Simple harmonic mass damper considering multi-order modal influence of high-rise building and method

Abstract

The invention belongs to the technical field of high-rise building vibration reduction (shock absorption), and particularly relates to a simple harmonic mass damper considering the multi-order modal influence of a high-rise building and a method. The simple harmonic mass damper considering the multi-order modal influence of the high-rise building comprises a mass block, a viscous damper, a rigidity adjusting device and a rolling pendulum. The method comprises the steps of measuring N-order modal parameters of a structure, distributing mass ratios according to formation participation coefficients, determining a damping ratio and natural vibration frequency, establishing a motion equation of the structure and MTMD, calculating a frequency domain transfer coefficient of the structure, and calculating an acceleration / interlayer displacement mean square value. And judging whether the vibration reduction effect meets the standard or not, and designing a rigidity adjusting device according to creep deformation of the steel balls. A passive control mode is adopted, the problems that energy input is needed and the follow-up maintenance cost is high are solved, and meanwhile the problem that the natural vibration frequency of the TMD is changed due to creep deformation is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of vibration reduction (shock absorption) of high-rise buildings, and particularly relates to a harmonic mass damper and method considering the influence of multi-order modes of high-rise buildings. Background Art

[0002] With the continuous development of social economy, the global urbanization rate exceeds 56%. The increase in building height leads to an extension of the natural vibration period and a significant increase in the sensitivity to wind loads. For example, the annual wind-induced vibration displacement of the Shanghai Tower reaches 0.8 m, and wind-induced vibration has become a core design bottleneck. Strong winds may cause along-wind vibration, across-wind vortex-induced resonance, and torsional coupling vibration, resulting in fatigue damage or even collapse of components. At the same time, when the acceleration at the top of the building exceeds 0.15 m / s 2 , people will feel dizzy. Traditional wind resistance methods increase the stiffness by increasing the cross-section of shear walls or columns, resulting in a 20% - 30% increase in construction costs, occupying usable floor area, and affecting the flexibility of building layout.

[0003] The TMD adjusts the vibration frequency of the damper system itself to be near the main frequency of the structure vibration. Through the interaction between the TMD and the main structure, the energy can be transferred from the main structure to the tuned mass damper system, achieving the purpose of reducing the vibration of the main structure. Currently, the more widely used ones are: 1. Pendulum TMD, which uses the swing of the pendulum to dissipate energy. It has a low construction cost. The mass block can be made of concrete, steel, or existing equipment can be modified. The mass block and the damper can be prefabricated and hoisted as a whole, shortening the construction period, and at the same time, the maintenance cost is extremely low. However, the swing amplitude is limited, and high-precision bearings are required, which are prone to wear and occupy a large building space. 2. Sliding mass block TMD, where the mass block slides along the guide rail, relying on hydraulic or viscous damping to achieve better vibration reduction effect. This type of TMD does not require the vertical suspension space of the pendulum TMD and can be horizontally arranged on the equipment floor. By adjusting the inclination angle of the guide rail or adding additional counterweights, the main structure frequency can be quickly matched, and the vibration in both the X and Y directions can be controlled simultaneously. However, the frictional resistance is large, and the response speed is slow. 3. Spring-mass system, which tunes the frequency through the spring stiffness, only requires a spring, a mass block, and a damper, with an extremely low failure rate and simple and convenient maintenance. By adjusting the spring stiffness or the weight of the mass block, different vibration control requirements can be met. However, the spring is prone to aging, and the long-term performance is unstable. 4. Active mass damper (AMD), where sensors monitor the vibration signal in real time, and the drive motor controls the movement of the mass block to generate a reverse force. High-precision control can be carried out to adapt to multi-modal coupling vibration. By adjusting the acting force in real time, the sensitivity of the passive TMD to frequency detuning can be overcome. However, the system cost is about 3 - 5 times that of the passive TMD. At the same time, continuous power supply is required, the hydraulic system is prone to oil leakage, and the maintenance complexity is high. Improper algorithm design may lead to overshoot or system oscillation. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present invention discloses a harmonic mass damper and method considering the influence of multi-order modes of high-rise buildings, and effectively controls the wind vibration of high-rise structures and reduces the seismic influence by inventing a rolling pendulum type TMD that can serve for a long time. Specifically, the present invention aims to achieve the following several purposes: to solve the problems commonly existing in traditional dampers, such as occupying a large amount of building space, having no damping effect when the wind load is small, and the installation being cumbersome due to the natural frequency being related to the mass, adopting a passive control method to avoid the problems of requiring energy input and high subsequent maintenance costs, and at the same time solving the problem of the change of the natural frequency of the TMD caused by creep.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A harmonic mass damper considering the influence of multi-order modes of high-rise buildings includes a mass block, a stiffness adjustment device, a rolling pendulum, and a viscous damper. The mass block is located above the roof of the high-rise building. A rolling pendulum is connected between the bottom end of the mass block and the upper end of the roof. A stiffness adjustment device and a viscous damper are also connected between the bottom end of the mass block where the outer circumference of the rolling pendulum is located and the roof.

