A simple harmonic mass damper and method considering multi-modal effects of high-rise buildings

Abstract

The present application belongs to the technical field of high-rise building vibration reduction (earthquake), and specifically relates to a simple harmonic mass damper and method considering the influence of multi-modal of high-rise buildings. The simple harmonic mass damper considering the influence of multi-modal of high-rise buildings comprises a mass block, a viscous damper, a stiffness adjusting device and a rolling pendulum. The method comprises the following steps: measuring the N-order modal parameters of the structure, distributing the mass ratio according to the array participation coefficient, determining the damping ratio and the natural frequency, establishing the motion equation of the structure and the MTMD, calculating the frequency domain transfer coefficient of the structure, calculating the acceleration / inter-story displacement mean square value, judging whether the vibration reduction effect meets the specification, and designing the stiffness adjusting device according to the creep of the steel ball. The present application adopts a passive control mode, avoids the problems of energy input and high subsequent maintenance cost, and solves the problem of change of the natural frequency of the TMD caused by creep.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-rise building vibration reduction, and in particular relates to a harmonic mass damper and a method for taking into account the multi-order modal influence of high-rise buildings. Background Art

[0002] With the continuous development of social economy, the global urbanization rate has exceeded 56%. The increase in building height has led to a longer natural vibration period and a significant increase in sensitivity to wind loads. For example, the annual wind-induced displacement of the Shanghai Tower reaches 0.8m. Wind-induced vibration has become a core design bottleneck. Strong winds may cause vibration in the direction of the wind, vortex-induced resonance in the direction of the wind, and torsional coupling vibration, leading to fatigue damage or even collapse of components. At the same time, the acceleration at the top of the building exceeds 0.15m / s. 2 Traditional wind-resistant methods increase stiffness by adding shear walls or column cross-sections, which increases construction costs by 20% to 30%, occupies usable floor space, and limits the flexibility of building layouts.

[0003] The TMD adjusts the damper system's own vibration frequency to near the dominant structural vibration frequency. Through interaction between the TMD and the primary structure, energy is transferred from the primary structure to the tuned mass damper system, reducing primary structure vibration. Currently, the most widely used TMDs include: 1. Pendulum TMDs, which utilize the swinging motion of a pendulum to dissipate energy. Construction costs are low, and the mass can be constructed of concrete, steel, or modified from existing equipment. The mass and damper can be prefabricated and hoisted as a single unit, shortening construction time and minimizing maintenance costs. However, these TMDs have limited swing amplitude and require high-precision bearings, which are prone to wear and occupy a large amount of building space. 2. Sliding-mass TMDs, in which the mass slides along a guide rail, rely on hydraulic or viscous damping for improved vibration reduction. This type of TMD does not require the vertical suspension space of the pendulum TMD and can be placed horizontally on the equipment floor. Adjusting the guide rail inclination or adding counterweights allows for rapid matching of the primary structure's frequency and simultaneous control of XY vibrations. However, these TMDs exhibit high friction resistance and slow response. 3. Spring-mass system: Frequency is tuned by spring stiffness. Only springs, masses, and dampers are required, resulting in an extremely low failure rate and simple and convenient maintenance. By adjusting the spring stiffness or mass weight, different vibration control requirements can be met. However, springs are susceptible to aging, resulting in unstable long-term performance. 4. Active mass damper (AMD): A sensor monitors vibration signals in real time and drives a motor to control the movement of the mass, generating a reverse force. This allows for high-precision control and adapts to multimodal coupled vibrations. By adjusting the force in real time, the passive TMD overcomes its sensitivity to frequency detuning. However, the system cost is approximately 3-5 times that of a passive TMD, requires a continuous power supply, and the hydraulic system is prone to oil leaks, making maintenance complex. Improper algorithm design can lead to overshoot or system oscillation. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present application discloses a simple harmonic mass damper and method considering the influence of multi-modal modes of high-rise buildings, which effectively controls wind vibration of high-rise structures and reduces seismic influence by means of a long-term serviceable rolling pendulum type TMD.

