CN117574685A

CN117574685A - Damper optimization method, device, electronic equipment and storage medium

Info

Publication number: CN117574685A
Application number: CN202410051180.XA
Authority: CN
Inventors: 曾璧环; 孔凡坊; 杨德栋; 潘勃利; 占鹭林; 林世溪; 张瑞; 张扬; 郑鑫磊
Original assignee: State Grid Zhejiang Electric Power Co Ltd; Wenzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd; Power Construction of Wenzhou
Current assignee: State Grid Zhejiang Electric Power Co Ltd; Wenzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd; Power Construction of Wenzhou
Priority date: 2024-01-15
Filing date: 2024-01-15
Publication date: 2024-02-20
Anticipated expiration: 2044-01-15
Also published as: CN117574685B

Abstract

The disclosure provides a damper optimization method, a damper optimization device, electronic equipment and a storage medium. The specific implementation scheme is as follows: the displacement transfer function and the speed transfer function of the SDOF system are optimized by adopting the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same and the principle that the extreme value of the transfer function is positioned at the two fixed points, so that the parameter sets of the optimal stiffness ratio and the optimal damping ratio of the two functions are obtained; optimizing the displacement transfer function and the speed transfer function by adopting root mean square response to obtain parameter sets of the optimal stiffness ratio and the optimal damping ratio of the two functions respectively; thereby selecting a target parameter set of the TID from the four parameter sets. By adopting the technical scheme disclosed by the invention, the shock absorption effect of the TID can be optimized.

Description

Damper optimization method, device, electronic equipment and storage medium

Technical Field

The present disclosure relates to the field of computer technology, and in particular, to the field of damper optimization. The disclosure relates to a damper optimization method, a damper optimization device, an electronic device and a storage medium.

Background

The building structure has higher vulnerability under the action of earthquake, and the main reason is that the self-vibration frequency of the structure is similar to the excellent frequency of external excitation, so that the vibration response is amplified. There are numerous methods for reducing seismic response dissipation devices and for designing these devices for different structures. Among them, tuned mass dampers (Tuned mass damper, TMD) are most widely used, with varying degrees of application in electronics, mechanics, and construction. Because the weight, size and height of the building structure are much larger than those of other equipment, the load condition is more complex, and larger size and mass are needed to achieve a certain vibration control effect. Meanwhile, for a structure with a large mass participation coefficient, in a high-intensity area and a seismic frequent area, the realization of the TMD-based wide-frequency vibration reduction is difficult.

In recent years, a vibration reduction (isolation) technique based on an inertial unit has been developed. Initially, a concept of a ball screw inertial container and a basic form of a rack-and-pinion inertial container are provided based on an electromechanical similarity theory, and a hydraulic inertial container is designed, so that the structure is simpler and the robustness is stronger. Subsequently, vibration dampers based on different topological connection patterns of the inertial unit are proposed, such as tuned viscous mass dampers (Tuned viscous mass damper, TVMD) and tuned inertial dampers (Tuned inerter damper, TID), etc. Meanwhile, a large number of researchers have proposed an optimal design method for an inertial navigation system. In some studies, a simple formula for TVMD optimization design was derived based on classical tuning theory. In some researches, parameter optimization researches are carried out on single-degree-of-freedom structures for installing different inertial measurement units, meanwhile, the inherent damping of the original structure and the output cost of the inertial measurement units are considered, the defect of tuning theory is overcome, and a general type optimization design method of a three-element inertial measurement unit damping system is provided. In some studies, a ball screw inertial system coupled to a support has been proposed. In some researches, the inertial damping system is applied to high-rise structures such as a chimney and a wind power tower, theoretical analysis and parameter optimization analysis of the system are performed, and the effectiveness of the inertial damping system in the high-rise structures is proved. At present, although some stone researches have been carried out on the inertial damping system for practical engineering, most of researches on the inertial damping system are still in a theoretical analysis and simulation stage, and only a simplified mechanical model is used for the vibration reduction and isolation analysis of various structures.