[0007] Preferably, the upper seat plate of the rolling pendulum is fixedly connected to the bottom end of the mass block, and the lower seat plate of the rolling pendulum is fixedly connected to the roof. Four grooves are arranged in a cross shape on the opposite surfaces of the upper and lower seat plates. Ball bearings are rollingly connected between the upper and lower opposite grooves to form a sub-TMD mechanism.

[0008] Preferably, the stiffness adjustment device includes three steel rods arranged coaxially in sequence. Stiffness adjustment springs are sleeved on the steel rods located on both sides respectively. Steel plates are detachably and fixedly connected to the outer ends of the steel rods on both sides. Supports are provided at the bottom ends of the two steel plates and at the bottom center position of the middle steel rod. The supports are fixed on the roof surface. Sleeve slides are slidably sleeved on the inner ends of the steel rods on both sides respectively. A connecting plate is connected between the tops of the two sleeve slides. A T-shaped slider is connected to the bottom end of the connecting plate. A T-shaped chute slidably matched with the T-shaped slider is formed on the middle steel rod. The top end of the connecting plate is connected to the bottom end of the mass block through a connecting member.

[0009] Preferably, the connecting member includes connecting parts rotatably connected to the bottom end of the mass block and the top end of the connecting plate respectively, and a transmission rod connected between the two connecting parts.

[0010] Preferably, both ends of the viscous damper are ball-jointly connected to the bottom end of the mass block and the roof surface respectively.

[0011] A design method of a harmonic mass damper considering the influence of multi-order modes of high-rise buildings includes:

[0012] (1) Before designing the rolling pendulum TMD, the modal parameters of the target building are obtained through modal testing. The time history curve of the building vibration acceleration at the selected points is measured on the roof of the target building. By synthesizing the Fourier transform amplitude spectra of each point, the first three natural frequencies for controlling the target building are obtained: the translational frequency in the short-axis direction; the torsional frequency; the translational frequency in the long-axis direction;

[0013] (2) When designing the rolling pendulum TMD, the motion equation of the rolling pendulum TMD under free vibration is as follows:

[0014]

[0015] In Equation (1), M is the mass of the TMD, c is the damping provided by the viscous damper, k is the stiffness provided by the stiffness adjustment device, R is the curvature radius of the seat plate groove, and u is the horizontal displacement of the TMD system;

[0016] (3) According to the first three natural frequencies obtained in step (1), the sub-TMD mechanisms of the multiple tuned mass dampers (MTMD) are designed respectively. Determine the total mass of the rolling pendulum TMD, and proportionally distribute the mass to the sub-TMD mechanisms according to the modal participation factor; design the corresponding sub-TMD mechanisms for each control frequency respectively; after determining the mass ratio, further determine the damping ratio of each sub-TMD mechanism, and calculate according to The damping coefficient is calculated according to c = 2ξωm, and the type of viscous damper required is determined according to the damping ratio; the formula for calculating the natural frequency of the rolling pendulum TMD is: When k in the formula is 0, that is, the stiffness adjustment device does not place a spring to provide additional stiffness, the formula for calculating the natural frequency of the TMD becomes: At this time, the natural frequency is only related to R. Substitute the natural frequencies of each mode into this formula to obtain the corresponding curvature radius;

[0017] (4) Evaluate the vibration reduction effect of the tuned mass damper considering the influence of multiple modes of high-rise buildings. The motion equation under wind vibration is:

[0018]

[0019] In Equations (2) and (3), are the mass, damping, and stiffness matrices of the MTMD respectively, is the displacement vector of the MTMD relative to the ground, P T is the position matrix of the MTMD, F is the pulsating wind force vector, O is the m-dimensional column vector, and f represents the vibration force vector of the MTMD system; Using the modal superposition method, the structural displacement is expressed by the modal vector and the generalized displacement, and the structural dynamic equation becomes:

[0020]

[0021] In equations (4) and (5):

[0022] C n = diag[2ξ j ω j (j = 1, 2, 3..., n)

[0023]

[0024] where ξ j , ω j are respectively the damping ratio and frequency of the j-th mode shape, n is the number of mode shapes considered for the structure, ξ k , ω k are respectively the damping ratio and frequency of the k-th sub-TMD mechanism. Considering the multimodal coupling of the structure, the vibration force vector of the MTMD system is:

[0025]

[0026] Substitute equation (6) into equation (4) and combine it with equation (5) into matrix form:

[0027]

[0028] In equation (7):

[0029]

[0030] where E1 is an n×n identity matrix and E2 is an m×m identity matrix;

[0031] Let its solution be substituted into the above equation, and we get:

[0032]

[0033] where are respectively the frequency-domain transfer function of the main structure and the frequency-domain transfer function of the TMD relative to the main structure, and I1 is an n-dimensional column vector; Solving equation (7) gives the frequency-domain transfer function:

[0034]

[0035] The coefficients A1 and A2 in equation (9) are solved as follows:

[0036] A1 = a 11 - a 12 (a 22 2 + b2 2 ) -1 a 22 a 21 (9 - a)

[0037] A2 = b1 + a 12 (a 22 2 + b2 2 ) -1 b2a 21 (9 - b)

[0038] Where:

[0039]

[0040] After obtaining the frequency - domain transfer function, calculate the acceleration of the k - th degree of freedom of the structure and the mean square value of the inter - story displacement response:

[0041]

[0042] Where, is the power spectral matrix of the acting force, and φ k,j is the displacement component of the k - th degree of freedom of the j - th vibration mode vector of the structure;

[0043] Substitute Equation (9) into Equation (10) to obtain the mean square value of the acceleration response of the k - th degree of freedom of the MTMD under wind load excitation. After obtaining the mean square value of the acceleration response, convert it to the peak acceleration, and its formula is:

[0044]

[0045] In Equation (11), g is the peak factor, take g = 3, calculate the peak acceleration response of the high - rise structure with the MTMD system and compare it with the limit value required by the code, that is, whether a peak ≤0.15m / s 2 , if the requirement is met, the designed TMD parameters can be applied in practice, and the design is completed; if the requirement is not met, the parameters of the TMD need to be adjusted, and the motion equation is re - established and verified according to the above steps until the vibration reduction effect meets the requirements.

[0046] Preferably, in the case of an earthquake, set the motion equation of the MTMD under earthquake excitation as:

[0047]

[0048] In Equations (12) and (13), I1 and I2 are n - dimensional and m - dimensional column vectors respectively;

[0049] Derive the frequency - domain transfer function of the building structure under coupled control according to the derivation process of Equations (12) and (13) The inter - story displacement transfer function of the k - th degree of freedom of the building structure is:

[0050]

[0051] Similarly, according to the random vibration theory, the mean square value of the inter-story displacement response of the k-th degree of freedom of the building structure under seismic excitation is obtained:

[0052]

[0053] In Equation (15), is the power spectral density of seismic acceleration;

[0054] After obtaining the mean square value of the inter-story displacement response, it is converted to a peak value to evaluate the vibration reduction effect, and the formula is:

[0055]

[0056] In Equation (16), g is taken as 3, and the inter-story displacement angle is calculated using the peak inter-story displacement to evaluate whether the vibration reduction effect meets the specification requirements; if the requirements are met, the designed TMD parameters can be applied in practice and the design is completed; if the requirements are not met, the parameters of the TMD need to be adjusted, the motion equation is re-established, and verified according to the above steps until the vibration reduction effect meets the requirements.

[0057] Preferably, after considering the action of the stiffness adjustment device, the calculation formula for the natural vibration frequency of the system becomes: where R' is the equivalent curvature radius after creep, M is the overlying mass, and k is the additional stiffness of the stiffness adjustment device. Let the adjusted natural vibration frequency f' be equal to the designed frequency to eliminate the influence of steel ball creep on the dynamic characteristics; in actual use, regularly measure the natural vibration frequency of the rolling pendulum, use the acceleration sensor to measure the data and draw the acceleration time history curve of the rolling pendulum, and transform it to the frequency domain through Fourier transform to obtain the natural vibration frequency of the rolling pendulum and compare it with the designed frequency. When the error between the two reaches 15%, the vibration reduction effect of the rolling pendulum decreases significantly. At this time, calculate the k value according to and replace the spring to improve the vibration reduction effect of the TMD.

[0058] The beneficial effects of the present invention, a harmonic mass damper and method considering the influence of multi-order modes of high-rise buildings, are as follows:

[0059] Compared with the sliding friction TMD system, the present invention replaces sliding friction with rolling friction, solves the problem that the front-swing pendulum damper before the sliding threshold has no vibration damping effect, and can still play a vibration damping role under small vibrations. Compared with the pendulum TMD, the design of the present invention is more concentrated, saving installation space and being more flexible in layout. Compared with the common TMD system of a mass damper plus a spring, the present invention separates frequency design and mass control, and can consider the two physical quantities separately, facilitating the design of the TMD. By changing the curvature radius of the track, the natural vibration frequency of the system can be controlled to achieve multi-order vibration control. At the same time, the system mass can be increased as much as possible to reduce the number of TMD arrangements and save space. Compared with the TMD system of the same type applying the rolling pendulum principle, the present invention further considers the influence of creep on the dynamic characteristics of the TMD system under long-term loads, adds a stiffness adjustment device, and eliminates the influence of creep by adjusting the system stiffness later, and also reduces the subsequent maintenance difficulty and cost. The present invention can change the system damping by adjusting the viscous damper to achieve different types and degrees of vibration damping requirements for wind vibration, earthquake, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a front view structural schematic diagram of an embodiment of the present invention.

[0061] Figure 2 It is a bottom view of the upper seat plate of the rolling pendulum.

[0062] Figure 3 It is a sectional view of the upper or lower seat plate in the A-A direction.

[0063] Figure 4 It is a bottom view layout diagram of the positional relationship among the mass block, the stiffness adjustment device, the rolling pendulum, and the viscous damper in an embodiment.

[0064] Figure 5 It is a front view structural schematic diagram of the stiffness adjustment device.

[0065] Figure 6 It is a partial structural schematic diagram of the stiffness adjustment device.

[0066] Figure 7 It is a sectional view structural schematic diagram of the present invention in the B-B direction.

[0067] Figure 8 It is a design flow chart of the present invention.

[0068] Figure 9 It is the time history curve of the building vibration acceleration at four points obtained by actual measurement on the roof of a certain building.

