A piezoelectric tuned mass-rate-independent damper and its parameter design method

Abstract

This invention discloses a piezoelectric tuned mass rate-independent damper and its parameter design method. Compared to traditional tuned mass dampers, the original linear viscous damping element in the damper is replaced with a rate-independent linear damping element, thereby providing a damping force independent of vibration frequency. Furthermore, after replacing the damping element, in order to optimize the piezoelectric tuned mass rate-independent damper's effect on the displacement response of the structure under seismic load excitation, the invention proposes a parameter optimization design method for the piezoelectric tuned mass rate-independent damper based on the displacement transfer function of the main structure and the ground motion, with the goal of minimizing the peak displacement response of the main structure.

Description

Technical Field

[0001] The present invention relates to the technical field of dampers, and in particular to the field of a piezoelectric tuned mass-rate independent damper and a design method thereof. Background Art

[0002] Conventional tuned mass dampers (TMDs) are susceptible to detuning when their operating environment changes. This detuning effect makes them insufficiently robust to changes in the external excitation frequency, leading to malfunction. Once a TMD detunes, it must be shut down for adjustment, which can also cause the damper to malfunction. Therefore, when the primary structure to be controlled is a long-period structure and is subject to a wide frequency band of excitation, TMDs may not necessarily meet the requirements for structural vibration control. Furthermore, while TMDs are a mature technology for structural vibration control, the relative displacement between the damper and the primary structure—the damper stroke—is a drawback. TMDs typically have a large stroke, requiring a significant distance between the damper and the primary structure during installation to prevent collisions during operation. Summary of the Invention

[0003] To address the above issues, the present invention provides a piezoelectric tuned mass rate-independent damper (TMRD). Compared to conventional tuned mass dampers (TMDs), the existing linear viscous damping element in the damper is replaced with a rate-independent linear damping (RLD) element. The difference between the two types of damping is that, in terms of complex stiffness, the imaginary part of linear viscous damping is proportional to the excitation frequency, while the imaginary part of rate-independent linear damping has a constant value. Therefore, rate-independent linear damping can provide a damping force that is independent of the vibration frequency.

[0004] Furthermore, in order to optimize the displacement response control effect of the piezoelectric tuned mass-rate-independent damper on the structure under seismic load excitation, the present invention proposes a parameter optimization design method for the piezoelectric tuned mass-rate-independent damper based on the main structure and ground motion displacement transfer function, with the goal of minimizing the peak displacement response of the main structure.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, an embodiment of the present application provides a piezoelectric tuned mass-rate-independent damper, comprising a mass block, a roller, a spring, and a damping element, wherein both ends of the spring and both ends of the damping element are respectively connected to the mass block and a main structure, and the mass block is connected to the main structure via the roller;

[0007] The damping element is a rate-independent linear damping element, and the damping force provided by the rate-independent linear damping element is independent of the excitation frequency;

[0008] The parameters of the piezoelectric tuned mass-rate-independent damper are obtained through fixed-point theory, and the parameters are the optimal stiffness and optimal damping ratio of the tuned mass-rate-independent damper.

[0009] Furthermore, the main structure is a building floor structure, including floor slabs, columns, and walls, and the excitation frequency is an external earthquake excitation frequency.

[0010] Furthermore, the damping element is a semi-active ball piezoelectric friction damper, comprising a friction plate, an upper steel plate, a lower steel plate, high-strength bolts in contact with each other, and a piezoelectric driver, wherein a ball is arranged between the piezoelectric driver and the friction plate; the upper steel plate is arranged on the friction plate and surrounds the piezoelectric driver; the friction plate is arranged on the lower steel plate;

[0011] The semi-active ball piezoelectric friction damper further comprises an actuating rod and a fixing rod, wherein one end of the friction plate is connected to the actuating rod in the horizontal direction, and the other end is connected to the fixing rod. The piezoelectric driver is a relaxor ferroelectric piezoelectric driver.

[0012] Furthermore, the fixed-point theory includes the following two conditions:

[0013] The |X / X0|-γ curve passes through two fixed points, and the values ​​of |X / X0| at the two fixed points are equal;

[0014] At the two fixed points, the value of |X / X0| reaches its maximum value;

[0015] The optimal damping ratio is obtained by using the fixed point theory to calculate the objective function R d Optimization is performed to obtain the objective function R d It is the square of the ratio of the amplitude of the main structure displacement to the ground motion displacement.