In general, an inertial tuned absorber consists of stiffness, damping and inertial volume, and is a three element vibration damping system. In some studies, based onH _∞ The analytic expression of the optimal rigidity ratio and the damping ratio can be obtained by a fixed-point method proposed by an optimization theory; at the same time adoptH ₂ Optimization theory can also derive closed-loop solution expressions, but both methods typically require empirical determination of the inertial ratio. In some researches, analytical calculation and optimization researches are carried out on a three-element inertial damping system, and a series of global optimization methods for simultaneously determining the optimal inertial ratio, damping ratio and stiffness ratio are determined. However, most of the optimized inertial system designs are developed by taking the reduced displacement or acceleration of the original structure as an objective function, and researches show that,the optimal parameter expression of displacement and acceleration indexes and the damping effect of the inertial-to-capacitance system are adopted to be slightly different.

In order to continuously define the energy consumption and vibration reduction mechanism of the inertial energy system, the embodiment of the disclosure selects a typical three-element inertial energy vibration damper TID as a research object, establishes a Single-degree-of-freedom (SDOF) system motion control equation for installing the TID, and further provides an optimization method for the TID.

Disclosure of Invention

The present disclosure provides a damper optimization method, apparatus, electronic device, and storage medium, which can solve the above-mentioned problems.

According to an aspect of the present disclosure, there is provided a damper optimization method including:

performing mechanical analysis on a single-degree-of-freedom SDOF system deployed with a tuned inertial damping device TID to obtain a displacement transfer function and a speed transfer function of the SDOF system;

based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, the displacement transfer function and the velocity transfer function are respectively calculated to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the velocity transfer function;

based on the principle that the extreme value of the transfer function is positioned at the two fixed points, calculating the displacement transfer function and the speed transfer function respectively to obtain a first optimal damping ratio of the displacement transfer function and a second optimal damping ratio of the speed transfer function;

substituting the displacement transfer function and the speed transfer function into a root mean square response function respectively to obtain a displacement root mean square response function and a speed root mean square response function of the SDOF system;

Taking the rigidity ratio and the damping ratio as partial derivatives respectively, and taking a derivation result as zero, and respectively carrying out derivation calculation on the displacement root mean square response function and the velocity root mean square response function to obtain a third optimal rigidity ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal rigidity ratio and a fourth optimal damping ratio of the velocity transfer function;

and determining a target parameter set of the TID from the parameter sets of the first optimal stiffness ratio and the first optimal damping ratio, the parameter sets of the second optimal stiffness ratio and the second optimal damping ratio, the parameter sets of the third optimal stiffness ratio and the third optimal damping ratio, and the parameter sets of the fourth optimal stiffness ratio and the fourth optimal damping ratio.

According to another aspect of the present disclosure, there is provided a damper optimizing apparatus including:

the transfer function determining module is used for carrying out mechanical analysis on a single-degree-of-freedom SDOF system deployed with a tuned inertial damping device TID to obtain a displacement transfer function and a speed transfer function of the SDOF system;

the first fixed point calculating module is used for calculating the displacement transfer function and the speed transfer function respectively based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, so as to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the speed transfer function;

The second fixed point calculation module is used for calculating the displacement transfer function and the speed transfer function based on the principle that the extreme value of the transfer function is at the two fixed points, so as to obtain a first optimal damping ratio of the displacement transfer function and a second optimal damping ratio of the speed transfer function;

the root mean square calculation module is used for substituting the displacement transfer function and the speed transfer function into a root mean square response function respectively to obtain a displacement root mean square response function and a speed root mean square response function of the SDOF system;

the random excitation calculation module is used for taking the rigidity ratio and the damping ratio as partial derivatives respectively, taking a derivation result as zero, and performing derivation calculation on the displacement root mean square response function and the speed root mean square response function respectively to obtain a third optimal rigidity ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal rigidity ratio and a fourth optimal damping ratio of the speed transfer function;

the target parameter determining module is configured to determine a target parameter set of the TID from parameter sets of the first optimal stiffness ratio and the first optimal damping ratio, parameter sets of the second optimal stiffness ratio and the second optimal damping ratio, parameter sets of the third optimal stiffness ratio and the third optimal damping ratio, and parameter sets of the fourth optimal stiffness ratio and the fourth optimal damping ratio.

