Nonlinear pendulum-type TMD device with adjustable stiffness, its parameter setting method and semi-active control method

Abstract

The present invention discloses a non-linear pendulum type TMD device with adjustable stiffness, which includes a pendulum rope, a pendulum ball and an additional support. The additional support is used to introduce non-linear stiffness during the swinging process of the pendulum ball to change the central position and radius length when the pendulum ball swings. The present invention also proposes a parameter setting method for the non-linear pendulum type TMD device with adjustable stiffness, which includes the following steps: Step 1: Construct a motion model of the non-linear pendulum type TMD device with adjustable stiffness; Step 2: Obtain a control model of the non-linear pendulum type TMD device with adjustable stiffness based on the constructed motion model; Step 3: Solve the position parameters of the fulcrum of the additional support based on the control model. The non-linear pendulum type TMD device with adjustable stiffness, its parameter setting method and semi-active control method of the present invention can effectively improve the vibration control performance by introducing non-linear stiffness. The present invention also discloses a semi-active control method for the non-linear pendulum type TMD device with adjustable stiffness.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration control, and particularly relates to a non-linear pendulum type TMD device with adjustable stiffness, its parameter setting method and semi-active control method. Background Art

[0002] The tuned mass damper (TMD) is a widely used vibration damper and has been extensively studied and developed in the field of civil engineering. The pendulum tuned mass damper (PTMD) is one of the most classical TMDs, which consists of a pendulum rope, a mass block and a damper. In the past few decades, PTMDs have been widely applied to the wind-induced vibration control of high-rise buildings. In engineering practice, PTMDs are usually designed to swing slightly to maintain linear characteristics, so their design often targets a relatively narrow frequency range of the structural fundamental frequency, that is, the effective frequency bandwidth of PTMDs is narrow, which makes them very sensitive to frequency changes. When the structure is subjected to complex external excitations, especially in the case of detuning, the performance of such devices may deteriorate.

[0003] To overcome this weakness, scholars have adopted the semi-active (Semi-Active Control) strategy to improve the performance of PTMDs, that is, an adjustable PTMD is obtained by changing the pendulum length. The results show that the semi-active variable pendulum length PTMD achieves the purpose of controllable restoring force and has significant vibration control effects. At the same time, many researchers have tried to introduce non-linearity into the classical PTMD system and proposed the non-linear tuned mass damper (NTMD). The research carried out has shown that NTMDs greatly broaden the control frequency bandwidth of TMDs, making them have better performance in vibration control than traditional linear TMDs, that is, introducing appropriate non-linearity can effectively improve the vibration control performance of traditional PTMDs.

[0004] Therefore, the present invention combines the characteristics of high-efficiency vibration reduction of semi-active control and frequency bandwidth broadening of NTMD, and proposes a non-linear pendulum type TMD device with adjustable stiffness, its parameter setting method and semi-active control method. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a non-linear pendulum type TMD device with adjustable stiffness, its parameter setting method and semi-active control method, which can effectively improve the vibration control performance by introducing non-linear stiffness.

[0006] To achieve the above purpose, the present invention provides the following technical solutions:

[0007] The present invention first proposes a non-linear pendulum type TMD device with adjustable stiffness, including a pendulum rope. The upper end of the pendulum rope is fixedly connected to a vibration control structure, and the lower end is connected to a pendulum ball. It further includes an additional support. The additional support is provided with a fulcrum located in the swinging plane of the pendulum ball for cooperating with the pendulum rope, and the additional support is used to introduce non-linear stiffness during the swinging process of the pendulum ball to change the central position and radius length when the pendulum ball swings.

[0008] Furthermore, the additional support is provided as at least one; or, the additional support is provided as at least one group, and each group includes two of the additional supports. The two additional supports belonging to the same group are symmetrically arranged with respect to the vertical plane passing through the connection point between the upper end of the pendulum rope and the vibration control structure.

[0009] Furthermore, let the connection point between the upper end of the pendulum rope and the vibration control structure be the initial fulcrum, and the vertical plane passing through the initial fulcrum be the plumb plane;

[0010] When there are at least two of the additional supports on the same side of the plumb plane, the distances d in the vertical direction between any two of the additional supports and the initial fulcrum are not equal. All the additional supports on the same side of the plumb plane are sorted in ascending order of the distance d as the 1st additional support, the 2nd additional support,..., the nth additional support; and among any i-th additional support and the (i + 1)-th additional support, the inclination angle of the line connecting the fulcrum of the i-th additional support and the initial fulcrum with respect to the plumb plane is less than the inclination angle of the line connecting the fulcrum of the (i + 1)-th additional support and the initial fulcrum with respect to the plumb plane, where i = 1, 2,..., n - 1; n ≥ 2.

[0011] Furthermore, it further includes a semi-active control system for adjusting the position of the additional support.

[0012] Furthermore, let the connection point between the upper end of the pendulum rope and the vibration control structure be the initial fulcrum, and the initial swing radius when the pendulum ball swings around the initial fulcrum is:

[0013]

[0014] where, l 0 is the initial swing radius when the pendulum ball swings around the initial fulcrum; g is the acceleration due to gravity; f is the first-order frequency of the vibration control structure.

[0015] Furthermore, viscous damping is provided in the swinging plane of the pendulum ball, and the viscous damping is connected to the pendulum ball and can move along the swinging trajectory of the pendulum ball.

[0016] The present invention also provides a method for setting parameters of a non-linear pendulum type TMD device with adjustable stiffness. The non-linear pendulum type TMD device with adjustable stiffness includes a pendulum rope and additional supports. The upper end of the pendulum rope is fixedly connected to a vibration control structure, and the lower end is connected to a pendulum ball. There are two additional supports, and the two additional supports are symmetrically arranged with respect to the vertical plane passing through the connection point between the upper end of the pendulum rope and the vibration control structure. A fulcrum for cooperating with the pendulum rope is provided on the additional support within the swinging plane of the pendulum ball. The additional support is used to introduce non-linear stiffness during the swinging process of the pendulum ball to change the central position and radius length when the pendulum ball swings. The method includes the following steps:

[0017] Step 1: Construct a motion model of the non-linear pendulum type TMD device with adjustable stiffness:

[0018] Step 2: Obtain a control model of the non-linear pendulum type TMD device with adjustable stiffness based on the constructed motion model;

[0019] Step 3: Solve the position parameters of the fulcrum of the additional support based on the control model.

[0020] Further, in Step 1, the motion model of the non-linear pendulum type TMD device with adjustable stiffness is:

[0021]

[0022] where m represents the mass of the vibration control structure; S is the arc length of the motion of the pendulum ball; represents the second derivative of S with respect to time; g is the acceleration due to gravity; θ is the simple pendulum rotation angle of the pendulum ball, and:

[0023]

[0024] where l 1 represents the radius when the pendulum ball swings around the fulcrum on the additional support; l 0 is the initial swing radius when the pendulum ball swings around the initial fulcrum, and the initial fulcrum is the connection point between the upper end of the pendulum rope and the vibration control structure; θ 0 represents the angle between the connection line between the fulcrum of the additional support and the initial fulcrum and the vertical plane.