[0016] Furthermore, the objective function R d It is obtained by the following formula:

[0017] The system dynamics equation is:

[0018]

[0019] Where x = Xeiωt is the main structural displacement, x0=X0e iωt is the ground motion displacement, x d =X d e iωt is the damper displacement, ω is the excitation frequency, X, X0, X d are the displacement amplitude of the main structure, the displacement amplitude of the ground motion, and the displacement amplitude of the damper, respectively, m d , m are the masses of the damper and the main structure respectively, k d , k are the stiffness of the damper and the main structure respectively, F d is the rate-independent damping force;

[0020] The expression of the rate-independent damping force in the frequency domain is:

[0021] F d =2iξk d sgn(ω)(X d -X)e jωt

[0022] Wherein, sgn(ω) is the sign function, ξ is the damping ratio of the damper;

[0023] According to the system dynamics equation and the expression of the rate-independent damping force in the frequency domain, the expression of the system dynamics equation in the frequency domain is obtained:

[0024]

[0025] From the expression of the system dynamics equation in the frequency domain, the amplitude ratio X / X0 of the main structure displacement and the ground motion displacement is obtained:

[0026]

[0027] The objective function is obtained by transforming the amplitude ratio X / X0, that is, the square of the amplitude ratio of the main structure displacement to the ground motion displacement R d as follows:

[0028]

[0029] Where μ = m d / m,β=ω d / ω0,γ=ω / ω0,the frequency of the main structure The frequency of the damper α=ξsgn(ω).

[0030] Furthermore, the parameters are obtained by applying the first condition of the fixed point theory to obtain the optimal frequency ratio of the tuned mass rate-independent damper to the main structure:

[0031]

[0032] The optimal stiffness of the piezoelectric tuned mass-rate-independent damper is obtained from the optimal frequency ratio:

[0033] k d opt =m d (β opt ·ω0) 2

[0034] Using the second condition and combining the optimal frequency ratio, the optimal damping ratios of the tuned mass rate-independent damper at fixed points A and B are obtained as follows:

[0035]

[0036]

[0037] The optimal damping ratio of the piezoelectric tuned mass-rate-independent damper is obtained by taking the square average of the optimal damping ratios obtained at two fixed points A and B:

[0038]

[0039] In a second aspect, an embodiment of the present application provides a parameter design method for a piezoelectric tuned mass-rate-independent damper, comprising:

[0040] S101. Based on the conceptual model of the piezoelectric tuned mass-rate-independent damper, establish the system dynamic equation:

[0041]

[0042] Where x = Xe iωt is the main structural displacement, x0=X0e iωt is the ground motion displacement, x d =X d e iωt is the damper displacement; ω is the excitation frequency; X, X0, X d are the main structure displacement amplitude, ground motion displacement amplitude, and damper displacement amplitude, respectively, m d , m are the masses of the damper and the main structure respectively, k d , k are the stiffness of the damper and the main structure respectively, F d is the rate-independent damping force;

[0043] S102. Establish an expression for the rate-independent damping force in the frequency domain:

[0044] F d =2iξk d sgn(ω)(X d -X)e iωt

[0045] Wherein, sgn(ω) is the sign function, ξ is the damping ratio of the damper;

[0046] S103. Based on the dynamic equation of the system and the expression of the rate-independent damping force in the frequency domain, establish the expression of the dynamic equation of the system in the frequency domain:

[0047]

[0048] S104. Derived from the frequency-domain expression of the system's dynamic equation, the amplitude ratio of the main structure displacement to the ground motion displacement is:

[0049]

[0050] S105, deriving the objective function from the amplitude ratio of the main structure displacement to the ground motion displacement, that is, the square of the amplitude ratio X / X0 of the main structure displacement to the ground motion displacement R d as follows:

[0051]

[0052] Where μ = m d / m,β=ω d / ω0,γ=ω / ω0,the frequency of the main structure The frequency of the damper α=ξsgn(ω);

[0053] S106. Optimize the objective function Rd using fixed-point theory to obtain the optimal stiffness and optimal damping ratio of the piezoelectric tuned mass-rate-independent damper:

[0054] k d opt =m d (β opt ·ω0) 2

[0055]

[0056] Furthermore, the fixed-point theory includes the following conditions:

[0057] The |X / X0|-γ curve passes through two fixed points, and the values ​​of |X / X0| at the two fixed points are equal;

[0058] At the two fixed points, the value of |X / X0| reaches its maximum value;