According to another aspect of the present disclosure, there is provided an electronic device including: at least one processor, and a memory communicatively coupled to the at least one processor;

wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform any one of the damper optimization methods of the disclosed embodiments.

According to another aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform any one of the damper optimization methods of the embodiments of the present disclosure.

According to the technology disclosed by the invention, aiming at a displacement transfer function and a speed transfer function of a single-degree-of-freedom SDOF system with a tuned inertial damper TID, a principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same and a principle that the extremum of the transfer function is positioned at the two fixed points are adopted, and a first optimal stiffness ratio and a first optimal damping ratio of the displacement transfer function and a second optimal stiffness ratio and a second optimal damping ratio of the speed transfer function are calculated; and simultaneously, under random excitation, substituting the displacement transfer function and the speed transfer function into root mean square response functions to obtain a displacement root mean square response function and a speed root mean square response function of the SDOF system, and then taking the rigidity ratio and the damping ratio as partial derivatives and taking a derivative result as zero to respectively conduct derivative calculation on the displacement root mean square response function and the speed root mean square response function to obtain a third optimal rigidity ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal rigidity ratio and a fourth optimal damping ratio of the speed transfer function. Thus, four parameter sets of the TID are obtained. Then, the target parameter set of the TID is preferentially selected from the four parameter sets of the TID, so that the optimization effect of the TID is improved.

It should be understood that the description in this section is not intended to identify key or critical features of the embodiments of the disclosure, nor is it intended to be used to limit the scope of the disclosure. Other features of the present disclosure will become apparent from the following specification.

Drawings

The drawings are for a better understanding of the present solution and are not to be construed as limiting the present disclosure. Wherein:

FIG. 1 is a flow chart of a damper optimization method of an embodiment of the present disclosure;

FIG. 2 is a block diagram of an inertial unit of an embodiment of the present disclosure;

FIG. 3 is a block diagram of a TID of an embodiment of the present disclosure;

FIG. 4 is a block diagram of an SDOF of an embodiment of the present disclosure;

FIG. 5 is a graph of the displacement transfer function of SDOF of an embodiment of the present disclosure;

FIG. 6 is a graph of a velocity transfer function of SDOF of an embodiment of the present disclosure;

FIG. 7 is a block diagram of a damper optimizing apparatus according to an embodiment of the present disclosure;

FIG. 8 is a block diagram of an electronic device of a damper optimization method of an embodiment of the present disclosure.

Detailed Description

Exemplary embodiments of the present disclosure are described below in conjunction with the accompanying drawings, which include various details of the embodiments of the present disclosure to facilitate understanding, and should be considered as merely exemplary. Accordingly, one of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.

FIG. 1 is a flow chart of a damper optimization method of an embodiment of the present disclosure.

As shown in fig. 1, the damper optimization method may include:

s110, carrying out mechanical analysis on a single-degree-of-freedom SDOF system deployed with a tuned inertial damping device TID to obtain a displacement transfer function and a speed transfer function of the SDOF system;

s120, based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, the displacement transfer function and the speed transfer function are respectively calculated to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the speed transfer function;

s130, respectively calculating a displacement transfer function and a speed transfer function based on the principle that the extreme value of the transfer function is positioned at two fixed points to obtain a first optimal damping ratio of the displacement transfer function and a second optimal damping ratio of the speed transfer function;

s140, substituting the displacement transfer function and the speed transfer function into root mean square response functions respectively to obtain a displacement root mean square response function and a speed root mean square response function of the SDOF system;

s150, taking the rigidity ratio and the damping ratio as partial derivatives respectively, and taking a derivation result as zero, and respectively performing derivation calculation on the displacement root mean square response function and the speed root mean square response function to obtain a third optimal rigidity ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal rigidity ratio and a fourth optimal damping ratio of the speed transfer function;

S160, determining a target parameter set of the TID from the parameter set of the first optimal stiffness ratio and the first optimal damping ratio, the parameter set of the second optimal stiffness ratio and the second optimal damping ratio, the parameter set of the third optimal stiffness ratio and the third optimal damping ratio, and the parameter set of the fourth optimal stiffness ratio and the fourth optimal damping ratio.