[0025] Further, in Step 2, the control model of the non-linear pendulum type TMD device with adjustable stiffness is:

[0026] Applying an external harmonic excitation F d = Fcos(ωt) to the oscillator installed with PTMD-AS, the control equation of the system can be obtained from the Lagrange equation as:

[0027]

[0028]

[0029] where m p represents the mass of the pendulum bob; c p represents the damping of the pendulum bob; F represents the amplitude of the excitation; ω represents the excitation frequency; t represents time; c represents the damping of the vibration control structure; k represents the stiffness of the vibration control structure; g is the acceleration due to gravity; represents the derivative of S with respect to time t; X represents the vibration displacement; represents the first derivative of the vibration displacement with respect to time; represents the second derivative of the vibration displacement with respect to time; l represents the calculated length of the swing radius of the pendulum bob, and:

[0030]

[0031] Introduce dimensionless parameters:

[0032]

[0033]

[0034] Rewrite the control equations using the dimensionless parameters as:

[0035] (1 + μ)x″ + 2ζx′ + x + μ(s″cosθ - s′ 2 γsinθ) = fcos(ατ)

[0036] s″ + 2ζ p s′ + β 2 sinθ + x′cosθ = 0

[0037] where x, Ω, and ζ are the dimensionless displacement, natural frequency, and damping ratio of the vibration control structure; γ is the ratio of l 0 to l, δ represents the ratio of l 1 to l 0 ; ω p and ζ p are the design frequency and damping ratio of the non-linear pendulum type TMD device with adjustable stiffness, μ is the mass ratio, α and β are the excitation frequency ratio and the single pendulum frequency ratio, f is the amplitude of the dimensionless excitation, and τ is the dimensionless time.

[0038] Furthermore, in the third step, under the conditions of determining x, Ω, ζ, μ, ω p , ζ p , α, β, f, and τ, the method for solving the position parameters (δ, θ 0 ) of the additional support fulcrum is:

[0039] 31) Define the objective function with the goal of minimizing the maximum response of the vibration control structure:

[0040] Minimize Fitness=max(H(δ,θ 0 ))

[0041] where H is the response amplitude vector of the vibration control structure under external excitations at different frequencies obtained by the EIHB method;

[0042] 32) Determine the selection range of the position parameters (δ, θ 0 ) of the additional support fulcrum;

[0043] 33) Use the gradient descent algorithm to search for the optimal position parameters of the additional support fulcrum. The method is as follows:

[0044] 331) Assign values to δ and θ 0 within the selection range;

[0045] 332) Calculate the amplitude vector H of the vibration control structure using the EIHB method;

[0046] 333) Calculate the value of the objective function to obtain the fitness value Fitness;

[0047] 334) Determine whether the current fitness value is less than the best fitness value: If so, replace the best fitness value with the current fitness value; if not, keep the historical fitness value unchanged;

[0048] 335) Determine whether the current iteration number m is less than the set maximum iteration number: If so, update the values of δ and θ 0 , execute step 332), and m = m + 1; if not, output the values of δ and θ 0 corresponding to the best fitness value to obtain the optimal position parameters of the additional support fulcrum.

[0049] The present invention also proposes a semi-active control method for a stiffness-adjustable nonlinear pendulum TMD device, including the following steps:

[0050] S1: Real-time collect the acceleration response and external load of the vibration control structure through sensors to obtain the amplitude and frequency of the external excitation;

[0051] S2: Use the parameter setting method of the stiffness-adjustable nonlinear pendulum TMD device described in any one of claims 7-9 to obtain the optimal position parameters of the additional support under the current external excitation conditions;

[0052] S3: Use the semi-active control system to adjust the additional support to reach the position corresponding to the optimal position parameters.

[0053] The beneficial effects of the present invention are as follows:

[0054] The stiffness - adjustable non - linear pendulum - type TMD device of the present invention sets an additional support in the swinging plane of the pendulum ball, and sets a fulcrum on the additional support for cooperation with the pendulum rope. Thus, when the pendulum rope moves to the fulcrum position, the center position and radius length of the pendulum ball's swing can be changed under the action of the fulcrum, so that the simple pendulum can have a bilinear stiffness. Specifically, it includes an initial stiffness that swings around the initial fulcrum and a hardening stiffness that swings around the fulcrum set on the additional support, thereby increasing the frequency bandwidth, improving the vibration reduction effect, and without the input of external energy, being easier to implement and safe and reliable.

[0055] The stiffness - adjustable non - linear pendulum - type TMD device of the present invention also has the following advantages:

[0056] (1) Based on the characteristic that the frequency of a simple pendulum depends entirely on the pendulum length, by restricting the swing of the pendulum rope with an additional support and changing the suspension point and pendulum length, the stiffness of the simple pendulum is increased and the energy consumption of the vibration reduction device is increased;

[0057] (2) The principle of the stiffness - adjustable non - linear pendulum - type TMD device of the present invention is intuitive, the structure is simple, and the simple pendulum and the additional support are independent structures, having the advantages of convenient processing and maintenance;

[0058] (3) The stiffness - adjustable non - linear pendulum - type TMD device of the present invention can reduce the cross - wind vibration response of high - rise buildings under wind loads, and can produce good economic and social benefits.

[0059] The parameter - setting method of the stiffness - adjustable non - linear pendulum - type TMD device of the present invention can obtain the optimal position parameters of the fulcrum of the additional support for the relevant parameters of different vibration - controlled structures and the relevant parameters of the pendulum - type TMD device (including the pendulum ball and the pendulum length), avoiding the adverse effects caused by excessive increase in the stiffness of the simple pendulum that restricts its swing amplitude and the bifurcation of the excitation frequency of the vibration - controlled structure.

[0060] The semi-active control method of the non-linear pendulum type TMD device with adjustable stiffness of the present invention can obtain the amplitude and frequency of the external excitation by collecting the acceleration response and external load of the vibration control structure subjected to the external excitation in real time; under the conditions of the amplitude and frequency of the external excitation, the optimal position parameter of the additional support is obtained by using the parameter setting method of the non-linear pendulum type TMD device with adjustable stiffness, and the position of the additional support is adjusted to the position corresponding to the optimal position parameter, which can effectively improve the vibration control performance of the vibration control structure. The semi-active control method of the non-linear pendulum type TMD device with adjustable stiffness of the present invention realizes the continuous adjustment of the damper stiffness and frequency by moving the position of the support, and because the stiffness is continuously adjustable, the suppression effect on the vortex-induced resonance of different frequencies can be achieved, so as to achieve the effect of suppressing the vibration of different modes. The intelligent control system is used for automatic data processing and operation, reducing the manual operation cost and improving the work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to make the objectives, technical solutions and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0062] Figure 1 It is a schematic structural diagram of an embodiment of the non-linear pendulum type TMD device with adjustable stiffness of the present invention, specifically a schematic structural diagram when a group of additional supports are provided;