[0059] Furthermore, the objective function R is calculated by using the fixed point theory. d The optimization includes applying the first condition of the fixed point theory to obtain an optimal frequency ratio between the piezoelectric tuned mass rate independent damper and the main structure:

[0060]

[0061] The optimal stiffness of the piezoelectric tuned mass-rate-independent damper is obtained from the optimal frequency ratio:

[0062] k d opt =m d (β opt ·ω0) 2

[0063] Using the second condition and combining the optimal frequency ratio, the optimal damping ratios of the piezoelectric tuned mass rate-independent damper at fixed points A and B are obtained as follows:

[0064]

[0065]

[0066] The optimal damping ratio of the piezoelectric tuned mass-rate-independent damper is obtained by taking the square average of the optimal damping ratios obtained at two fixed points A and B:

[0067] BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a schematic diagram of the structure of a traditional tuned mass damper model;

[0069] Figure 2 1 is a schematic diagram of the structure of a tuned mass rate-independent damper model provided in an embodiment of the present application;

[0070] Figure 3 Schematic diagram of the physical structure of a piezoelectric tuned mass-rate-independent damper provided in an embodiment of the present application;

[0071] Figure 4 Schematic diagram of the structure of a semi-active ball piezoelectric friction self-resetting damper provided in an embodiment of the present application;

[0072] Figure 5Schematic diagram of the structure of the friction plate and slots provided in the embodiment of the present application;

[0073] Figure 6 is a cross-sectional view of the friction plate slot provided in an embodiment of the present application;

[0074] Figure 7 A parameter design method for a piezoelectric tuned mass-rate-independent damper is provided in an embodiment of the present application;

[0075] Figure 8 is a graph of |X / X0|-γ provided in the examples of the present application;

[0076] Figure 9 This is a comparison diagram of the amplitude ratio curves of the damper main structure displacement and ground motion displacement provided by the embodiment of the present application;

[0077] Figure 10 This is a comparison diagram of the damper stroke curves provided in the embodiments of the present application. DETAILED DESCRIPTION

[0078] The following will be combined with the accompanying drawings to clearly and completely describe the technical solutions in the embodiments of the present disclosure. Obviously, the embodiments described are only part of the embodiments of the present disclosure, rather than all the embodiments. Based on the embodiments provided by the present disclosure, all other embodiments obtained by ordinary technicians in this field are within the scope of protection of the present disclosure.

[0079] In the description of the present disclosure, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present disclosure and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present disclosure.

[0080] Unless the context requires otherwise, throughout the specification and claims, the term "comprising" is to be interpreted as having an open, inclusive meaning, that is, "including, but not limited to." For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units that are not listed, or may optionally include other steps or units that are inherent to the process, method, product, or apparatus.

[0081] When describing some embodiments, the term "connected" and its derivatives may be used. For example, when describing some embodiments, the term "connected" may be used to indicate that two or more components are in direct physical or electrical contact with each other. However, the term "connected" may also refer to two or more components that are not in direct contact with each other but still cooperate or interact with each other. The embodiments disclosed herein are not necessarily limited to the contents herein.

[0082] In the context of this disclosure, the meanings of “on,” “over,” and “over” should be interpreted in the broadest manner, so that “on” means not only “directly on something,” but also includes “on something” with intervening features or layers, and “over” or “over” means not only “over” or “above” something, but also includes “over” or “above” something with no intervening features or layers (i.e., directly on something).

[0083] Exemplary embodiments are described herein with reference to cross-sectional and / or plan views that are idealized exemplary drawings. In the drawings, the thicknesses of layers and regions are exaggerated for clarity. Therefore, variations in shape relative to the drawings due to, for example, manufacturing techniques and / or tolerances are contemplated. Therefore, the exemplary embodiments should not be construed as limited to the shapes of the regions shown herein, but rather include deviations in shape due to, for example, manufacturing. Therefore, the regions shown in the drawings are schematic in nature, and their shapes are not intended to illustrate the actual shape of regions of the device and are not intended to limit the scope of the exemplary embodiments.

[0084] To address the aforementioned problem of traditional tuned mass dampers being prone to detuning, which can cause them to malfunction, the present invention provides a piezoelectric tuned mass rate-independent damper that replaces the original linear viscous damping element with a rate-independent linear damping element. This provides a damping force that is independent of vibration frequency.