For the tuning inertial damper TID, as shown in FIG. 2, compared with a common mass unit, the inertial unit can realize an apparent mass amplification effect in a ball guide wire rotation mode and the like, and two ends of the unit have different accelerations, and the output force is also in direct proportion to the relative acceleration of the two ends, and can be expressed as:

（1）

wherein,f _I is the output force of the inertial unit,a ₁ anda ₂ for the acceleration of both ends,bis the inertial coefficient of the inertial unit, which may also be referred to as the inertial coefficient of the TID.

As shown in fig. 3, which shows a mechanical model of TID, wherein,k _d 、c _d andbis the rigidity, damping and inertial coefficient of the TID.

As shown in fig. 4, which shows a mechanical model of a single degree of freedom SDOF system deployed with a tuned inertial damper TID.m、kAndcthe mass, rigidity and damping coefficient of the original structure are respectively. The following describes the mechanical analysis of the SDOF system to obtain the displacement transfer function and the velocity transfer function of the SDOF system, specifically as follows.

Is provided withuAndu _d the displacement responses of SDOF and TID, respectively, equation (2) is the motion control equation of SDOF that arranges TID:

（2）

wherein,a _g acceleration is excited for earthquake motion.

Meanwhile, parameters defining SDOF and TID are as follows:

（3）

（4）

wherein,ζ ₀ andωdamping ratio and circular frequency for SDOF;κ、μandζthe stiffness ratio, the inertial ratio and the nominal damping ratio of the TID, respectively.

Therefore, the above (2) is written as the following formula:

（5）

the laplace transform is performed on the above formula (5), resulting in the following formula:

（6）

wherein,s=iΩ，Ωfor the ground vibration excitation frequency,iin units of imaginary numbers,U、U _d andA _g respectively isu、u _d Anda _g is a laplace transform of (c). Therefore, solving the linear equation set (6) can obtainUThe following are provided:

（7）

thus, the displacement transfer function of SDOFH _U And a velocity transfer functionH _V The following are provided:

（8）

therefore, according to the mechanical analysis process, the displacement transfer function and the velocity transfer function of the SDOF system can be obtained.

It will be appreciated that the two steps S120 and S130 may be performed in parallel, or may be performed sequentially, and that the steps S140 and S150 may look at one step, and that the steps S120 and S130 may be performed in parallel.

It will be appreciated that steps S120 and S130 described above are processes for minimizing the maximum amplitude of an SDOF system that is excited by simple harmonics, and may be referred to as H _∞ And (5) optimizing. I.e. to minimize the resonance response in the frequency domain, the resulting set of TID parameters. Wherein the TID parameter set includes an optimal stiffness ratio and an optimal damping ratio.The above steps S120 and S130 can also be considered as solving the optimal stiffness ratio and the optimal damping ratio of TID using the fixed point rule.

As shown in fig. 5 and 6, if the inherent damping of the SDOF system is ignored, there is a ratio of the displacement transfer function and the velocity transfer function of the SDOF system in which the TID is installed to the nominal dampingζIndependent of setpoint P and setpoint Q, wherein,β=Ω/ωis the relative excitation frequency. Thus, the fixed point rule is: 1) The transfer function passes through two points P and Q; 2) The transfer function takes extreme values at two points. The transfer function is a displacement transfer function and a speed transfer function.

Therefore, the displacement transfer function and the speed transfer function are respectively solved by utilizing the fixed point rule, and corresponding TID parameter sets are respectively obtained.

It will be appreciated that steps S140 and S150 described above are a process of minimizing the total vibrational energy of the randomly excited SDOF system at all frequencies, and may be referred to asH ₂ And (5) optimizing.

It is understood that any one parameter set among the parameter set of the first optimal stiffness ratio and the first optimal damping ratio, the parameter set of the second optimal stiffness ratio and the second optimal damping ratio, the parameter set of the third optimal stiffness ratio and the third optimal damping ratio, and the parameter set of the fourth optimal stiffness ratio and the fourth optimal damping ratio is selected as the target parameter set of the TID. Or, according to the performance requirement of the TID or SDOF, selecting a corresponding parameter set from the parameter sets as a target parameter set of the TID.