[0063] Figure 2 It is a schematic structural diagram when two groups of additional supports are provided;

[0064] Figure 3 It is a schematic structural diagram of a non-linear pendulum type TMD device provided with a semi-active control system;

[0065] Figure 4 It is a theoretical model diagram of the non-linear pendulum type TMD device with adjustable stiffness of this embodiment; (a) Schematic diagram of the horizontal oscillator installing PTMD-AS; (b) Schematic diagram of PTMD-AS;

[0066] Figure 5 It is a force-displacement relationship diagram;

[0067] Figure 6 It is a displacement-frequency relationship diagram;

[0068] Figure 7 It is the time history response of the single pendulum rotation angle at different δ;

[0069] Figure 8 It is the amplitude-frequency response of the system at different δ (θ 0 = 0.1 rad): (a) Response of the oscillator; (b) Response of the pendulum;

[0070] Figure 9 It is for different θ 0Amplitude-frequency response of the system at a certain time (δ = 0.8): (a) Response of the oscillator; (b) Response of the pendulum;

[0071] Figure 10 Amplitude-frequency response of the system for different excitation amplitudes f (δ = 0.85, θ 0 = 0.1 rad): (a) Response of the oscillator; (b) Response of the pendulum;

[0072] Figure 11 For θ 0 = 0.1 rad and δ = 0.2, amplitude-frequency response of the oscillator;

[0073] Figure 12 Time history response and phase diagram of the oscillator for different excitation frequencies;

[0074] Figure 13 Bifurcation diagram in the interval of excitation frequency ratio [1.06, 1.11] for δ = 0.2;

[0075] Figure 14 Wind field and pressure measurement point arrangement in the wind tunnel experiment;

[0076] Figure 15 Lift coefficient obtained through the wind tunnel experiment: (a) Time history of the lift coefficient C l ; (b) Power density spectrum;

[0077] Figure 16 Lift coefficient obtained through the wind tunnel experiment: (a) Time history of the lift coefficient C l ; (b) Power density spectrum;

[0078] Figure 17 Comparison of standard deviation of structural displacement response under different wind speeds v: (a) Structural detuning ±5%; (b) Structural detuning ±10%.

[0079] Explanation of reference numerals:

[0080] 1 - Pendulum rope; 2 - Vibration control structure; 3 - Pendulum ball; 4 - Additional support; 4a - First additional support; 4b - Second additional support; 5 - Fulcrum; 5a - First fulcrum; 5b - Second fulcrum; 6 - Initial fulcrum; 7 - Vertical plane; 8 - Viscous damping; 9 - Sensor; 10 - Microcontroller; 11 - Stepper motor. Detailed implementation manners

[0081] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments given are not intended to limit the present invention.

[0082] 1. Nonlinear pendulum type TMD device with adjustable stiffness

[0083] As shown Figure 1 in the figure, the stiffness - adjustable non - linear pendulum - type TMD device (PTMD - AS) of this embodiment includes a pendulum rope 1 and an additional support 4. The upper end of the pendulum rope 1 is fixedly connected to the vibration control structure 2, and the lower end is connected to a pendulum ball 3. On the additional support 4, there is a fulcrum 5 located in the swinging plane of the pendulum ball 3 for cooperating with the pendulum rope 1, and the additional support 4 is used to introduce non - linear stiffness during the swinging process of the pendulum ball to change the central position and radius length when the pendulum ball 3 swings. Specifically, the number of additional supports 4 can be set to at least one according to the needs of the actual application scenario, and the position of each additional support 4 is arranged according to the application scenario. Of course, the additional support 4 can also be set as at least one group, and each group includes two additional supports 4. The two additional supports 4 belonging to the same group are symmetrically arranged with respect to the vertical plane passing through the connection point between the upper end of the pendulum rope 1 and the vibration control structure 2. As shown Figure 1 in the figure, the additional support 4 is set as one group; Figure 2 the additional support 4 shown in the figure is set as two groups.

[0084] Specifically, in this embodiment, the connection point between the upper end of the pendulum rope 1 and the vibration control structure 2 is set as the initial fulcrum 6, and the vertical plane passing through the initial fulcrum 6 is the plumb plane 7. When there are at least two additional supports 4 on the same side of the plumb plane, the vertical distances d between any two additional supports 4 and the initial fulcrum 6 are not equal. All the additional supports located on the same side of the plumb plane are sorted in ascending order of the distance d as the 1st additional support, the 2nd additional support,..., the nth additional support; and among any the ith additional support and the (i + 1)th additional support, the inclination angle of the line connecting the fulcrum 5 of the ith additional support and the initial fulcrum 6 with respect to the plumb plane 7 is less than the inclination angle of the line connecting the fulcrum 5 of the (i + 1)th additional support and the initial fulcrum 6 with respect to the plumb plane 7, where i = 1, 2,..., n - 1; n≥2. As shown Figure 2 in the figure, there are two additional supports 4 on the same side of the plumb plane 7. The additional support 4 closer to the initial fulcrum 6 in the vertical direction is the first additional support 4a, and the additional support 4 farther from the initial fulcrum 6 in the vertical direction is the second additional support 4b. The inclination angle θ of the line connecting the fulcrum 5a of the first additional support 4a and the initial fulcrum 6 with respect to the plumb plane 7 1 is less than the inclination angle θ of the line connecting the fulcrum 5b of the second additional support 4b and the initial fulcrum 6 with respect to the plumb plane 7 2 .

[0085] In the preferred implementation manner of this embodiment, there is a viscous damper 8 in the swinging plane of the pendulum ball 3. The viscous damper 8 is connected to the pendulum ball 3 and can move along the swinging trajectory of the pendulum ball 3 as the pendulum ball 3 swings.

[0086] As shown Figure 3As shown, in another implementation of this embodiment, the stiffness-adjustable non-linear pendulum TMD device further includes a semi-active control system for adjusting the position of the additional support 4, so that the position of the additional support 4 can be changed according to different working conditions, achieving better vibration control performance. Specifically, the semi-active control system includes the following four parts: ① sensor subsystem; ② data acquisition and transmission subsystem; ③ data processing and management subsystem; ④ structural vibration evaluation and control subsystem. The specific working steps are as follows: ① Each sensor in the sensor subsystem acquires signals at key positions; ② The sensor signals collected are converted into digital signals and stored in a local industrial computer, and at the same time, they are transmitted to the data processing and management subsystem through a computer fiber optic network; ③ The computer system completes the post-processing, archiving, display, and storage of the data; ④ The structural vibration evaluation system analyzes, statistics, and discriminates thresholds based on the data sent by the monitoring system, and gives evaluation opinions and adjustment support information.