[0085] In order to optimize the displacement response control effect of the piezoelectric tuned mass-rate-independent damper on the structure under seismic load excitation, the embodiment of the present application proposes a parameter optimization design method for the piezoelectric tuned mass-rate-independent damper.

[0086] The following will be described in detail with reference to the accompanying drawings.

[0087] In the embodiment of the present application, a conventional tuned mass damper is attached to, for example, a single-degree-of-freedom main structure. The conventional tuned mass damper is composed of a mass block, a spring, and a linear viscous damping element. Figure 1 This is a schematic diagram of the traditional tuned mass damper model structure, where x d is the damper displacement, k d is the damper stiffness, md is the mass of the damper, c d is a linear viscous damper element, x is the main structural displacement, k is the main structural stiffness, m is the main structural mass, and x0 is the ground motion displacement.

[0088] When subjected to seismic excitation, a tuned mass damper attached to the single-degree-of-freedom main structure absorbs some of the main structure's vibration energy by altering the structural resonance characteristics, reducing the energy acting on the main structure and, in turn, minimizing the main structure's dynamic response, thereby achieving vibration control. Furthermore, based on this structure, a damper parameter optimization design method—fixed-point theory—has been developed to minimize the peak displacement response of the main structure. By selecting the damper-to-main structure mass ratio and designing the damper using fixed-point theory, the optimal damper design parameters can be obtained: the optimal damper stiffness and optimal damping ratio.

[0089] It should be noted that although the conceptual model provided in the embodiment of the present application is designed based on a single-degree-of-freedom main structure model, in actual use, it can also be a multi-degree-of-freedom main structure, wherein the main structure can be a layer of a multi-degree-of-freedom main structure, and this application does not limit this.

[0090] Figure 2 A schematic diagram of the structure of a tuned mass rate-independent damper model provided in an embodiment of the present application is shown in FIG. Figure 2 As shown, the traditional linear damping element c d Replaced by rate-independent linear damping element c i The difference between the two types of damping is that, in the complex stiffness, the imaginary part of linear viscous damping is proportional to the excitation frequency, while the rate-independent linear damping has a constant imaginary part. Therefore, the rate-independent linear damping can provide a damping force that is independent of the vibration frequency.

[0091] Figure 3 A schematic diagram of the physical structure of a piezoelectric tuned mass-rate-independent damper provided in an embodiment of the present application (for a clearer explanation, the schematic diagram includes the main structure 5), including a mass block 1, a roller 2, a spring 3, a damping element 4, and a main structure 5. The mass block 1 provides the mass m of the damper in the conceptual model. d , roller 2 changes the sliding friction between mass block 1 and main structure 5 into rolling friction, reducing the friction between them, and spring 3 provides the stiffness k of the damper in the conceptual model d , damping element 4 corresponds to the rate-independent linear damping element c i The main structure 5 can be a building floor structure (including floor slabs, columns, walls, etc.).

[0092] In one embodiment provided in this application, the damping element 4 is a semi-active ball piezoelectric friction damper. Figure 4Schematic diagram of the structure of a semi-active ball piezoelectric friction self-resetting damper provided in an embodiment of the present application. Figure 4 As shown, the piezoelectric friction damper includes an actuator rod 4-3, a fixing rod 4-4, a high-strength bolt 4-5, a piezoelectric driver 4-6, an upper steel plate 4-7, a ball 4-8, a friction plate 4-9, and a lower steel plate 4-14. In a feasible embodiment of the present application, the piezoelectric friction damper may also include a fixing bolt 4-1, a spring 4-2, a damper box 4-10, a sleeve 4-11, a fixing nut 4-12, and a high-strength nut 4-13.

[0093] The left and right walls of the damper housing 4-10 have openings for the actuating rod and the fixed rod to extend therethrough. The left end of the damper housing 4-10 is connected to the actuating rod 4-3, which extends through the opening at the left end of the damper housing 4-10 into the damper housing 4-10. A set of springs 4-2 is fixed between the right end baffle of the actuating rod 4-3 and the left wall of the damper housing 4-10. The number of springs in a set of springs 4-2 is at least one, which is not limited in this application. The spring 4-2 has a self-resetting function. The right end baffle of the actuating rod 4-3 is connected to the friction plate 4-9.