[0069] Figure 10 It is the peak spectrum of each measuring point.

[0070] Figure 11Schematic diagram for the selection of measuring points on the building roof.

[0071] In the figure: 1. Mass block; 2. Rolling pendulum; 21. Upper seat plate; 22. Groove; 23. Connecting hole; 3. Viscous damper; 4. Stiffness adjustment device; 41. Pier; 42. Steel plate; 43. Spring; 44. Steel rod; 45. Connector; 46. T-shaped slider; 47. T-shaped chute; 48. Sleeve; 49. Connecting plate; 5. Roof. Detailed implementation mode

[0072] The following description is only for the preferred embodiments of the present invention and is not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0073] The following embodiments can be understood as separately expressing a part of the local structure or method of the present invention, or can also be understood as the combination of embodiments to explain the connotation of the structure or method of a larger scope of the present invention.

[0074] Embodiment 1

[0075] A harmonic mass damper considering the influence of multi-order modes of high-rise buildings, as Figures 1-7 shown, includes a mass block 1, a stiffness adjustment device 4, a rolling pendulum 2, and a viscous damper 3. The mass block 1 is located above the roof 5 of the high-rise building. A rolling pendulum 2 is connected between the bottom end of the mass block 1 and the upper end of the roof 5. A stiffness adjustment device 4 and a viscous damper 3 are also connected between the bottom end of the mass block 1 where the outer circumference of the rolling pendulum 2 is located and the roof 5.

[0076] In this embodiment, the rolling pendulum, i.e., TMD, uses the rolling of the ball in the groove to dissipate energy, changing the common sliding friction energy dissipation to rolling friction energy dissipation, solving the problem that there is a threshold for sliding friction, and can also play a vibration reduction role under smaller vibrations. The damping force of the rolling pendulum TMD is provided by the viscous damper 3, and its stiffness adjustment is provided by the stiffness adjustment device, thus constituting a harmonic mass damper considering the influence of multi-order modes of high-rise buildings.

[0077] Embodiment 2

[0078] Based on Embodiment 1, this embodiment discloses:

[0079] As Figures 1-4 shown, the upper seat plate 21 of the rolling pendulum 2 is fixedly connected to the bottom end of the mass block 1, the lower seat plate of the rolling pendulum 2 is fixedly connected to the roof 5, and 4 grooves 22 are arranged in a cross shape on the opposite surfaces of the upper and lower seat plates. A ball is rollingly connected between the upper and lower opposite grooves 22 to form a sub-TMD mechanism, that is, each rolling pendulum 2 includes 4 sub-TMD structures.

[0080] In this embodiment, the upper and lower seat plates are made of 40CrMo, with a surface hardness of HRC62 or above and a quenching penetration depth of 5 mm. The balls are made of GCr15 bearing steel, with a surface hardness of not less than HRC62 and a quenching penetration depth of not less than 5 mm. As Figure 3 shown, it is a sectional view of the upper or lower seat plate in the A-A direction. The curvature of the groove is divided into two parts, the inner curvature radius R and the edge curvature radius r. The natural vibration frequency of the rolling pendulum TMD is related to R, and the value of r should be equivalent to the radius of the ball to ensure that the ball does not break away from the seat plate during movement. As Figure 4 shown, in one embodiment, it is a layout plan of the positional relationship among the mass block 1, the stiffness adjustment device 4, the rolling pendulum 2, and the viscous damper 3 from a bottom view. Of course, it can also be designed in other layout forms according to needs. It should be noted that the number of rolling pendulums arranged should be determined by the weight of the mass block, and the stress borne by each ball should not exceed the yield stress of the material.

[0081] Embodiment 3

[0082] As Figures 5-7 shown, the stiffness adjustment device includes three steel rods 44 arranged coaxially in sequence. Stiffness adjustment springs 43 are sleeved on the steel rods 44 on both sides respectively. Steel plates 42 are detachably and fixedly connected to the outer ends of the steel rods 44 on both sides. Supports 41 are provided at the bottom ends of the two steel plates 42 and at the bottom center position of the middle steel rod 44, and the supports 41 are fixed on the surface of the roof 5; Sliding sleeves 48 are respectively slidably sleeved on the inner ends of the steel rods 44 on both sides. A connecting plate 49 is connected between the tops of the two sliding sleeves 48. A T-shaped slider 46 is connected to the bottom end of the connecting plate 49. A T-shaped chute 47 that slidably cooperates with the T-shaped slider 46 is provided on the middle steel rod 44. The top end of the connecting plate 49 is connected to the bottom end of the mass block 1 through a connecting member 45.

[0083] As Figure 5 shown, the connecting member 45 includes connecting parts that are respectively rotatably connected to the bottom end of the mass block 1 and the top end of the connecting plate 49, and a transmission rod connected between the two connecting parts.

[0084] As Figure 1 shown, the two ends of the viscous damper 3 are respectively ball-jointed to the bottom end of the mass block 1 and the surface of the roof.

