren-type grounded variable mass dynamic vibration absorber model is carried out, and the system dynamic differential equation is: （3） （4） The matrix form is: （5） In the formula, are the displacement, velocity and acceleration of the main system (1), are the displacement, velocity and acceleration of the Ren-type grounded variable mass dynamic vibration absorber, respectively, and F0 is the amplitude of the excitation force; 2-2: Use the complex number method to solve equation (5) express , let the solution of the differential equation be of the form , , then the amplitude expression of the main system (1) and the Ren-type grounded variable mass dynamic absorber is: Main system (1) Amplitude expression X1: （6） The amplitude expression of Ren-type grounded variable mass dynamic vibration absorber X2: （7） In the formula, ; ; ; , represents the imaginary unit, i.e. ; The steady-state amplitudes of the main system (1) and the Human-type grounded variable mass dynamic absorber are shown in equations (8) and (9): （8） （9） In the formula, ; ; 2-3: Introducing the intermediate variable main system damping ratio 、Human-type grounded variable mass dynamic vibration absorber damping ratio , quality ratio , natural frequency ratio and forced vibration frequency ratio After performing intermediate variable substitution calculation, the amplitude magnification coefficient expression of the main system (1) is: （10） In the formula, ; ; ; ; - static deformation of the system; ——mass ratio; —— natural frequency of the main system (1); ——Natural frequency of human-type grounded variable mass dynamic vibration absorber; ——natural frequency ratio; - forced vibration frequency ratio, expressed as a multiple of the exciting force frequency and the resonant frequency of the main system (1); ——damping ratio of the main system; ——Damping ratio of humanoid grounded variable mass dynamic vibration absorber; 2-4: The frequency response function L1 of the main system (1) is: （11） In the formula, ; ; ; .

5. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 4 is characterized in that: The damping ratio of the Ren-type grounded variable mass dynamic vibration absorber in step 3 is The frequency response relationship with the main system (1) is as follows: As the damping ratio of the Ren-type grounded variable mass dynamic vibration absorber As the value increases, the effect at the best vibration absorption frequency becomes worse and the peak value of the frequency response of the main system (1) decreases.

6. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 5 is characterized in that: The mass ratio of the humanoid ground-type variable mass dynamic vibration absorber in step 4 is The relationship with the main system frequency response is: as the mass ratio As the frequency response value of the main system (1) decreases when the Human-type grounded variable mass dynamic vibration absorber is at the optimal working frequency, the vibration absorption effect becomes better.

7. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 6 is characterized in that: In the step five, a visualization model is established based on Simulink, and the model is solved using the Runge-Kutta method in the Simulink environment. By changing the step size and frequency, analytical solutions and approximate analytical solutions under different parameters are obtained to realize the simulation analysis of the Ren-type grounded variable mass dynamic vibration absorber.

8. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 7 is characterized in that: In step six, the snake algorithm + Levy flight strategy is used to improve the snake optimization algorithm.

9. The parameter optimization method based on the Ren-type ground-connected variable mass dynamic vibration absorber according to claim 8 is characterized in that: The parameter optimization function corresponding to minimizing the maximum value of the main system frequency response function in step 6 is: , where the constraints are: , , , Hz, is the excitation force frequency.

Images