[0005] In order to achieve the above-mentioned purposes, the technical scheme of the present application is as follows:

[0006] A simple harmonic mass damper considering the influence of multi-modal modes of high-rise buildings, comprising a mass block, a stiffness adjusting device, a rolling pendulum and a viscous damper, wherein 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, and a stiffness adjusting device and a viscous damper are further connected between the bottom end of the mass block and the roof where the outer periphery of the rolling pendulum is located.

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

[0008] Preferably, the stiffness adjusting device comprises three steel rods arranged coaxially in sequence, stiffness adjusting springs are sleeved on the steel rods on both sides, respectively, steel plates are detachably fixedly connected with the outer end of the steel rods on both sides, buttresses are arranged at the bottom end of the two steel plates and the bottom end of the central steel rod, respectively, the buttresses are fixed to the surface of the roof, sliding sleeves are slidably sleeved on the inner end of the steel rods on both sides, respectively, a connecting plate is connected between the top portions of the two sliding sleeves, a T-shaped sliding block is connected with the bottom end of the connecting plate, a T-shaped sliding groove is formed in the central steel rod and slidably matched with the T-shaped sliding block, and the top end of the connecting plate is connected with the bottom end of the mass block through a connecting piece.

[0009] Preferably, the connecting piece comprises connecting portions rotatably connected with 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 portions.

[0010] Preferably, the two ends of the viscous damper are connected with the bottom end of the mass block and the surface of the roof, respectively.

[0011] A design method of a simple harmonic mass damper considering the influence of multi-modal modes of high-rise buildings, comprising:

[0012] (1) Before designing the rolling pendulum, modal tests are performed to obtain the parameters of each order of vibration mode of the target building. The time history curve of the building vibration acceleration at the selected point is obtained by actual measurement on the roof of the target building. The Fourier transform amplitude spectrum of each point is integrated to obtain the first three frequencies of the target building as the control: the translation frequency in the short axis direction; the torsional frequency; and the translation 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 formula (1), M is the mass of 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) Based on the first three frequencies obtained in step (1), design the sub-TMD mechanisms of each order of the multiple harmonic mass damper (MTMD), determine the total mass of the rolling pendulum TMD, and distribute the mass proportionally to the sub-TMD mechanisms according to the mode participation coefficient; design the corresponding sub-TMD mechanism for each order of control frequency; after the mass ratio is determined, further determine the damping ratio of each sub-TMD mechanism, according to Calculate the damping coefficient as c = 2ξωm, and determine the type of viscous damper required based on the damping ratio; the natural frequency of the rolling pendulum TMD is calculated as follows: When k in the formula is 0, that is, no spring is placed in the stiffness adjustment device to provide additional stiffness, the calculation formula for the natural frequency of the TMD becomes: At this time, the natural frequency is only related to R. Substituting the natural frequency of each vibration mode into this formula, the corresponding curvature radius is obtained;

[0017] (4) The vibration reduction effect of the harmonic mass damper considering the multi-order modal influence of high-rise buildings is evaluated. The motion equation under wind vibration is:

[0018]

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

[0020]

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

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

[0023]

[0024] Among them, ξ j ,ω j are the damping ratio and frequency of the jth mode, n is the mode order of the structure considered, ξ k ,ω k are the damping ratio and frequency of the kth sub-TMD mechanism respectively. Considering the multi-modal 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 a matrix form:

[0027]

[0028] In formula (7):

[0029]

[0030] Among them, E1 is the n×n dimensional identity matrix, E2 is the m×m dimensional identity matrix;

[0031] Let it solve Substituting into the above equation, we get:

[0032]

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

[0034]

[0035] The coefficients A1 and A2 in formula (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] in:

[0039]

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

[0041]

[0042] in, is the force power spectrum matrix, φ k,j is the displacement component of the kth degree of freedom of the jth-order vibration mode vector of the structure;