[0094] The right end of the damper housing is connected to fixed rod 4-4, which extends through an opening at the right end of damper housing 4-10 and into damper housing 4-10. The left end baffle of fixed rod 4-4 is fixed to the right wall of the damper housing. In this embodiment, the right wall of damper housing 4-10 and the left end baffle of fixed rod 4-4 are connected by welding, but this is not limited to this. The embodiments of this application do not restrict the connection method. A set of springs 4-2 is fixed between the left end baffle of fixed rod 4 and the friction plate. The number of springs in a set of springs 4-2 is at least one, which is not limited in this application. Spring 4-2 has a self-resetting function.

[0095] When an external force acts on the actuating rod 4-3, the actuating rod 4-3 drives the friction plate 4-9 to move, realizing friction energy consumption between the friction plate 4-9 and the upper steel plate 4-7 and the lower steel plate 4-14. The friction force generated by the spring 4-2 and the friction plate 4-9 jointly performs structural vibration reduction control. When the external force is removed, the spring 4-2 plays a reset role.

[0096] The damper housing is mainly assembled with steel plates, which provide support for the spring, position the bolts and rods, and protect the internal structure;

[0097] The left end of the friction plate 4-9 is connected to the actuating rod 4-3 by welding, and the right end is connected to the spring 4-2 by welding, and is connected to the fixed rod 4-4 baffle through the spring 4-2. The upper steel plate 4-7 and the lower steel plate 4-14 sandwich the friction plate 4-9 and fit with the friction plate 4-9 respectively, while ensuring that the friction plate and the upper and lower steel plates can slide relative to each other.

[0098] In this embodiment, the piezoelectric material of the piezoelectric friction actuator is a relaxor ferroelectric. The relaxor ferroelectric has the characteristics of high dielectric constant and large electrostrictive effect, which ensures that the piezoelectric actuator can provide sufficient positive pressure to the friction plate. Figure 4 As shown, the relaxor ferroelectric piezoelectric driver is wrapped with a sleeve 4-11, and a high-strength bolt hole is opened on the upper wall of the damper box 4-10. The relaxor ferroelectric driver and its sleeve are fixedly connected to the damper box 4-10 through high-strength bolts 4-5 and high-strength nuts 4-13. The high-strength nuts 4-13 are applied with a pre-tightening force to ensure that the positive pressure provided by the relaxor ferroelectric piezoelectric driver is transmitted to the friction plate. The relaxor ferroelectric is a cylinder or a rectangular parallelepiped.

[0099] A hole the size of the relaxor ferroelectric driver and its sleeve is provided in the center of the upper steel plate 4-7. The relaxor ferroelectric driver and its sleeve are placed and positioned in the hole. Balls 4-8 are densely spread between the bottom of the relaxor ferroelectric piezoelectric driver and the friction plate. That is, the bottom of the relaxor ferroelectric piezoelectric driver applies positive pressure to the friction plate 4-9 through the balls 4-8. The balls 4-8 are smooth spheres, ellipsoids, or any one or more combinations of cylinders, and the embodiments of the present application are not limited thereto. The addition of the balls greatly reduces the friction force on the bottom of the relaxor ferroelectric. In addition, the relaxor ferroelectric material selected for the relaxor ferroelectric driver has a relatively small height-to-width ratio in its longitudinal cross-section shape, that is, the height of the relaxor ferroelectric material is reduced, its diameter is increased, and the possibility of shear damage is further reduced.

[0100] The upper steel plate 7 and the lower steel plate 4-14 sandwich the friction plate 4-9 in the middle, and bolt holes are respectively provided on the upper steel plate 4-7, the lower steel plate 4-14 and the bottom plate of the damper box 4-10. Figure 5 As shown, a slotted hole 4-91 is provided on the friction plate 4-9, and the fixing bolt 4-1 passes through the bolt hole and the slotted hole from below in sequence through the bottom plate of the damper box 4-10, the lower steel plate 4-14, the friction plate 4-9, the upper steel plate 4-7 and is fixed with a fixing nut 4-12, as shown in FIG. Figure 6 As shown in the cross-sectional view of the friction plate slot, the horizontal length of the slot in the friction plate 4-9 is greater than the diameter of the bolt hole. This ensures that when the friction plate 4-9 moves with the actuator 4-3, there is sufficient space for the fixing bolts 4-1 that secure the upper and lower steel plates 4-7 and 4-14. In this embodiment, the upper and lower steel plates and the friction plate 4-9 are assembled to the damper housing via a total of 4-4 fixing bolts. In practice, the number of fixing bolts may be multiple, for example, greater than 4, and this is not a limitation in this embodiment. The lower surface of the upper steel plate 4-7, the upper surface of the lower steel plate 4-14, and the upper and lower surfaces of the friction plate 4-9 are coated with a hard alloy WC-Co coating.