According to the embodiment, for the displacement transfer function and the speed transfer function of the single-degree-of-freedom SDOF system with the tuned inertial damper TID, a principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same and a principle that the extremum of the transfer function is positioned at the two fixed points are adopted, so that the first optimal stiffness ratio and the first optimal damping ratio of the displacement transfer function and the second optimal stiffness ratio and the second optimal damping ratio of the speed transfer function are calculated; and simultaneously, under random excitation, substituting the displacement transfer function and the speed transfer function into root mean square response functions to obtain a displacement root mean square response function and a speed root mean square response function of the SDOF system, and then taking the rigidity ratio and the damping ratio as partial derivatives and taking a derivative result as zero to respectively conduct derivative calculation on the displacement root mean square response function and the speed root mean square response function to obtain a third optimal rigidity ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal rigidity ratio and a fourth optimal damping ratio of the speed transfer function. Thus, four parameter sets of the TID are obtained. Then, the target parameter set of the TID is preferentially selected from the four parameter sets of the TID, so that the optimization effect of the TID is improved.

In one embodiment, based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, the displacement transfer function and the velocity transfer function are respectively calculated to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the velocity transfer function, the method comprises the following steps: determining a displacement transfer function ignoring the inherent damping ratio of the SDOF system and a velocity transfer function ignoring the inherent damping ratio of the SDOF system, respectively, based on the displacement transfer function and the velocity transfer function; performing modular square calculation on the displacement transfer function neglecting the inherent damping ratio of the SDOF system to obtain a normalized displacement transfer function; performing modular square calculation on a speed transfer function neglecting the inherent damping ratio of the SDOF system to obtain a normalized speed transfer function; based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, the normalized displacement transfer function and the normalized velocity transfer function are respectively calculated to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the velocity transfer function.

Illustratively, according to the optimization principle of the fixed point method, the position of the non-zero fixed point should be determined first. If the inherent damping ratio of the SDOF system is ignored, the displacement transfer functionH _U And a velocity transfer functionH _V The method comprises the following steps:

（9）

（10）

taking the displacement transfer function as an example, the displacement transfer function of the inherent damping ratio of the SDOF system will be ignoredH _U Taking the square modulus, the normalized expression of the square of the modulus can be obtained:

（11）

similarly, the velocity transfer function for ignoring the inherent damping ratio of an SDOF systemH _V Taking the square modulus, a normalized representation of the modulus squared thereof can also be obtained. Here, this is not a list.

According to the embodiment, the inherent damping of the SDOF system is ignored for the displacement transfer function and the velocity transfer function of the SDOF system, and then the square mode of the SDOF system is taken to obtain the normalized expression of the two transfer functions, so that the first optimal stiffness ratio of the displacement transfer function and the second optimal stiffness ratio of the velocity transfer function are conveniently obtained by subsequent calculation by adopting a fixed point rule.

In one embodiment, based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, the normalized displacement transfer function and the normalized velocity transfer function are respectively calculated to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the velocity transfer function, the method comprises the following steps:

Under the principle that the normalized displacement transfer function passes through the first fixed point and the second fixed point under any damping ratio, respectively inputting the normalized displacement transfer function with the damping ratio of 0 and the damping ratio of infinity, and making two results output by the normalized displacement transfer function equal to each other to obtain a first equation;

solving the first equation to obtain the relative excitation frequency of the first fixed point and the relative excitation frequency of the second fixed point;

respectively inputting the square of the relative excitation frequency of the first fixed point and the square of the relative excitation frequency of the second fixed point into a normalized displacement transfer function, and making the two results output by the normalized displacement transfer function equal to obtain a second equation;

solving an equation set consisting of a first equation and a second equation to obtain a first optimal stiffness ratio of a displacement transfer function;

under the principle that the normalized speed transfer function passes through the third fixed point and the fourth fixed point under any damping ratio, respectively inputting the damping ratio of 0 and the damping ratio of infinity into the normalized speed transfer function, and equalizing two results output by the normalized speed transfer function to obtain a third equation;

solving the third equation to obtain the relative excitation frequency of the third fixed point and the relative excitation frequency of the fourth fixed point;

Respectively inputting the square of the relative excitation frequency of the third fixed point and the square of the relative excitation frequency of the fourth fixed point into a normalized speed transfer function, and making the two results output by the normalized speed transfer function equal to obtain a fourth equation;

and solving an equation set formed by the third equation and the fourth equation to obtain a second optimal stiffness ratio of the speed transfer function.