[0043] Substituting formula (9) into formula (10) yields 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, it is converted into peak acceleration, and the formula is:

[0044]

[0045] In formula (11), g is the peak factor, and g = 3. The peak acceleration of the high-rise structure with MTMD system is calculated and compared with the limit value required by the specification, that is, whether a peak ≤0.15m / s 2 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 TMD parameters need to be adjusted and the motion equations need to be 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, the motion equation of the MTMD under earthquake excitation is set to:

[0047]

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

[0049] According to the derivation process of formula (12) and (13), the frequency domain transfer function of the building structure under coupling control is obtained: The inter-story displacement transfer function of the kth 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 kth degree of freedom of the building structure under earthquake excitation is obtained:

[0052]

[0053] In formula (15), is the power spectrum density of earthquake acceleration;

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

[0055]

[0056] 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 requirements of the specification. 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 TMD parameters need to be adjusted, the motion equation needs to be re-established, and verification is carried out according to the above steps until the vibration reduction effect meets the requirements.

[0057] Preferably, after considering the effect of the stiffness adjustment device, the calculation formula of the system natural frequency becomes: Among them, R' is the equivalent curvature radius after creep, M is the overlying mass, and k is the additional stiffness of the stiffness adjustment device. When the adjusted natural frequency f' is equal to the design frequency, the influence of the creep of the steel ball on the dynamic characteristics is eliminated. In actual use, the natural frequency of the rolling pendulum is measured regularly, and the acceleration time history curve of the rolling pendulum is drawn using the data measured by the acceleration sensor. The data is converted to the frequency domain through Fourier transform, and the natural frequency of the rolling pendulum is compared with the design frequency. When the error between the two reaches 15%, the shock absorption effect of the rolling pendulum is significantly reduced. At this time, according to Calculate the k value and replace the spring to improve the vibration damping effect of the TMD.

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

[0059] Compared with the sliding friction TMD system, the rolling friction is used to replace the sliding friction in the application, the problem of no damping effect of the sliding threshold pendulum damper is solved, and the damping effect can still be played under small vibration. Compared with the pendulum TMD, the design of the application is more concentrated, the installation space is saved, and the arrangement is more flexible. Compared with the common mass damper and spring TMD system, the frequency design and mass control are separated in the application, the two physical quantities can be considered separately, the design of the TMD is facilitated, the natural frequency of the system can be controlled by changing the curvature radius of the track, the multi-order vibration control is realized, meanwhile, the system mass can be increased as much as possible to reduce the number of TMD arrangement and save the space. Compared with the TMD system of the same type using the rolling pendulum principle, the influence of the creep on the dynamic characteristics of the TMD system under long-term load is further considered in the application, the stiffness adjusting device is added, the influence of the creep is eliminated through the adjustment of the system stiffness in the later period, and the maintenance difficulty and cost are also reduced. The application can change the system damping by adjusting the viscous damper, and realize different types and different degrees of damping requirements such as wind vibration and earthquake. BRIEF DESCRIPTION OF DRAWINGS

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

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

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

[0063] Figure 4 It is a bottom layout view of the position relationship among the mass block, the stiffness adjusting 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 adjusting device.

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

[0066] Figure 7 It is a sectional view structural schematic diagram of the application B-B.

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

[0068] Figure 9 It is a four-point building vibration acceleration time history curve of a building roof actually measured.

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

[0070] Figure 11Schematic diagram for selecting measurement 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. connecting piece; 46. T-shaped slider; 47. T-shaped slide groove; 48. sliding sleeve; 49. connecting plate; 5. roof. DETAILED DESCRIPTION

[0072] The following description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

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

[0074] Example 1

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

[0076] In this embodiment, the rolling pendulum (TMD) utilizes the rolling motion of balls in grooves to dissipate energy, replacing conventional sliding friction with rolling friction. This solves the problem of sliding friction having a threshold value and provides vibration reduction even under relatively low vibration levels. The damping force of the TMD is provided by the viscous damper 3, and its stiffness is adjusted by the stiffness adjustment device, thereby forming a harmonic mass damper that accounts for the multi-order modal effects of high-rise buildings.