[0101] When the external force transmitted to the actuating rod 4-3 is relatively small, the tightening force of the high-strength bolts 4-5 and the high-strength nuts 4-13 provide positive pressure for the friction plate 4-9 and the upper and lower steel plates, and the friction force generated by the movement of the actuating rod 4-3 is used to passively dissipate energy. When the external force transmitted to the actuating rod 4-3 is relatively large, the positive pressure of the relaxor ferroelectric on the friction plate 4-9 is adjusted by adjusting the voltage of the external voltage driver, thereby increasing the friction between the friction plate 4-9 and the upper and lower steel plates, thereby achieving semi-active control.

[0102] It should be noted that the semi-active ball piezoelectric friction damper in this embodiment is only one of the preferred embodiments of the present application, and the structure and design of the damping element 4 are not limited to the above Figure 3 For example, the damping element 4 can also be a magnetorheological damper. Any damper whose damping force can be adjusted or which passively realizes such damping force is within the protection scope of this application, and this application does not impose any restrictions on this.

[0103] In the above embodiment, after replacing the damping element of the traditional tuned mass damper, a piezoelectric tuned mass rate-independent damper is obtained. In order to optimize the displacement response control effect of the piezoelectric tuned mass rate-independent damper on the structure under external excitation such as seismic load excitation, the present invention is based on the fixed-point theory and aims to minimize the peak displacement response of the main structure (the displacement amplitude ratio at two fixed points is equal and reaches a peak value), and discloses a parameter optimization design method for a piezoelectric tuned mass rate-independent damper, which will be described in detail in conjunction with the embodiments below.

[0104] For the convenience of explanation, let ω be the excitation frequency, x = Xe iωt is the main structural displacement, x0=X0e iωt is the ground motion displacement, x d =X d e iωt is the damper displacement, where X d is the damper amplitude, X is the main structure amplitude, X0 is the ground motion amplitude; k and k d are the main structure stiffness and damper stiffness, m and m respectively d are the main structure mass and damper mass, respectively, so they are not repeated; ξ is the damping ratio of the damper.

[0105] Further, see Figure 7 , Figure 7 A parameter design method for a piezoelectric tuned mass-rate-independent damper is provided, comprising the following steps:

[0106] S101. Based on the tuned mass rate-independent damper model described above, the system dynamics equation is established as follows:

[0107]

[0108] In the above formula, x d -x is the relative displacement between the damping element 4 and the main structure, such as the building floor structure, that is, the deformation of the spring 3, F d is the rate-independent damping force.

[0109] S102. The expression of the rate-independent damping force in the frequency domain is:

[0110] F d =2iξk d sgn(ω)(X d -X)e iωt (2)

[0111] In the above formula, sgn(ω) is a sign function. In some embodiments, the damping force can be achieved by the semi-active ball piezoelectric friction damper as described above: according to the relative displacement between the damper and the main structure, such as the building floor structure, the deformation of the spring 3, that is, (x d -x)=(X d -X)e iωt , and substitute it into formula (2) to calculate the corresponding damping force, and adjust the input voltage value of the semi-active ball piezoelectric friction damper 4 in a semi-active control manner so that it outputs the corresponding damping force.

[0112] It should be noted that the structure and design of the damping element 4 are not limited to the example of the above-mentioned semi-active ball piezoelectric friction damper. Any damper with adjustable damping force or passive damping force is within the scope of protection of this application, and this application does not impose any restrictions on this.

[0113] S103. Substituting formula (2) into formula (1), we can obtain the expression of the dynamic equation in the frequency domain:

[0114]

[0115] S104. The amplitude ratio of the main structure displacement and the ground motion displacement can be further derived from Formula 3 as follows:

[0116]

[0117] S105. According to formula (4), the square of the amplitude ratio of the main structure displacement to the ground motion displacement can be further obtained: d as follows:

[0118]

[0119] In order to facilitate further derivation and calculation, the dimensionless parameter μ=m is introduced d / m,β=ω d / ω0,γ=ω / ω0,α=ξsgn(ω), where the main structural frequency Damper frequency R d Simplified as follows:

[0120]

[0121] S106, given the mass ratio μ value, apply the following two conditions of the fixed point theory to the objective function R d To optimize:

[0122] (1) The |X / X0|-γ curve passes through two fixed points, and the values ​​of |X / X0| at the two fixed points are equal;

[0123] (2) At the two fixed points, the value of |X / X0| reaches its maximum value.