[0087] Specifically, in this embodiment, the sensor 9 is installed on the vibration control structure 2, and the monitoring objects of the sensor 9 are divided into 2 categories: ① load monitoring: wind load, atmospheric temperature and humidity, and structural temperature; ② structural response monitoring: acceleration, stress and strain. Since the PTMD is usually used to control the first mode with the largest horizontal vibration response at the top of the structure, an acceleration sensor is installed at the top layer or section of the structure. The microcontroller 10 is connected to the sensor 9 and the stepping motor 11 through wires. The sensor 9 can monitor the acceleration response and external load of the vibration control structure in real time. The microcontroller 10 receives the signals from the sensor 9, analyzes them, inputs the environmental conditions, and calculates the optimal support parameters according to the parameter optimization program. Then, the stepping motor 11 moves the additional support to the optimal position according to the electrical signal instructions sent from the control center, and re-adjusts the stiffness of the PTMD. Therefore, this device can further adopt a semi-active control strategy to continuously adjust the stiffness and frequency of the damper by moving the position of the additional support. Since the stiffness is continuously adjustable, it can achieve an inhibitory effect on vortex-induced resonance of different frequencies, thereby achieving the effect of suppressing vibrations of different modes. The intelligent control system is used for automatic data processing and operation, reducing the manual operation cost and improving the work efficiency.

[0088] In the stiffness-adjustable non-linear pendulum TMD device of this embodiment, the swinging frequency of the pendulum ball 3 when swinging around the initial fulcrum 6 is consistent with the natural frequency of the vibration control structure 2. Since the frequency of a simple pendulum depends entirely on the pendulum length, in this embodiment, the initial swinging radius of the pendulum ball 3 when swinging around the initial fulcrum 6 is:

[0089]

[0090] where, l 0is the initial swing radius when the pendulum ball swings around the initial fulcrum; g is the acceleration due to gravity; f is the primary frequency of the vibration control structure.

[0091] In this embodiment, a set of additional supports 4 is provided, that is, an additional support 4 is symmetrically provided on each side of the vertical plane 7. When the pendulum ball 3 swings, the radius length changes from the initial designed pendulum length l when the pendulum rope 1 touches the additional support 4 0 to the hardened pendulum length l 1 , so as to achieve the effect of variable stiffness. The position of the additional support 2 in this implementation scheme is determined by the parameters δ = l 1 / l 0 and θ 0 , where θ 0 is the inclination angle of the connection line between the fulcrum 5 of the additional support 4 and the initial fulcrum 6 relative to the vertical plane 7. The pendulum ball 3 in this embodiment is made of an austenitic stainless steel mass block, and the viscous damping 8 moves along the swing trajectory of the pendulum ball 3. Thus, the damping force F c and the restoring force F r of the variable-stiffness nonlinear pendulum-type TMD device in this embodiment are as follows:

[0092]

[0093] where c is the damping coefficient of the viscous damping; S is the swing arc length of the pendulum ball; denotes taking the derivative of S with respect to time t; θ is the pendulum angle of the simple pendulum, and its determination method is as follows:

[0094]

[0095] where l 1 represents the radius when the pendulum ball 3 swings around the fulcrum 5 on the additional support 4; l 0 is the initial swing radius when the pendulum ball 3 swings around the initial fulcrum 6, and the initial fulcrum 6 is the connection point between the upper end of the pendulum rope 1 and the vibration control structure 2; θ 0 represents the angle between the connection line between the fulcrum 5 of the additional support 4 and the initial fulcrum 6 and the vertical plane (vertical plane 7).

[0096] In order to achieve the best vibration reduction effect, it should be noted in this implementation scheme that:

[0097] 1) Reasonably select the mass of the pendulum ball 3 to achieve a better vibration reduction effect;

[0098] 2) Reasonably select the length of the pendulum rope 1 so that the swing frequency of the simple pendulum is as close as possible to the natural frequency of the vibration control structure 2;

[0099] 3) Reasonably select the position of the additional support 4 so that the variable-stiffness nonlinear pendulum-type TMD device proposed in this embodiment achieves the optimal vibration absorption and reduction effect;

[0100] 4) Reasonably select the movement direction and swing plane of the pendulum ball to achieve the optimal energy consumption effect;

[0101] 5) Install the stiffness-adjustable nonlinear pendulum TMD device proposed in this embodiment at the position with the largest structural displacement response to achieve the best vibration reduction effect.

[0102] 2. Parameter setting method

[0103] Specifically, for the position selection of the additional support 4, this embodiment also proposes a parameter setting method for the stiffness-adjustable nonlinear pendulum TMD device. In the stiffness-adjustable nonlinear pendulum TMD device targeted by the method of this embodiment, the additional support 4 is set as a group, that is, the stiffness-adjustable nonlinear pendulum TMD device includes a pendulum rope 1 and an additional support 4. The upper end of the pendulum rope 1 is fixedly connected to the vibration control structure 2, and the lower end is connected with a pendulum ball 3. The additional support 4 is set as two, and the two additional supports 4 are symmetrically arranged with respect to the vertical plane passing through the connection point between the upper end of the pendulum rope 3 and the vibration control structure 2. The additional support 4 is provided with a fulcrum located in the swing plane of the pendulum ball 3 for cooperating with the pendulum rope. The additional support 4 is used to introduce nonlinear stiffness during the swinging process of the pendulum ball to change the center position and radius length when the pendulum ball swings. As Figure 4 shown, in this embodiment, an oscillator with a mass of m is used to simulate the mass of the vibration control structure 2, an elastic coefficient of k is used to simulate the stiffness of the vibration control structure 2, and a damping of c is used to simulate the damping of the vibration control structure 2. The mass, damping, and rotation angle of the pendulum ball are m p , c p and θ, l 0 is the length of the pendulum rope, and l 1 is the calculated length after the pendulum rope touches the support. The position of the support can be determined by the parameters δ = l 1 / l 0 and θ 0 . The additional supports are symmetrically installed in the movement plane of the pendulum. Specifically, the parameter setting method for the stiffness-adjustable nonlinear pendulum TMD device in this embodiment includes the following steps:

[0104] Step 1: Construct the motion model of the stiffness-adjustable nonlinear pendulum TMD device

[0105] The motion model of the stiffness-adjustable nonlinear pendulum TMD device is:

[0106]

[0107] where m represents the mass of the vibration control structure; S is the arc length of the pendulum ball's movement; represents the second-order derivative of S with respect to time; g is the acceleration due to gravity, g = 9.8 m / s 2 ; θ is the simple pendulum rotation angle of the pendulum ball, and:

[0108]

[0109] Among them, l 1 represents the radius when the pendulum bob swings around the fulcrum on the additional support; l 0 is the initial swing radius when the pendulum bob swings around the initial fulcrum, and the initial fulcrum is the connection point between the upper end of the pendulum rope and the vibration control structure; θ 0 represents the angle between the connection line between the fulcrum of the additional support and the initial fulcrum and the vertical plane.