[0077] Example 2

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

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

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

[0081] Example 3

[0082] like Figures 5-7 As shown, the stiffness adjustment device includes three steel rods 44 coaxially arranged in sequence, and stiffness adjustment springs 43 are respectively sleeved on the steel rods 44 on both sides, and steel plates 42 are detachably fixedly connected to the outer ends of the steel rods 44 on both sides. Piers 41 are provided at the bottom ends of the two steel plates 42 and the bottom end of the center position of the middle steel rod 44, and the piers 41 are fixed to 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, and a connecting plate 49 is connected between the tops of the two sliding sleeves 48, and the bottom end of the connecting plate 49 is connected to a T-shaped slider 46, and a T-shaped slot 47 that slides with the T-shaped slider 46 is provided on the middle steel rod 44, and the top of the connecting plate 49 is connected to the bottom end of the mass block 1 by a connecting piece 45.

[0083] like Figure 5 As shown, the connecting member 45 includes connecting parts that are 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] like Figure 1 As shown, the two ends of the viscous damper 3 are respectively spherically hinged to the bottom end of the mass block 1 and the roof surface.

[0085] In this embodiment, the viscous damper 3 is ball-hinged with a support, and the support is welded to the roof and the mass block. A connector 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 connected to the end steel plates with bolts to ensure that springs of different stiffness can be removed and replaced during subsequent TMD maintenance. Among them, a T-shaped groove 47 is provided on the middle steel bar to cooperate with the T-shaped slider 46 to ensure the stability of the sliding trajectory of the sleeve. When the TMD vibrates, the mass block 1 drives the connector and the sleeve to move together, causing the sleeve to compress the spring in the corresponding direction, providing additional restoring force for the TMD system. At the same time, the stroke of the T-shaped slider 46 can be set so that its maximum sliding distance is equal to the maximum horizontal displacement of the rolling pendulum.

[0086] Example 4

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

[0088] A design method for harmonic mass dampers considering the multi-order modal effects of high-rise buildings, such as Figure 8 Shown, including:

[0089] (1) Before designing the rolling pendulum, modal tests are performed to obtain the parameters of each order of vibration mode of the target building. The time history curve of the building vibration acceleration at the selected point is obtained by actual measurement on the roof of the target building. The Fourier transform amplitude spectrum of each point is integrated to obtain the first three frequencies of the target building as the control: the translation frequency in the short axis direction; the torsional frequency; and the translation frequency in the long axis direction.

[0090] This invention aims to control wind vibrations, while maintaining the comfort level in daily use, and to reduce the structural response acceleration and inter-story displacement under extreme wind and earthquake conditions. Before designing the rolling pendulum, modal tests were performed to obtain the vibration parameters of each order of the target building. Figure 9 For a building roof, four points were selected (the measurement points were arranged as follows Figure 11 As shown in the figure, where measuring points 1 and 2 measure the vibration in the short axis direction, and measuring points 3 and 4 measure the vibration in the long axis direction), the building vibration acceleration time history curve is obtained. Figure 10 As shown in the figure, the Fourier transform amplitude spectrum of each point is integrated, and the first three frequencies of the control target building are 0.342Hz, 0.488Hz, and 0.513Hz, which are the translation frequency in the short axis direction, the torsional frequency, and the translation frequency in the long axis direction, respectively.

[0091] (2) After determining the target frequency of building vibration control, the rolling pendulum TMD is designed 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 are listed, and the motion equation of the rolling pendulum TMD system under free vibration is listed:

[0092]

[0093] In formula (1), M is the mass of 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;

[0094] (3) Based on 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 frequency of the system, and the system damping. Based on the first three frequencies obtained in step (1), the sub-TMD mechanisms of each order of the multiple harmonic 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 mode participation coefficient. The corresponding sub-TMD mechanism is 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 0.5% to 3%, and the specific value is determined according to the actual situation of the building.