[0085] In this embodiment, the viscous damper 3 is ball-jointed with a support, and the support is welded to both the roof and the mass block. A connecting member 45 is provided between the stiffness adjustment device 4 and the mass block 1 to ensure that the stiffness adjustment device 4 and the rolling pendulum 2 are connected to the mass block 1 at the same height. The steel bars on both sides are bolted to the end steel plates to ensure that springs with different stiffnesses can be disassembled and replaced during the subsequent maintenance of the TMD. Among them, a T-shaped chute 47 is provided on the middle steel bar to cooperate with the T-shaped slider 46 to ensure the stable sliding track of the sliding sleeve. When the TMD vibrates, the mass block 1 drives the connecting member and the sliding sleeve to move together, causing the sliding sleeve to compress the springs in the corresponding directions, providing an additional restoring force for the TMD system. At the same time, the stroke of the T-shaped slider 46 can be set such that its maximum sliding distance is equal to the maximum horizontal displacement of the rolling pendulum.

[0086] Embodiment 4

[0087] Based on the above embodiments, this embodiment discloses:

[0088] A design method for a harmonic mass damper considering the influence of multi-order modes of high-rise buildings, as Figure 8 shown, includes:

[0089] (1) Before designing the rolling pendulum, the modal parameters of the target building are obtained through modal testing. The time history curve of the building vibration acceleration at the selected points is measured on the roof of the target building. By synthesizing the Fourier transform amplitude spectra of each point, the first three frequencies for controlling the target building are obtained: the translational frequency in the short-axis direction; the torsional frequency; the translational frequency in the long-axis direction;

[0090] The main objective of the present invention is to control wind vibration. On the basis of maintaining the comfort during daily use, the structural response acceleration and inter-story displacement under extreme wind disasters and earthquake actions are reduced. Before designing the rolling pendulum, the modal parameters of the target building are obtained through modal testing. Figure 9 For a certain building roof, the time history curve of the building vibration acceleration is measured based on the selected 4 points (the measurement points are arranged as Figure 11 shown, where measurement points 1 and 2 measure the vibration in the short-axis direction, and measurement points 3 and 4 measure the vibration in the long-axis direction). As Figure 10 shown, by synthesizing the Fourier transform amplitude spectra of each point, the first three frequencies for controlling the target building are obtained as 0.342 Hz, 0.488 Hz, and 0.513 Hz, which are the translational frequency in the short-axis direction; the torsional frequency; the translational frequency in the long-axis direction, respectively.

[0091] (2) After determining the target frequency of building vibration control, the design of the rolling pendulum TMD is carried out. According to Figure 1 the influence of each part of the TMD on the dynamic properties and the relationship between the groove shape and the horizontal displacement of the TMD, the motion equation of the rolling pendulum TMD system under free vibration is listed: that is:

[0092]

[0093] In Equation (1), M is the mass of the TMD, c is the damping provided by the viscous damper, k is the stiffness provided by the stiffness adjustment device, R is the radius of curvature of the seat plate groove, and u is the horizontal displacement of the TMD system;

[0094] (3) From the overall motion equation (1) and the design process Figure 8 It can be seen that there are three main design parameters, namely the mass ratio, the natural vibration frequency of the system, and the system damping; according to the first three natural frequencies obtained in step (1), the sub-TMD mechanisms of each order of the multiple tuned mass damper (MTMD) are designed respectively, the total mass of the rolling pendulum TMD is determined, and the mass is proportionally distributed to the sub-TMD mechanisms according to the participation coefficient of the vibration mode; the corresponding sub-TMD mechanisms are designed for each order of control frequency. The mass ratio, that is, the ratio of the total mass of the TMD to the structural mass, has a great influence on the vibration reduction effect of the MTMD. The larger the mass ratio, the better the vibration reduction effect. However, considering the limitations of building space and bearing capacity, the mass ratio is generally taken as 0.5% - 3%, and it is specifically determined according to the actual situation of the building.

[0095] After the mass ratio is determined, further determine the damping ratio of each sub-TMD mechanism, according to Calculate, the damping coefficient is calculated according to c = 2ξωm, and the type of viscous damper required is determined according to the damping ratio; the formula for calculating the natural vibration frequency of the rolling pendulum TMD is: When k in the formula is 0, that is, the stiffness adjustment device does not place a spring to provide additional stiffness, the formula for calculating the natural vibration frequency of the TMD becomes: At this time, the natural vibration frequency is only related to R, and the corresponding radius of curvature is obtained by substituting the natural vibration frequencies of each vibration mode into this formula;

[0096] (4) Evaluate the vibration reduction effect of the tuned mass damper considering the influence of multi-order modes of high-rise buildings. The motion equation under wind vibration is:

[0097]

[0098] In Equations (2) and (3), are the mass, damping, and stiffness matrices of the MTMD respectively, is the displacement vector of the MTMD relative to the ground, P T is the position matrix of the MTMD, F is the pulsating wind force vector, O is an m-dimensional column vector (m is the number of sub-TMD mechanisms), and f represents the vibration force vector of the MTMD system; using the modal superposition method, the structural displacement is expressed by the vibration mode vector and the generalized displacement, and the structural dynamic equation becomes:

[0099]

[0100] In Equations (4) and (5):

[0101] C n = diag[2ξ j ω j (j = 1, 2, 3..., n)

[0102]