[0110] Assume m p = 1.0 kg, l 0 = 9.8 m, θ 0 = 0.1 rad. Then the restoring force F r (θ) = mgsin(θ) of the system and the relationship with the single pendulum path S are as Figure 5 shown. The restoring force includes an initial branch and an extended branch, which are connected at the intersection point (0.98 m, 0.978 N). It can be seen from Figure 5 that as δ becomes smaller, the stiffness of the pendulum gradually increases. Figure 6 The relationship between the single pendulum frequency and the amplitude under different δ conditions is given. When the amplitude of the pendulum arc is less than S 0 = 0.98 m, the single pendulum frequencies with different amplitudes remain ω 0 = 1.0 rad / s. However, when the amplitude of the pendulum arc exceeds S 0 , the single pendulum frequency curve bends towards the high-frequency direction, indicating that the system has a hardening characteristic. At the same time, it can also be seen that the smaller δ is, the faster the single pendulum frequency increases.

[0111] The free vibration time history response of the single pendulum rotation angle θ is as Figure 7 shown. The time history response curve of the ordinary single pendulum is a sine curve; while the pendulum angle curve of the single pendulum with an additional support undergoes four turns within each motion cycle. Since the pendulum length shortens after the additional support contacts the pendulum rope, the stiffness of the single pendulum increases and the smaller δ leads to a smaller motion period of the single pendulum.

[0112] Step 2: Obtain the control model of the stiffness-adjustable nonlinear pendulum-type TMD device based on the constructed motion model

[0113] Apply the external harmonic excitation F d = Fcos(ωt) to the oscillator installed with PTMD-AS. The control equation of the system can be obtained from the Lagrange equation as follows:

[0114]

[0115]

[0116] Among them, mp represents the mass of the pendulum bob; c p represents the damping of the pendulum bob;

[0117] c represents the damping of the vibration control structure; k represents the stiffness of the vibration control structure; represents the derivative of S with respect to time t; X represents the vibration displacement; represents the first derivative of the vibration displacement with respect to time; represents the second derivative of the vibration displacement with respect to time; l represents the calculated length of the swing radius of the pendulum bob, and:

[0118]

[0119] Introduce the dimensionless parameters:

[0120]

[0121]

[0122] Rewrite the control equations using the dimensionless parameters as:

[0123] (1 + μ)x″ + 2ζx′ + x + μ(s″cosθ - s′ 2 γsinθ) = fcos(ατ)

[0124] s″ + 2ζ p s′ + β 2 sinθ + x″cosθ = 0

[0125] where x, Ω, and ζ are the dimensionless displacement, natural frequency, and damping ratio of the vibration control structure; γ is the ratio of l 0 to l, δ represents l 1 to l 0 ratio; ω p and ζ p are the design frequency and damping ratio of the stiffness - adjustable nonlinear pendulum - type TMD device, μ is the mass ratio, α and β are the excitation frequency ratio and the single - pendulum frequency ratio, f is the amplitude of the dimensionless excitation, and τ is the dimensionless time. The prime superscript on the variable represents the derivative with respect to τ.

[0126] Step 3: Solve for the position parameters of the additional support fulcrum based on the control model

[0127] Under the conditions of determining x, Ω, ζ, μ, ω p , ζ p , α, β, f, and τ, the method for solving the position parameters (δ, θ 0 ) is as follows:

[0128] 31) Define the objective function with the goal of minimizing the maximum response of the vibration control structure:

[0129] Minimize Fitness = max(H(δ, θ 0 ))

[0130] Wherein, H is the response amplitude vector of the vibration control structure obtained by the EIHB method under external excitations of different frequencies;

[0131] 32) Determine the position parameters (δ, θ 0 ) of the additional support fulcrum and the selection range

[0132] The method for determining the selection range of the position parameters (δ, θ 0 ) is as follows:

[0133] (1) Determine the parameters of the system (the mass ratio μ, the structural damping ratio ζ, and the excitation amplitude f can be reasonably selected according to the actual high-rise building parameters and the local encounterable loads. The frequency ratio β and the damping ratio ζ of the PTMD p can then be determined with reference to the empirical formulas of linear design theory. When considering the additional support, the frequency ratio β should be less than the linear design value to make full use of the stiffness hardening effect);

[0134] (2) Select the search range of the additional support position parameters (δ, θ 0 ) (The author used the Extended Incremental Harmonic Balance (EIHB) to quantitatively analyze the system response of the device, and determined the optimal value δ of the support position parameter δ by minimizing the maximum value of the amplitude-frequency response. opt To avoid response bifurcation and unstable vibration control performance, the minimum value δ min was determined. For example, under the conditions of the parameters μ = 0.02, ζ = 0.02, f = 0.005, β = 0.95, and ζ p = 0.08, the value of δ min is in the range of [0.48, 0.59]. Therefore, the search ranges of δ and θ 0 can be reasonably set with reference to the numerical simulation data to improve the calculation efficiency as much as possible).

[0135] 33) Use the gradient descent algorithm to search for the optimal position parameters of the additional support fulcrum. The method is as follows:

[0136] 331) Assign values to δ and θ 0 within the selection range;

[0137] 332) Use the EIHB method to calculate the amplitude vector H of the vibration control structure;

[0138] 333) Calculate the objective function value to obtain the fitness value Fitness;

[0139] 334) Determine whether the current fitness value is less than the best fitness value: if so, replace the best fitness value with the current fitness value; if not, keep the historical fitness value unchanged;

[0140] 335) Determine whether the current iteration number m is less than the set maximum iteration number: if so, update the values of δ and θ 0 and execute step 332), m = m + 1; if not, output the values of δ and θ corresponding to the best fitness value 0 to obtain the optimal position parameters of the additional support fulcrum.

[0141] 3. Semi - active control method

[0142] The semi - active control method of the stiffness - adjustable non - linear pendulum - type TMD device in this embodiment includes the following steps:

[0143] S1: Real - time collect the acceleration response and external load of the vibration - controlled structure through the sensor 9 to obtain the amplitude and frequency of the external excitation;

[0144] S2: Use the parameter - setting method of the stiffness - adjustable non - linear pendulum - type TMD device as described above in this embodiment to obtain the optimal position parameters of the additional support under the current external excitation conditions;

[0145] S3: Use the semi - active control system to adjust the additional support 4 to reach the position corresponding to the optimal position parameters.

[0146] Specifically, the semi - active control system is used to control the movement of the additional support within the swing plane of the pendulum ball, and can be realized in a variety of existing ways. For example, two mutually perpendicular linear motion mechanisms can be used to drive the additional support to move within the swing plane. Specifically, in this embodiment, the semi - active control system is set in one - to - one correspondence with the additional support to respectively control the position of the corresponding additional support. Specifically, as Figure 3 shown, the semi - active control system changes the position of the additional support 4 according to different working conditions, achieving better vibration control performance, so that the position of the additional support 4 can be changed according to different working conditions to achieve better vibration control performance. The semi - active control system includes the following four parts: ① sensor subsystem; ② data acquisition and transmission subsystem; ③ data processing and management subsystem; ④ structure vibration evaluation and control subsystem. The specific working steps are as follows: ① Each sensor of the sensor subsystem obtains signals of key parts; ② Convert the collected sensor signals into digital signals and store them in the local industrial computer, and at the same time transmit them to the data processing and management subsystem through the computer fiber - optic network; ③ The computer system completes the post - processing, archiving, display and storage of the data; ④ The structure vibration evaluation system analyzes, statistics, discriminates the threshold based on the data sent by the monitoring system and gives evaluation opinions and adjustment support information.