It will be appreciated that the process of solving the first optimal stiffness ratio of the displacement transfer function is the same as the process of solving the second optimal stiffness ratio of the velocity transfer function. Therefore, a procedure for solving the first optimal stiffness ratio of the displacement transfer function will be specifically described below as an example. Specifically, the following is described.

Since one of the fixed point rules is at any damping ratioζThe transfer function passes through the fixed point at any value, e.g. for the displacement transfer function, the normalized displacement transfer function passes through the first fixed point and the second fixed point at any damping ratio, thusζ=0Andζ=∞substituting formula (11) can give the following formula:

（12）

the following formula can be obtained by sorting the formula (12):

（13）

solving the equation (13) to obtain the relative excitation frequency of the first fixed point and the second fixed pointβ _P Andβ _Q the following formula:

（14）

Wherein,λ _P =β _P ² ，λ _Q =β _Q ² 。

since for the displacement transfer function, the normalized displacement transfer function passes through the first fixed point and the second fixed point under any damping ratio, the displacement transfer function has the same value at the first fixed point and the second fixed point, and the following formula needs to be satisfied:

（15）

the formula (15) is arranged to obtain:

（16）

it will be appreciated that (13) above is the first equation above and (16) above is the second equation above. Solving the first equation and the second equation set to obtain the optimal stiffness ratio of the displacement transfer function, that is, the first optimal stiffness ratio, as follows:

（17）

similarly, by similarly optimizing the speed transfer function according to the above-described calculation procedures (12) to (17), an optimum stiffness ratio of the speed transfer function, that is, the above-described second optimum stiffness ratio can be obtained as follows:

（18）

according to the above embodiment, the damping ratio is set at any arbitrary damping ratioζThe transfer function under the value is input into the transfer function respectively with the damping ratio of 0 and the damping ratio of infinity according to the principle of fixed points, and two results output by the transfer function are equal to each other, so as to obtain a first equation, and then the first equation is solved to obtain the relative excitation frequency of the first fixed point and the relative excitation frequency of the second fixed point; respectively inputting squares of the two functions into a transfer function, and making two results output by the transfer function equal to obtain a second equation; finally, solving the two equations can obtain the optimal stiffness ratio of the transfer function.

In one embodiment, based on the principle that the extreme value of the transfer function is located at two fixed points, the displacement transfer function and the velocity transfer function are respectively calculated to obtain a first optimal damping ratio of the displacement transfer function and a second optimal damping ratio of the velocity transfer function, including:

under the principle that the extremum of the normalized displacement transfer function is positioned at the first fixed point and the second fixed point, respectively inputting the square of the relative excitation frequency of the first fixed point and the square of the relative excitation frequency of the second fixed point into the normalized displacement transfer function, deriving the normalized displacement transfer function, and solving an equation enabling the two derived results to be zero to obtain the optimal damping ratio of the normalized displacement transfer function at the first fixed point and the optimal damping ratio at the second fixed point;

solving the square root of the mean value of the square sum of the optimal damping ratio at the first fixed point and the optimal damping ratio at the second fixed point to obtain a first optimal damping ratio;

under the principle that the extremum of the normalized speed transfer function is positioned at the third fixed point and the fourth fixed point, respectively inputting the square of the relative excitation frequency of the third fixed point and the square of the relative excitation frequency of the fourth fixed point into the normalized speed transfer function, deriving the normalized speed transfer function, and solving an equation enabling the obtained two derived results to be zero to obtain the optimal damping ratio of the normalized speed transfer function at the third fixed point and the optimal damping ratio at the fourth fixed point;

And solving the square root of the mean value of the square sum of the optimal damping ratio at the third fixed point and the optimal damping ratio at the fourth fixed point to obtain a second optimal damping ratio.