[0103] where ξ j , ω j are the damping ratio and frequency of the j-th mode shape respectively, n is the number of mode shapes considered for the structure, ξ k , ω k are the damping ratio and frequency of the k-th sub-TMD mechanism respectively. Considering the multimodal coupling of the structure, the vibration force vector of the MTMD system is:

[0104]

[0105] Substitute Equation (6) into Equation (4) and combine it with Equation (5) into matrix form:

[0106]

[0107] In Equation (7):

[0108]

[0109] where E1 is an n×n identity matrix and E2 is an m×m identity matrix;

[0110] Let its solution be substituted into the above equation, and we get:

[0111]

[0112] where are the frequency-domain transfer functions of the main structure and the TMD relative to the main structure respectively, and I1 is an n-dimensional column vector; Solve Equation (7) to obtain the frequency-domain transfer function:

[0113]

[0114] The coefficients A1 and A2 in Equation (9) are solved as follows:

[0115] A1 = a 11 -a 12 (a 22 2 + b2 2 ) -1 a 22 a 21 (9 - a)

[0116] A2 = b1 + a 12 (a 22 2 + b2 2 ) -1 b2a 21 (9 - b)

[0117] Where:

[0118]

[0119] After obtaining the frequency-domain transfer function, calculate the acceleration of the k-th degree of freedom of the structure and the mean square value of the inter-story displacement response:

[0120]

[0121] Where, is the power spectral matrix of the acting force, and φ k,j is the displacement component of the k-th degree of freedom of the j-th vibration mode vector of the structure;

[0122] Substitute Equation (9) into Equation (10) to obtain the mean square value of the acceleration response of the k-th degree of freedom of the MTMD under wind load excitation. After obtaining the mean square value of the acceleration response, convert it into the peak acceleration, and its formula is:

[0123]

[0124] In Equation (11), g is the peak factor, take g = 3, calculate the peak acceleration response of the high-rise structure with the MTMD system and compare it with the limit value required by the code, that is, whether a peak ≤0.15m / s 2 , if the requirement is met, the designed TMD parameters can be applied in practice and the design is completed; if the requirement is not met, the parameters of the TMD need to be adjusted and the motion equation needs to be re-established and verified according to the above steps until the vibration reduction effect meets the requirement.

[0125] Example 5

[0126] As Figure 8 shown, in the case of an earthquake, set the motion equation of the MTMD under earthquake excitation as:

[0127]

[0128] In Equations (12) and (13), I1 and I2 are n-dimensional and m-dimensional column vectors (n is the degree of freedom of the structure);

[0129] Derive the frequency-domain transfer function of the building structure under coupled control according to the derivation process of Equations (12) and (13) The inter-story displacement transfer function of the k-th degree of freedom of the building structure is:

[0130]

[0131] Similarly, according to the random vibration theory, the mean square value of the inter-story displacement response of the k-th degree of freedom of the building structure under seismic excitation is obtained as follows:

[0132]

[0133] In Equation (15), is the power spectral density of seismic acceleration;

[0134] After obtaining the mean square value of the inter-story displacement response, in order to evaluate the vibration reduction effect, it is converted into a peak value, and the formula is:

[0135]

[0136] In Equation (16), g is taken as 3, and the inter-story displacement angle is calculated using the peak inter-story displacement to evaluate whether the vibration reduction effect meets the specification requirements; if the requirements are met, the designed TMD parameters can be applied in practice and the design is completed; if the requirements are not met, the parameters of the TMD need to be adjusted, the motion equation is re-established, and verified according to the above steps until the vibration reduction effect meets the requirements.

[0137] Example 6

[0138] As Figure 8 shown, after considering the action of the stiffness adjustment device, the calculation formula for the natural vibration frequency of the system becomes: where R' is the equivalent curvature radius after creep, M is the overlying mass, and k is the additional stiffness of the stiffness adjustment device. Let the adjusted natural vibration frequency f' be equal to the designed frequency, that is, the influence of steel ball creep on the dynamic characteristics is eliminated; in actual use, the natural vibration frequency of the rolling pendulum is measured regularly, the acceleration time history curve of the rolling pendulum is drawn using the data measured by the acceleration sensor, and it is transformed into the frequency domain through Fourier transform to obtain the natural vibration frequency of the rolling pendulum and compare it with the designed frequency. When the error between the two reaches 15%, the vibration reduction effect of the rolling pendulum decreases significantly. At this time, calculate the value of k according to and replace the spring to improve the vibration reduction effect of the TMD.

[0139] In this embodiment, the service life of the TMD is very long, basically equivalent to the service life of the building. Under the action of long-term stable pressure load, although the yield stress is not exceeded, the ball will still undergo a certain degree of strain, which is called creep. Creep will affect the rolling of the ball and increase the natural vibration frequency of the system. When the difference from the original design value is too large, the vibration reduction effect will decrease. The present invention configures a stiffness adjustment device to solve this problem.