[0147] In this embodiment, the sensor 9 is installed on the vibration control structure 2. The monitoring objects of the sensor 9 are divided into two categories: ① Load monitoring: wind load, atmospheric temperature and humidity, and structural temperature; ② Structural response monitoring: acceleration, stress and strain. Since the PTMD is usually used to control the first mode with the largest horizontal vibration response at the top of the structure, an acceleration sensor is installed at the top layer or section of the structure. The microcontroller 10 is connected to the sensor 9 and the stepping motor 11 through wires. The sensor 9 can monitor the acceleration response and external load of the vibration control structure in real time. The microcontroller 10 receives the signals from the sensor 9 and analyzes them, inputs the environmental conditions, and calculates the optimal bearing parameters according to the parameter optimization program. Then, the stepping motor 11 moves the additional bearing to the optimal position according to the electrical signal instructions sent from the control center, and re-adjusts the stiffness of the PTMD. Therefore, this device can further adopt a semi-active control strategy, continuously adjust the stiffness and frequency of the damper by moving the position of the additional bearing, and since the stiffness is continuously adjustable, it can achieve an inhibitory effect on the vortex-induced resonance of different frequencies, thereby achieving the effect of suppressing the vibration of different modes. An intelligent control system is used for automatic data processing and operation, reducing the manual operation cost and improving the work efficiency.

[0148] 4. Sensitivity analysis and stability analysis

[0149] The parameter values of the above model refer to the following values for actual high-rise buildings and TMD devices: μ = 0.02, ζ = 0.02, the initial frequency ratio (β) and damping ratio (ζ p ) of the PTMD-AS are 0.95 and 0.08 respectively, and the external excitation amplitude f = 0.005.

[0150] 4.1 Sensitivity analysis

[0151] The influence of the bearing position parameters (δ, θ 0 ) and the excitation amplitude on the vibration response of the system will be discussed in detail in this section. The EIHB method is used to calculate the amplitude-frequency response of the system.

[0152] Figure 8 Shows the variation of the system response curves with different δ. There are two peaks on each response curve, corresponding to the resonances of the first and second order modes of the system respectively. From Figure 8 (a), it can be seen that as δ decreases, the left resonance peak of the curve gradually increases, the right resonance peak gradually decreases, and the stiffness of the pendulum increases simultaneously. Figure 8(b) shows the amplitude-frequency response of the simple pendulum. It can be found that when the response amplitude is less than 0.1 rad, the pendulum rope does not contact the additional support, and the response curves of the simple pendulum with the additional support basically coincide; when the response amplitude is greater than 0.1 rad, as δ decreases, the response curve bends towards the high-frequency direction on the right, revealing its hardening characteristic. It should be noted that when δ = 0.2, the maximum response amplitude decreases significantly, which means that an excessive increase in the stiffness of the simple pendulum restricts its swing amplitude instead, indicating that the additional support is not always beneficial for structural vibration control. Therefore, when applying the additional support in PTMD, its parameters need to be reasonably set.

[0153] Figure 9 For δ = 0.8 and different θ 0 are the system response curves. Figure 9 (a) shows the amplitude-frequency response of the oscillator. It can be found that the left resonance peak of the curve increases as θ 0 decreases, and at the same time the right resonance peak gradually decreases. The change trend of the response peak of the simple pendulum is the same as that of the oscillator, as shown in Figure 9 (b). In addition, compared with Figure 8 (b), θ 0 has less influence on the maximum response amplitude of the pendulum.

[0154] The results show that a smaller θ 0 or δ is beneficial for the simple pendulum to have greater stiffness, but for a smaller δ value (such as δ = 0.2), when the pendulum rope contacts the additional support, the response curve changes significantly.

[0155] By adjusting the support parameters, the two peaks of the response curve can be made almost equal, and the maximum response of the oscillator is minimized, as shown by the black solid line in Figure 10 (a). When δ = 0.85 and θ 0 = 0.1 rad, the vibration control performance is optimal under the condition of f = 0.005. Figure 10 Shows the variation of the response amplitude when the external excitation amplitudes are 0.004, 0.005, and 0.006 respectively. It can be seen that as the excitation amplitude increases, the response amplitude increases non-linearly. When f = 0.006, the left peak is 10.33% higher than the right peak, while when f = 0.004, the right peak is 15.83% higher than the left peak. The results show that the control effect of the PTMD-AS proposed in this embodiment is sensitive to the excitation amplitude, which is different from the linear TMD. This characteristic is one of the advantages of the non-linear TMD and can be utilized in the wind-resistant design of high-rise buildings, because it is well known that both the amplitude and frequency of the wind load increase with the increase of the incident wind speed.

[0156] 4.2 Stability analysis

[0157] As mentioned above, when the pendulum rope is combined with the additional support, the stiffness crossing phenomenon can be observed. When the degree of stiffness hardening is large, there may likely be unstable solutions in the system. Therefore, it is necessary to analyze the stability of the solutions.

[0158] The Floquet theory is adopted to Figure 8 analyze the stability of the numerical solutions in Figure 11 (a). As shown, the solid lines represent stable solutions, while the dashed lines represent unstable solutions. Bifurcation usually leads to a large sudden change in the amplitude of the system response, so bifurcation should be avoided as much as possible during the operation of a well-designed vibration damping device. At δ = 0.2, two different bifurcations can be observed: saddle-node bifurcation (SN) and Hopf bifurcation (HF). It is found that when δ = 0.2, unstable solutions can be observed, and when the excitation frequency ratio is in the range of [1.094, 1.116], multiple solutions appear in the oscillator response.

[0159] When α = 1.11, the displacement response of the oscillator converges to a stable periodic solution, as shown in Figure 12 (a). The responses obtained by the EIHB method and the Runge - Kutta method (R - K) are in good agreement, verifying the accuracy of the EIHB method. However, when the excitation frequency slightly changes to α = 1.1, the response converges to a strong modulation solution, as shown in Figure 12 (c). The corresponding phase diagrams are shown in Figure 12 (b) and (d), and the phase trajectories change from a single loop at α = 1.11 to multiple loops at α = 1.1. The results show that due to bifurcation, the oscillator response changes significantly from periodic motion to aperiodic motion.

[0160] Figure 13 The bifurcation diagram of the oscillator displacement response with respect to the excitation frequency is given. It can be seen that as the excitation frequency increases, the oscillator response suddenly changes from periodic to aperiodic at α = 1.062, and then suddenly changes back to periodic at α = 1.108. It can also be found that when bifurcation is induced, the response amplitude of the oscillator suddenly increases. This means that bifurcation is not a favorable phenomenon for vibration control structures and should be avoided in practical applications.