[0095] After the mass ratio is determined, the damping ratio of each sub-TMD mechanism is further determined according to Calculate the damping coefficient as c = 2ξωm, and determine the type of viscous damper required based on the damping ratio; the natural frequency of the rolling pendulum TMD is calculated as follows: When k in the formula is 0, that is, no spring is placed in the stiffness adjustment device to provide additional stiffness, the calculation formula for the natural frequency of the TMD becomes: At this time, the natural frequency is only related to R. Substituting the natural frequency of each vibration mode into this formula, the corresponding curvature radius is obtained;

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

[0097]

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

[0099]

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

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

[0102]

[0103] Among them, ξ j ,ω j are the damping ratio and frequency of the jth mode, n is the mode order of the structure considered, ξ k ,ω k are the damping ratio and frequency of the kth sub-TMD mechanism respectively. Considering the multi-modal 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 a matrix form:

[0106]

[0107] In formula (7):

[0108]

[0109] Among them, E1 is the n×n dimensional identity matrix, E2 is the m×m dimensional identity matrix;

[0110] Let it solve Substituting into the above equation, we get:

[0111]

[0112] in, are the frequency domain transfer function of the main structure and the frequency domain transfer function of TMD relative to the main structure, respectively. I1 is an n-dimensional column vector. Solving equation (7) yields the frequency domain transfer function:

[0113]

[0114] The coefficients A1 and A2 in formula (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] in:

[0118]

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

[0120]

[0121] in, is the force power spectrum matrix, φ k,j is the displacement component of the kth degree of freedom of the jth mode vector of the structure;

[0122] Substituting formula (9) into formula (10) yields 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, it is converted into peak acceleration, and the formula is:

[0123]

[0124] In formula (11), g is the peak factor, and g = 3. The peak acceleration of the high-rise structure with MTMD system is calculated and compared with the limit required by the specification, that is, whether a peak ≤0.15m / s 2 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 TMD parameters need to be adjusted and the motion equations need to be re-established and verified according to the above steps until the vibration reduction effect meets the requirements.

[0125] Example 5

[0126] like Figure 8 As shown in Figure 2, in the case of earthquake, the motion equation of MTMD under earthquake excitation is set as:

[0127]

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

[0129] According to the derivation process of formula (12) and (13), the frequency domain transfer function of the building structure under coupling control is obtained: The inter-story displacement transfer function of the kth 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 kth degree of freedom of the building structure under earthquake excitation is obtained:

[0132]

[0133] In formula (15), is the power spectrum density of earthquake acceleration;

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

[0135]

[0136] 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 requirements of the specification. 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 TMD parameters need to be adjusted, the motion equation needs to be re-established, and verification is carried out according to the above steps until the vibration reduction effect meets the requirements.

[0137] Example 6

[0138] like Figure 8 As shown in Figure 2, after considering the effect of the stiffness adjustment device, the calculation formula for the system's natural frequency becomes: Among them, R' is the equivalent curvature radius after creep, M is the overlying mass, and k is the additional stiffness of the stiffness adjustment device. When the adjusted natural frequency f' is equal to the design frequency, the influence of the creep of the steel ball on the dynamic characteristics is eliminated. In actual use, the natural frequency of the rolling pendulum is measured regularly, and the acceleration time history curve of the rolling pendulum is drawn using the data measured by the acceleration sensor. The data is converted to the frequency domain through Fourier transform, and the natural frequency of the rolling pendulum is compared with the design frequency. When the error between the two reaches 15%, the shock absorption effect of the rolling pendulum is significantly reduced. At this time, according to Calculate the k value and replace the spring to improve the vibration damping 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 thus increase the natural frequency of the system. When the difference from the original design value is too large, the vibration reduction effect will decrease. The present invention is equipped with a stiffness adjustment device to solve this problem.