[0140] The working principle of the present invention:

[0141] 1. The present invention is a TMD based on the form of a rolling pendulum, and provides a set of design and full-cycle maintenance methods for a tuned mass damper (MTMD) system considering the influence of multi-order modes of high-rise buildings to perform multi-modal vibration reduction control on high-rise structures. The present invention utilizes the characteristic that the natural vibration frequency of the rolling pendulum is independent of mass, and separately configures a viscous damper to achieve the separate design of the important parameters of the TMD, simplifies the design steps, and at the same time considers the coupling effect of multiple vibration modes of the structure when evaluating the vibration reduction effect, which is more in line with engineering practice and more accurately evaluates the vibration reduction effect of multi-order modes. And for different load conditions such as wind vibration and earthquake, different indicators such as response acceleration or inter-story drift angle are used to reflect the vibration reduction effect, and structural vibration reduction control can be considered for various different external excitations.

[0142] 2. The present invention considers the influence of ball creep on the dynamic characteristics of the TMD under long-term load, and cancels the influence of creep by adding a stiffness adjustment device. The stiffness adjustment device is equipped with two springs. When the TMD generates a horizontal displacement, the part of the stiffness adjustment device connected to the connecting piece can slide and squeeze the spring to cause deformation, providing an additional restoring force for the system to eliminate the influence of creep. When initially designing, the stiffness adjustment device is not considered, that is, it is calculated without installing springs. After the TMD is put into use, the actual natural vibration frequency of the TMD should be monitored. If the natural vibration frequency deviates too much from the design value due to the influence of creep, the required spring stiffness is calculated according to the given formula with the design frequency as the target. During the entire service life of the TMD, the natural vibration frequency may change multiple times due to creep. Springs with different stiffnesses need to be replaced according to the monitoring results and the calculation formula. This device not only eliminates the influence of creep but also facilitates the later maintenance of the TMD.

Claims

1. A harmonic mass damper considering the influence of multi-order modes of high-rise buildings, characterized in that: It includes a mass block, a stiffness adjustment device, a rolling pendulum, and a viscous damper. The mass block is located above the roof of a high-rise building. A rolling pendulum is connected between the bottom end of the mass block and the upper end of the roof. A stiffness adjustment device and a viscous damper are also connected between the bottom end of the mass block where the outer periphery of the rolling pendulum is located and the roof.

2. The harmonic mass damper considering the influence of multi-order modes of high-rise buildings according to claim 1, characterized in that: The upper seat plate of the rolling pendulum is fixedly connected to the bottom end of the mass block, and the lower seat plate of the rolling pendulum is fixedly connected to the roof. Four grooves are arranged in a cross shape on the opposite surfaces of the upper and lower seat plates. Ball bearings are rollingly connected between the upper and lower opposite grooves to form a sub-TMD mechanism.

3. The harmonic mass damper considering the influence of multi-order modes of high-rise buildings according to claim 2, characterized in that: The stiffness adjustment device includes three steel rods arranged coaxially in sequence. Stiffness adjustment springs are sleeved on the steel rods located on both sides respectively. Steel plates are detachably and fixedly connected to the outer ends of the steel rods on both sides. Piers are provided at the bottom ends of the two steel plates and at the bottom end of the center position of the middle steel rod. The piers are fixed on the roof surface; Sleeve slides are respectively sleeved on the inner ends of the steel rods on both sides. A connecting plate is connected between the tops of the two sleeve slides. A T-shaped slider is connected to the bottom end of the connecting plate. A T-shaped chute that slidably cooperates with the T-shaped slider is opened on the middle steel rod. The top end of the connecting plate is connected to the bottom end of the mass block through a connecting member.

4. The harmonic mass damper considering the influence of multi-order modes of high-rise buildings according to claim 3, characterized in that: The connecting member includes connecting parts respectively rotatably connected to the bottom end of the mass block and the top end of the connecting plate, and a transmission rod connected between the two connecting parts.

5. The harmonic mass damper considering the influence of multi-order modes of high-rise buildings as described in claim 4, characterized in that: Both ends of the viscous damper are respectively ball-jointed to the bottom end of the mass block and the roof surface.