[0161] 5. Application of Wind - induced Vibration Control in High - rise Buildings

[0162] 5.1 General Situation

[0163] In this embodiment, a high - rise building is selected to further verify the structural vibration control performance of PTMD - AS under wind excitation. The high - rise building is 320 meters high, with a cross - section of 40×40 meters and an aspect ratio of 8, so it is relatively sensitive to wind excitation. The mass density (ρ 1 ) of the building is 200 kg / m 3 , and the first - order modal frequency (f 1) is 0.16 Hz, and the damping ratio (ζ 1 ) is 2%.

[0164] A wind tunnel test with a scale ratio of 1:800 was conducted at Tokyo Polytechnic University

[14] . The building model and roughness elements are arranged as Figure 14 shown. The urban terrain roughness with a wind speed profile exponent of 0.27 is adopted. Ten layers of pressure measurement points are arranged on the model. For the bottom two layers, 3 pressure measurement points are arranged on each surface. Starting from the 3rd layer, the number of pressure measurement points on each surface becomes 5. The sampling time for pressure measurement is 75 s, and the sampling frequency is 1000 Hz. The average wind speed at the top of the model is 10.5 m / s.

[0165] This building is assumed to be located in Chongqing, China. According to the Chinese code, the wind speeds v 10 at 10 m above the ground corresponding to the return periods of 10 years, 50 years, and 100 years are 17.89, 23.66, and 26.83 m / s respectively. Then the corresponding average wind speeds v H at the top of the building are 45.6, 60.3, and 68.4 m / s respectively. Therefore, in this paper, the wind speed range of 40 - 70 m / s is selected, the wind speed scale ratio is 3 / 20 - 21 / 80, and the time scale ratio is 1 / 210 - 1 / 120.

[0166] Since vortex-induced vibration basically only excites the first mode of the high-rise building structure in the cross-wind direction, the response of the first mode is studied. Using the experimental data, the modal force F l of the lift can be calculated by the following formula:

[0167]

[0168]

[0169] where the air density ρ is 1.22 Kg / m 3 ; v H is the average wind speed at the top of the building; C pi is the wind pressure coefficient at the i-th pressure measurement point; A i is the bearing area of the measurement point i; I and f j are the total number of measurement points and the wind load on the j-th layer respectively; H j is the height of the measurement points on the j-th layer; is the first vibration mode, which can be simplified to z / H, where z is the height. The corresponding modal mass, stiffness, and damping can be expressed as k = (2πf 1 ) 2 m, c = 4πf 1 mξ 1 .

[0170] The lift coefficient can be defined as:

[0171]

[0172] where A is the area of the side of the structure, and A = H·B.

[0173] The time series of the lift coefficient C l is as shown in Figure 15 (a), and the power spectral density is as shown in Figure 15 (b). Obviously, the frequency components are distributed in a relatively wide range, and the peak is located at 0.12, which is the same as the Strouhal number S t of the square-section cylinder.

[0174] 5.2 Research on the Vibration Damping Effect under Wind Excitation

[0175] To test the performance of PTMD-AS, three dampers with the same mass and damping (μ = 0.03, ζ P = 0.10) were considered. The optimal design parameters of the three were obtained by the gradient optimization algorithm as follows: (1) the traditional PTMD (β = 0.995); (2) PTMD-AS (β = 0.95, δ = 0.74, and θ 0 = 0.18 rad); (3) PTMD-AS (β = 0.9, δ = 0.62, and θ 0 = 0.15 rad). Figure 16 is the standard deviation of the structural displacement response in the range of [40, 70] m / s. It can be seen that the structural responses of the two PTMD-AS installations are almost the same as those of the traditional PTMD. Compared with the displacement of the uncontrolled structure, about 50% of the displacement response is attenuated.

[0176] To further test the robustness of PTMD-AS, the vibration suppression effect under the condition of structural detuning was studied. Figure 17 shows the standard deviation of the structural displacement when the structural frequency is detuned by ±5% and ±10%. By comparing Figure 17 (a) the response curves in the range where the wind speed is lower than 60 m / s (the design wind speed with a 50-year return period), it can be found that the structural response of the PTMD installation is the largest, and the use of PTMD-AS can reduce the response. When the structure is detuned by -5%, under the wind load of v H = 45 m / s, the standard deviations corresponding to β = 0.95 and β = 0.95 are reduced by 5.2% and 8.8% respectively; when the detuning is +5%, the vibration damping effects of the three are similar. Figure 17 (b) shows that the advantage of PTMD-AS is more obvious in the case of -10% detuning. For example, when v HWhen the velocity is 45 m / s, the structural responses corresponding to PTMD-AS with β = 0.95 and β = 0.95 are further reduced by 7.4% and 12% respectively. However, when the detuning is +10%, the control effect of PTMD-AS is slightly weaker than that of the traditional PTMD. The results show that PTMD-AS has better robustness than the traditional PTMD under the condition of structural detuning.

[0177] 6. Conclusions

[0178] In this embodiment, a two-degree-of-freedom model is established to evaluate the vibration control performance of the proposed PTMD-AS, and the control equation is derived by Lagrange's equation. The frequency response curve of the system is calculated by the EIHB method, and the time history response of the system is calculated by the R-K method. Through a series of numerical simulations, the following conclusions are obtained:

[0179] (1) First, four cases of no support and additional support position parameters δ = 0.8, 0.5, and 0.2 are selected to explore the influence of stiffness crossover on the dynamic characteristics of the pendulum. When the pendulum rope contacts the additional support, the stiffness hardening phenomenon of the pendulum appears, and the smaller the δ, the greater the degree of stiffness hardening, and the faster the frequency of the pendulum increases with the increase of the amplitude.

[0180] (2) Then, the sensitivity analysis shows that as δ or θ 0 decreases, the stiffness of the pendulum increases, the first-order resonance peak of the response curve increases, and the second-order resonance peak decreases simultaneously. The stability analysis shows that multiple solutions and non-linear solutions appear in the single pendulum response corresponding to δ = 0.2. In addition, the numerical results obtained by the EIHB method and the R-K method are in good agreement.

[0181] (3) Finally, under the action of wind excitation obtained from the wind tunnel experiment, the vibration control performances of PTMD-AS and the traditional PTMD for high-rise buildings are compared. By comparing the standard deviations of the structural displacements, it is found that the vibration reduction effects of PTMD-AS and the traditional PTMD are almost the same. Further studying the structural detuning situation, the results show that PTMD-AS has better robustness.