[0124] The above two optimization conditions will be used to obtain the optimal frequency ratio of the piezoelectric tuned mass-rate-independent damper and the single-degree-of-freedom main structure, and further the optimal stiffness value and the optimal damping ratio of the piezoelectric tuned mass-rate-independent damper will be obtained from the optimal frequency ratio.

[0125] First, we use the first optimization condition, namely, the equal values ​​of |X / X0| at the two fixed points, to solve the optimal frequency ratio of the damper to the main structure. Since the amplitude-frequency curves |X / X0|-γ of different damping ratios all pass through the two fixed points, and the values ​​of |X / X0| at the two fixed points are equal, let the damping ratio of the damper tend to 0 and ∞ respectively. According to formula (6), we can obtain:

[0126]

[0127]

[0128] At a fixed point, the right sides of equations (7) and (8) are equal:

[0129]

[0130] After removing the absolute value, it can be simplified to:

[0131] -2γ 4 (1+μ)+γ 2 [2+μ+2β 2 (1+μ) 2 ]-2β 2 (1+μ)=0 (10)

[0132] Assume that the two fixed points are A and B. Since the values ​​of γ at the two fixed points A and B are the roots of formula (10), according to Vieta's theorem:

[0133]

[0134]

[0135] At the same time, the values ​​on the right side of equation (8) corresponding to the two fixed points A and B must also be equal:

[0136]

[0137] After removing the absolute value, we can simplify it to get:

[0138]

[0139] According to equations (11), (12) and (14), the optimal frequency ratio of the piezoelectric tuned mass-rate-independent damper to the single-degree-of-freedom main structure can be solved as:

[0140]

[0141] By the damper frequency The damper stiffness can be obtained:

[0142] k d =m d ω d 2 (16)

[0144] The frequency ratio of the damper to the main structure is β = ω d / ω0, the relationship between the damper stiffness and the frequency ratio β can be further obtained as follows:

[0145] k d =m d (β·ω0) 2 (17)

[0146] Among them, the main structure frequency Is a fixed value.

[0147] Combining the optimal frequency ratio of the piezoelectric tuned mass-rate-independent damper and the single-degree-of-freedom main structure in formula (15), the optimal stiffness of the piezoelectric tuned mass-rate-independent damper can be obtained as:

[0148] k d opt =m d (β opt ·ω0) 2 (18)

[0149] After obtaining the optimal frequency ratio of the piezoelectric tuned mass rate-independent damper and the single-degree-of-freedom main structure as described above, the second optimization condition can be used, that is, the value of |X / X0| reaches the maximum at two fixed points to solve the optimal damping ratio of the piezoelectric tuned mass rate-independent damper. The value of |X / X0| reaches the maximum at the two fixed points, which also means that the square of |X / X0| R d Also reaches the maximum value, then at two fixed points R d The derivative of Γ is 0, that is:

[0150]

[0151] Therefore, by taking the derivative of formula (6), we can get:

[0152]

[0153] Combined with formula (15), the optimal damping ratio of the piezoelectric tuned mass rate-independent damper at fixed points A and B can be obtained as follows:

[0154]

[0155]

[0156] The optimal damping ratio of the piezoelectric tuned mass-rate-independent damper can be obtained by taking the square average of the optimal damping ratios obtained at fixed points A and B:

[0157]

[0158] The above conceptual model is designed based on a single-degree-of-freedom main structure model, but in actual use, it can also be a multi-degree-of-freedom main structure, where the main structure can be a layer of the multi-degree-of-freedom main structure, and this application does not limit this.

[0159] The present invention optimizes the design of the piezoelectric tuned mass rate-independent damper through the fixed-point theory, and obtains the optimal damping ratio of the piezoelectric tuned mass rate-independent damper, such as Figure 8 As shown in Figure 2, under the condition of optimal damping ratio, the peak displacement response of the main structure is reduced to the minimum (the displacement amplitude ratio is equal and reaches the peak value at the fixed point).