6. The design method of a harmonic mass damper considering the influence of multi-order modes of high-rise buildings as described in claim 5, characterized in that, It includes: (1) Before designing the rolling pendulum, the vibration mode parameters of the target building are obtained through modal testing. The time history curve of the building vibration acceleration at the selected points is obtained through actual measurement on the roof of the target building. By synthesizing the Fourier transform amplitude spectra of each point, the first three frequencies for controlling the target building are obtained: the translational frequency in the short-axis direction; the torsional frequency; the translational frequency in the long-axis direction; (2) When designing the rolling pendulum TMD, the motion equation of the rolling pendulum TMD under free vibration is as follows: In Equation (1), M is the mass of the TMD, c is the damping provided by the viscous damper, k is the stiffness provided by the stiffness adjustment device, R is the curvature radius of the seat plate groove, and u is the horizontal displacement of the TMD system; (3) Based on the first three natural frequencies obtained in step (1), design the sub-TMD mechanisms of each order of the multiple tuned mass dampers MTMD respectively, determine the total mass of the rolling pendulum TMD, and proportionally distribute the mass to the sub-TMD mechanisms according to the modal participation factor; design the corresponding sub-TMD mechanisms for each order of control frequency respectively; after determining the mass ratio, further determine the damping ratio of each sub-TMD mechanism, and calculate according to The damping coefficient is calculated as c = 2ξωm. Determine the type of viscous damper required based on the damping ratio; the formula for the natural frequency of the rolling pendulum TMD is: When k in the formula is 0, that is, the stiffness adjustment device does not place a spring to provide additional stiffness, the formula for the natural frequency of the TMD becomes: At this time, the natural frequency is only related to R. Substitute the natural frequencies of each mode into this formula to obtain the corresponding radius of curvature; (4) Evaluate the vibration reduction effect of the harmonic mass damper considering the influence of multiple modes of the high-rise building. The motion equation under wind vibration is: In equations (2) and (3), are the mass, damping, and stiffness matrices of the MTMD, respectively, is the displacement vector of the MTMD relative to the ground, P T is the MTMD position matrix, F is the fluctuating wind force vector, O is an m-dimensional column vector, and f represents the vibration force vector of the MTMD system; using the mode superposition method, the structural displacement is expressed by the mode shape vector and the generalized displacement, and the structural dynamic equation becomes: In Equations (4) and (5): C n = diag[2ξ j ω j (j = 1, 2, 3..., n) where ξ j , ω j are the damping ratio and frequency of the j-th vibration mode respectively, n is the number of vibration modes considered for the structure, ξ k , ω k are the damping ratio and frequency of the k-th sub-TMD mechanism respectively. Considering the multi-modal coupling of the structure, the vibration force vector of the MTMD system is: Substitute Equation (6) into Equation (4) and combine it with Equation (5) into a matrix form: In Equation (7): Among them, E1 is an n×n-dimensional identity matrix, and E2 is an m×m-dimensional identity matrix; Let its solution Substituting into the above equation, we get: Among them, are the frequency-domain transfer functions of the main structure and the frequency-domain transfer function of the TMD relative to the main structure respectively, and I1 is an n-dimensional column vector; Solving equation (7) gives the frequency-domain transfer function: The solutions of the coefficients A1 and A2 in Equation (9) are as follows: A1 = a 11 -a 12 (a 22 2 + b2 2 ) -1 a 22 a 21 (9 - a) A2 = b1 + a 12 (a 22 2 + b2 2 ) -1 b2a 21 (9 - b) Among them: After obtaining the frequency-domain transfer function, calculate the acceleration, and the mean square value of the inter-story displacement response of the kth degree of freedom of the structure: Among them, is the acting force power spectrum matrix, and φ k,j is the displacement component of the k-th degree of freedom of the j-th order vibration mode vector of the structure; Substitute Equation (9) into Equation (10) to obtain the mean square value of the acceleration response of the kth degree of freedom of the MTMD under wind load excitation. After obtaining the mean square value of the acceleration response, convert it into the peak acceleration. The formula is: In Equation (11), g is the peak factor, taking g = 3. The peak acceleration response of the high-rise structure with the MTMD system will be calculated and compared with the limit value required by the code, that is, whether a peak ≤0.15m / s 2 , if the requirement is met, the designed TMD parameters can be applied in practice and the design is completed; if the requirement is not met, the parameters of the TMD need to be adjusted, the motion equation is re-established, and verified according to the above steps until the vibration reduction effect meets the requirements.

7. The design method of a harmonic mass damper considering the influence of multi-order modes of high-rise buildings as described in claim 6, characterized in that: In the case of an earthquake, set the motion equation of the MTMD under earthquake excitation as: In Equations (12) and (13), I1 and I2 are respectively n-dimensional and m-dimensional column vectors; According to the derivation process of formulas (12) and (13), the frequency-domain transfer function of the building structure under coupled control is obtained The inter-story displacement transfer function of the k-th degree of freedom of the building structure is as follows: Similarly, according to the random vibration theory, the mean square value of the inter-story displacement response of the k-th degree of freedom of the building structure under seismic excitation is obtained: In Equation (15), is the power spectral density of seismic acceleration; After obtaining the mean square value of the inter-story displacement response, it is converted into a peak value for evaluating the vibration reduction effect, and the formula is: In formula (16), g is taken as 3, and the inter-story displacement angle is calculated using the peak inter-story displacement to evaluate whether the vibration reduction effect meets the specification requirements; if the requirements are met, the designed TMD parameters can be applied in practice and the design is completed; if the requirements are not met, the parameters of the TMD need to be adjusted, the motion equation is re-established, and verified according to the above steps until the vibration reduction effect meets the requirements.

8. The design method of a harmonic mass damper considering the influence of multi-order modes of high-rise buildings as claimed in claim 7, characterized in that: After considering the effect of the stiffness adjustment device, the calculation formula for the natural vibration frequency of the system becomes: wherein, R' is the equivalent curvature radius after creep, M is the overlying mass, k is the additional stiffness of the stiffness adjustment device, and making the adjusted natural vibration frequency f' equal to the design frequency can eliminate the influence of steel ball creep on the dynamic characteristics; during actual use, regularly measure the natural vibration frequency of the rolling pendulum, use the acceleration sensor to measure the data and draw the acceleration time history curve of the rolling pendulum, and transform it to the frequency domain through Fourier transform to obtain the natural vibration frequency of the rolling pendulum and compare it with the design frequency. When the error between the two reaches 15%, the damping effect of the rolling pendulum decreases significantly. At this time, calculate the k value according to and replace the spring to improve the damping effect of the TMD.

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