[0182] The above-described embodiments are only preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A non-linear pendulum type TMD device with adjustable stiffness, comprising a pendulum rope, the upper end of the pendulum rope is fixedly connected to a vibration control structure, and the lower end is connected with a pendulum ball. Characterized in that: It further includes an additional support, on which there is a fulcrum located in the swinging plane of the pendulum ball for cooperating with the pendulum rope, and the additional support is used to introduce non-linear stiffness during the swinging process of the pendulum ball to change the central position and radius length when the pendulum ball swings; The additional supports are set as at least one group, each group includes two additional supports, and the two additional supports belonging to the same group are symmetrically arranged with respect to the vertical plane passing through the connection point between the upper end of the pendulum rope and the vibration control structure; Let the connection point between the upper end of the pendulum rope and the vibration control structure be the initial fulcrum, and the vertical plane passing through the initial fulcrum be the plumb plane; When there are at least two additional supports on the same side of the plumb plane, the vertical distances d between any two additional supports and the initial fulcrum are not equal. All the additional supports on the same side of the plumb plane are sorted in ascending order of the distance d as the 1st additional support, the 2nd additional support,..., the nth additional support; and among any the i-th additional support and the (i + 1)-th additional support, the inclination angle of the line connecting the fulcrum of the i-th additional support and the initial fulcrum with respect to the plumb plane is less than the inclination angle of the line connecting the fulcrum of the (i + 1)-th additional support and the initial fulcrum with respect to the plumb plane, where i = 1, 2,..., n - 1; n ≥ 2; Let the connection point between the upper end of the pendulum rope and the vibration control structure be the initial fulcrum, and the initial swinging radius when the pendulum ball swings around the initial fulcrum is: where l 0 is the initial swing radius when the pendulum ball swings around the initial fulcrum; g is the acceleration due to gravity; f is the first-order frequency of the vibration control structure.

2. The non-linear pendulum type TMD device with adjustable stiffness according to claim 1, Characterized in that: There is viscous damping in the swinging plane of the pendulum ball, and the viscous damping is connected to the pendulum ball and can move along the swinging trajectory of the pendulum ball.

3. The non-linear pendulum type TMD device with adjustable stiffness according to claim 1 or 2, Characterized in that: It further includes a semi-active control system for adjusting the position of the additional support.

4. A parameter setting method for a non-linear pendulum type TMD device with adjustable stiffness, Characterized in that: The non-linear pendulum type TMD device with adjustable stiffness includes a pendulum rope and additional supports, the upper end of the pendulum rope is fixedly connected to a vibration control structure, the lower end is connected with a pendulum ball, and the additional supports are set as two, and the two additional supports are symmetrically arranged with respect to the vertical plane passing through the connection point between the upper end of the pendulum rope and the vibration control structure; there is a fulcrum located in the swinging plane of the pendulum ball on the additional support for cooperating with the pendulum rope, and the additional support is used to introduce non-linear stiffness during the swinging process of the pendulum ball to change the central position and radius length when the pendulum ball swings; the method includes the following steps: Step 1: Construct a motion model of the non-linear pendulum type TMD device with adjustable stiffness; Step 2: Obtain a control model of the non-linear pendulum type TMD device with adjustable stiffness based on the constructed motion model; Step 3: Solve the position parameters of the additional bearing fulcrum based on the control model; In Step 1, let the connection point between the upper end of the pendulum rope and the vibration control structure be the initial fulcrum, and the motion model of the stiffness-adjustable nonlinear pendulum type TMD device is: Wherein, m represents the mass of the vibration control structure; S is the arc length of the pendulum ball's motion; represents the second derivative of S with respect to time; g is the acceleration due to gravity; θ is the simple pendulum rotation angle of the pendulum ball, and: wherein, l 1 represents the radius when the pendulum bob swings around the fulcrum on the additional support; l 0 is the initial swing radius when the pendulum bob swings around the initial fulcrum, and the initial fulcrum is the connection point between the upper end of the pendulum rope and the vibration control structure; θ 0 represents the angle between the connecting line between the fulcrum of the additional support and the initial fulcrum and the vertical plane; In Step 2, the control model of the stiffness-adjustable nonlinear pendulum type TMD device is: Apply the external harmonic excitation F d = Fcos(ωt) to the oscillator of the non-linear pendulum type TMD device PTMD-AS with adjustable installation stiffness. The control equation of the system can be obtained from the Lagrange equation as follows: where m p represents the mass of the pendulum bob; c p represents the damping of the pendulum bob; F represents the amplitude of the excitation; ω represents the excitation frequency; t represents time; c represents the damping of the vibration control structure; k represents the stiffness of the vibration control structure; g is the acceleration due to gravity; represents the derivative of S with respect to time t; X represents the vibration displacement; represents the first derivative of the vibration displacement with respect to time; represents the second derivative of the vibration displacement with respect to time; l represents the calculated length of the pendulum bob swing radius, and: Introduce dimensionless parameters: Rewrite the control equation using dimensionless parameters as: (1 + μ)x″ + 2ζx′ + x + μ(s″cosθ - s′ 2 γsinθ) = fcos(ατ) s″ + 2ζ p s′ + β 2 sinθ + x″cosθ = 0 where x, Ω, and ζ are the dimensionless displacement, natural frequency, and damping ratio of the vibration control structure; γ is the ratio of l 0 to l, and δ represents l 1 to l 0 ratio; ω p and ζ p are the design frequency and damping ratio of the stiffness-adjustable nonlinear pendulum-type TMD device, μ is the mass ratio, α and β are the excitation frequency ratio and pendulum frequency ratio, f is the amplitude of the dimensionless excitation, and τ is the dimensionless time; In step 3, under the conditions of determining x, Ω, ζ, μ, ω p , ζ p , α, β, f and τ, the method for solving the position parameters (δ, θ 0 ) of the additional support fulcrum is as follows: 31) Define the objective function with the goal of minimizing the maximum response of the vibration control structure: Minimize Fitness=max(H(δ,θ 0 )) where H is the response amplitude vector of the vibration control structure under external excitations of different frequencies obtained by the EIHB method; 32) Determine the selection range of the position parameters (δ, θ) of the additional support fulcrum 0 ) 33) Use the gradient descent algorithm to search for the optimal position parameters of the additional bearing fulcrum, and the method is: 331) Assign values to δ and θ within the selected range 0 ; 332) Calculate the amplitude vector H of the vibration control structure using the EIHB method; 333) Calculate the objective function value to obtain the fitness value Fitness; 334) Determine whether the current fitness value is less than the best fitness value: if so, replace the best fitness value with the current fitness value; if not, keep the historical fitness value unchanged; 335) Determine whether the current iteration number m is less than the set maximum iteration number: If so, update the values of δ and θ, execute step 332), and m = m + 1; if not, output the values of δ and θ corresponding to the best fitness value, and obtain the optimal position parameters of the additional bearing fulcrum. 0 0 ​ 5. A semi-active control method for a stiffness-adjustable nonlinear pendulum type TMD device, characterized in that: It includes the following steps: S1: Real-time collect the acceleration response and external load of the vibration control structure through sensors to obtain the amplitude and frequency of the external excitation; S2: Use the parameter setting method of the stiffness-adjustable nonlinear pendulum type TMD device as described in claim 4 to obtain the optimal position parameters of the additional bearing under the current external excitation conditions; S3: Use the semi-active control system to adjust the additional bearing to reach the position corresponding to the optimal position parameters.

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