[0160] The control effects of the piezoelectric tuned mass rate-independent damper (TMRD) and the traditional tuned mass damper (TMD) using linear viscous damping elements are further compared. Figure 9The following is a comparison of the amplitude ratio curves of the main structure displacement and ground motion displacement of the two dampers under the same damping ratio, for example, α = 0.05 and α = 0.20. From the comparison chart, it can be seen that under a given damping ratio, the piezoelectric tuned mass rate-independent damper has a smaller amplitude ratio of the main structure displacement to the ground motion displacement than the traditional tuned mass damper, and has a better control effect on the structural displacement response than the traditional tuned mass damper.

[0161] Figure 10 The following is a comparison chart of the two damper strokes under the same damping ratio, for example, α=0.05 and α=0.20. It can be seen from the comparison chart that, under a given damping ratio, the piezoelectric tuned mass-independent damper also shows significant advantages in the stroke of the damper itself. Its damper stroke is smaller, and there is no need for a very large space between the damper and the main structure to prevent collision, which facilitates the installation of the damper.

[0162] By using the piezoelectric tuned mass rate-independent damper and its parameter optimization design method in the embodiment shown above, the original linear viscous damping element in the damper is replaced with a rate-independent linear damping element, thereby providing a damping force independent of the vibration frequency.

[0163] Based on the displacement transfer function of the main structure and ground motion, and with the goal of minimizing the peak displacement response of the main structure, a parameter optimization design method for a piezoelectric tuned mass-rate-independent damper is proposed, so that the piezoelectric tuned mass-rate-independent damper can achieve the optimal control effect on the displacement response of the structure under seismic load excitation; and the damper itself also has significant advantages in its stroke, which facilitates the installation of the damper.

[0164] The above embodiments are merely descriptions of preferred implementation methods of the present application and are not intended to limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions made by ordinary technicians in this field should fall within the scope of protection of the claims of the present application.

Claims

1. A parameter design method for a piezoelectric tuned mass-rate-independent damper, comprising: S101. Based on the conceptual model of the piezoelectric tuned mass-rate-independent damper, establish the system dynamic equation: Where x = Xe iωt is the main structural displacement, x0=X0e iωt is the ground motion displacement, x d =X d e iωt is the damper displacement; ω is the excitation frequency; X, X0, X d are the main structure displacement amplitude, ground motion displacement amplitude, and damper displacement amplitude, respectively, m d , m are the masses of the damper and the main structure respectively, k d , k are the stiffness of the damper and the main structure respectively, F d is the rate-independent damping force; S102. Establish an expression for the rate-independent damping force in the frequency domain: F d =2iξk d sgn(ω)(X d -X)e iωt Wherein, sgn(ω) is the sign function, ξ is the damping ratio of the damper; S103. Based on the dynamic equation of the system and the expression of the rate-independent damping force in the frequency domain, establish the expression of the dynamic equation of the system in the frequency domain: S104. Derived from the frequency-domain expression of the system's dynamic equation, the amplitude ratio of the main structure displacement to the ground motion displacement is: S105, deriving the objective function from the amplitude ratio of the main structure displacement to the ground motion displacement, that is, the square of the amplitude ratio X / X0 of the main structure displacement to the ground motion displacement R d as follows: Where μ = m d / m,β=ω d / ω0,γ=ω / ω0,the frequency of the main structure The frequency of the damper α=ξsgn(ω); S106. Optimize the objective function Rd using fixed-point theory to obtain the optimal stiffness and optimal damping ratio of the piezoelectric tuned mass-rate-independent damper: k d opt =m d (b opt ·ω0) 2 Among them, β opt The optimal frequency ratio for the main structure.

2. The method according to claim 1, characterized in that The fixed point theory These include the following conditions: The first condition: the |X / X0|-γ curve passes through two fixed points, and the values ​​of |X / X0| at the two fixed points are equal; The second condition: At the two fixed points, the value of |X / X0| reaches its maximum value.

3. The method according to claim 2, characterized in that The objective function R is calculated by using the fixed point theory. d The optimization includes applying the first condition of the fixed point theory to obtain the optimal frequency ratio of the piezoelectric tuned mass rate independent damper to the main structure: The optimal stiffness of the tuned mass rate-independent damper is obtained from the optimal frequency ratio: k d opt =m d (b opt ·ω0) 2 Using the second condition and combining the optimal frequency ratio, the optimal damping ratios of the piezoelectric tuned mass rate-independent damper at fixed points A and B are obtained as follows: The optimal damping ratio of the piezoelectric tuned mass-rate-independent damper is obtained by taking the square average of the optimal damping ratios obtained at two fixed points A and B:

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