[0140] Working principle of the present invention:

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

[0142] 2. The present invention takes into account the effect of ball creep under long-term load on the dynamic characteristics of the TMD and offsets the effect of creep by adding a stiffness adjustment device. The stiffness adjustment device is equipped with two springs. When the TMD produces horizontal displacement, the part connected to the stiffness adjustment device and the connector can slide and squeeze the spring to cause it to deform, providing additional restoring force for the system to eliminate the effect of creep. The stiffness adjustment device is not considered in the initial design, that is, the calculation is based on no spring installation. After the TMD is put into use, the actual natural frequency of the TMD should be monitored. If the natural frequency is too different from the design value due to creep, the given formula is used. The required spring stiffness is calculated based on the design frequency. During the TMD's lifecycle, creep can cause the natural frequency to change multiple times. Springs of varying stiffnesses must be replaced based on monitoring results and calculations. This device eliminates creep effects while also facilitating subsequent maintenance of the TMD.

Claims

1. A harmonic mass damper that considers the multi-modal effects of high-rise buildings, characterized by: The invention comprises 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, and the rolling pendulum is connected between the bottom end of the mass block and the top end of the roof. The stiffness adjustment device and the 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. The upper base plate of the rolling pendulum is fixedly connected to the bottom end of the mass block, and the lower base plate of the rolling pendulum is fixedly connected to the roof. Four grooves are cross-shaped on the opposite surfaces of the upper and lower base plates. Balls are rollingly connected between the upper and lower opposite grooves to form a sub-TMD mechanism. The stiffness adjustment device includes three steel rods coaxially arranged in sequence, and stiffness adjustment springs are respectively sleeved on the steel rods on both sides. Steel plates are detachably fixedly connected to the outer ends of the steel rods on both sides, and piers are provided at the bottom ends of the two steel plates and the bottom end of the center position of the middle steel rod. The piers are fixed to the roof surface; sliding sleeves are respectively slidably sleeved on the inner ends of the steel rods on both sides, and a connecting plate is connected between the tops of the two sliding sleeves. The bottom end of the connecting plate is connected to a T-shaped slider, and a T-shaped slot that slides with the T-shaped slider is provided on the middle steel rod. The top of the connecting plate and the bottom end of the mass block are connected by a connecting piece.

2. The harmonic mass damper according to claim 1, wherein: The connecting member includes a connecting portion which is 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 portions.

3. The harmonic mass damper according to claim 2, wherein: The two ends of the viscous damper are respectively spherically hinged to the bottom end of the mass block and the roof surface.

4. The design method of a harmonic mass damper considering the multi-order modal effects of a high-rise building as claimed in claim 3 is characterized by: include: (1) Before designing the rolling pendulum, modal tests are performed to obtain the parameters of each order of vibration mode of the target building. The time history curve of the building vibration acceleration at the selected point is obtained by actual measurement on the roof of the target building. The Fourier transform amplitude spectrum of each point is integrated to obtain the first three frequencies of the target building as the control: the translation frequency in the short axis direction; the torsional frequency; and the translation 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 formula (1), M is the mass of 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 frequencies obtained in step (1), design the sub-TMD mechanisms of each order of the multiple harmonic mass damper MTMD respectively, determine the total mass of the rolling pendulum TMD, and distribute the mass proportionally to the sub-TMD mechanisms according to the mode participation coefficient; design the corresponding sub-TMD mechanism for each order of control frequency; after the mass ratio is determined, further determine the damping ratio of each sub-TMD mechanism, according to Calculate the damping coefficient as c = 2ξωm, and determine the type of viscous damper required based on the damping ratio; the natural frequency of the rolling pendulum TMD is calculated as follows: When k in the formula is 0, that is, no spring is placed in the stiffness adjustment device to provide additional stiffness, the calculation formula for the natural frequency of the TMD becomes: At this time, the natural frequency is only related to R. Substituting the natural frequency of each vibration mode into this formula, the corresponding curvature radius is obtained; (4) The vibration reduction effect of the harmonic mass damper considering the multi-order modal influence of high-rise buildings is evaluated. The motion equation under wind vibration is: In formula (2) and (3), are the mass, damping and stiffness matrices of MTMD, is the displacement vector of MTMD relative to the ground, P T is the MTMD position matrix, F is the fluctuating wind force vector, O is the m-dimensional column vector, and f is the vibration force vector of the MTMD system. Using the modal superposition method, the structural displacement is expressed by the mode shape vector and the generalized displacement, and the structural dynamic equation becomes: In formulas (4) and (5): Among them, ξ j ,ω j are the damping ratio and frequency of the jth mode, n is the mode order of the structure considered, ξ k ,ω k are the damping ratio and frequency of the kth 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 formula (7): Among them, E1 is the n×n dimensional identity matrix, E2 is the m×m dimensional identity matrix; Let it solve Substituting into the above equation, we get: in, are the frequency domain transfer function of the main structure and the frequency domain transfer function of TMD relative to the main structure, respectively. I1 is an n-dimensional column vector. Solving equation (7) yields the frequency domain transfer function: The coefficients A1 and A2 in formula (9) are solved 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) in: After obtaining the frequency domain transfer function, calculate the acceleration of the kth degree of freedom of the structure and the mean square value of the inter-story displacement response: in, is the force power spectrum matrix, φ k,j is the displacement component of the kth degree of freedom of the jth-order vibration mode vector of the structure; Substituting formula (9) into formula (10) yields 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, it is converted into peak acceleration, and the formula is: In formula (11), g is the peak factor, and g = 3. The peak acceleration of the high-rise structure with MTMD system is calculated and compared with the limit value required by the specification, that is, whether a peak ≤0.15m / s 2 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 TMD parameters need to be adjusted and the motion equations need to be re-established and verified according to the above steps until the vibration reduction effect meets the requirements.

5. The method for designing a harmonic mass damper considering the multi-order modal effects of a high-rise building according to claim 4 is characterized by: In the case of earthquakes, the motion equation of MTMD under earthquake excitation is set as: In formulas (12) and (13), I1 and I2 are n-dimensional and m-dimensional column vectors respectively; According to the derivation process of formula (12) and (13), the frequency domain transfer function of the building structure under coupling control is obtained: The inter-story displacement transfer function of the kth degree of freedom of the building structure is: Similarly, according to the random vibration theory, the mean square value of the inter-story displacement response of the kth degree of freedom of the building structure under earthquake excitation is obtained: In formula (15), is the power spectrum density of earthquake acceleration; After obtaining the mean square value of the inter-story displacement response, it is converted into a peak value to evaluate the vibration reduction effect. 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 requirements of the specification. 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 TMD parameters need to be adjusted, the motion equation needs to be re-established, and verification is carried out according to the above steps until the vibration reduction effect meets the requirements.

6. The method for designing a harmonic mass damper considering the multi-modal effects of high-rise buildings according to claim 5, wherein: After considering the effect of the stiffness adjustment device, the calculation formula of the system natural frequency becomes: Among them, R' is the equivalent curvature radius after creep, M is the overlying mass, and k is the additional stiffness of the stiffness adjustment device. When the adjusted natural frequency f' is equal to the design frequency, the influence of the creep of the steel ball on the dynamic characteristics is eliminated. In actual use, the natural frequency of the rolling pendulum is measured regularly, and the acceleration time history curve of the rolling pendulum is drawn using the data measured by the acceleration sensor. The data is converted to the frequency domain through Fourier transform, and the natural frequency of the rolling pendulum is compared with the design frequency. When the error between the two reaches 15%, the shock absorption effect of the rolling pendulum is significantly reduced. At this time, according to Calculate the k value and replace the spring to improve the vibration damping effect of the TMD.

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