It will be appreciated that the process of solving the first optimal damping ratio of the displacement transfer function is the same as the process of solving the second optimal damping ratio of the velocity transfer function. Therefore, a procedure for solving the first optimal damping ratio of the displacement transfer function will be specifically described below as an example. Specifically, the following is described.

Illustratively, since the second of the fixed point rules takes extremum for the transfer function at two fixed points, e.g., taking the displacement transfer function as an example, the displacement transfer function takes extremum at the first and second fixed points, the normalized displacement transfer function can be optimized using extremum conditions as follows:

（19）

the optimal damping ratio of the normalized displacement transfer function at the first fixed point can be calculated according to the formula (19)ζ _opt,P And normalizing the optimal damping ratio of the displacement transfer function at the second pointζ _opt,Q . Then, the square root obtained by solving the mean value of the square sums of the two is used as the optimal nominal damping ratio of the displacement transfer function, namely the first optimal damping ratio, as follows:

（20）

Similarly, by similarly optimizing the speed transfer function according to the calculation procedures of (19) to (20), an optimum nominal damping ratio of the speed transfer function, that is, the second optimum damping ratio, can be obtained as follows:

（21）

according to the above embodiment, under the principle that the extremum of the transfer function is located at two fixed points, the squares of the relative excitation frequencies of the two fixed points are respectively input into the transfer function and derived, and the obtained equations with the two derived results being zero are solved to obtain the optimal damping ratio of the transfer function at the first fixed point and the optimal damping ratio at the second fixed point; then, the square root is solved for the mean of the sum of squares of the optimal damping ratios at the two points, resulting in the optimal damping ratio of the transfer function. Thus, the above optimization is performed for the displacement transfer function and the velocity transfer function, and the optimal damping ratio of the two can be obtained.

In one embodiment, taking the stiffness ratio and the damping ratio as partial derivatives and taking the derivative result as zero, respectively performing derivative calculation on the displacement root mean square response function and the velocity root mean square response function to obtain a third optimal stiffness ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal stiffness ratio and a fourth optimal damping ratio of the velocity transfer function, including:

Respectively carrying out normalization processing on the displacement root mean square response function and the velocity root mean square response function to obtain a normalized displacement root mean square response function and a normalized velocity root mean square response function;

and taking the rigidity ratio and the damping ratio as partial derivatives respectively, taking a derivation result as zero, and respectively carrying out derivation calculation on the normalized displacement root mean square response function and the normalized velocity root mean square response function to obtain a third optimal rigidity ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal rigidity ratio and a fourth optimal damping ratio of the velocity transfer function.

It will be appreciated that the above calculation process is a process that minimizes the total vibration energy of the SDOF system that is randomly excited at all frequencies. Assuming that the random excitation is a smooth white noise process, according to the random vibration theory, any root mean square responseσThe method comprises the following steps:

（22）

wherein S is ₀ Is the gaussian white noise power spectral density,is a transfer function.

For SDOF systems, the combined type (7) and (22) can obtain the displacement root mean square response of the SDOF systemσ _U Sum velocity root mean square responseσ _V . The method comprises the following steps:

（23）

using the above equation, normalized random response performance index for introducing displacement and velocity response of SDOF system I _U AndI _V . The method comprises the following steps:

（24）

wherein the normalized displacement root mean square response function is normalized random response performance indexI _U The normalized speed root mean square response function is normalized random response performance indexI _V 。

For normalized random response indexI _U AndI _V analysis is carried out along with the variation trend of the TID rigidity ratio and the nominal damping ratio, and the analysis can be knownI _U AndI _V the smaller the TID, the more pronounced the damping effect.

When the inertial ratio is fixed, the optimal combination of the rigidity ratio and the nominal damping ratio is always obtained, so that the performance index of the original structureI _U AndI _V obtaining the minimum value, optimizing by using extreme value conditions, and neglecting the inherent damping of the structure to obtain:

（25）

from equation (25), the performance index of the SDOF system is considered under random excitationI _U AndI _V is the optimal stiffness ratio of (2)Closed solution version of optimal damping ratio:

（26）

wherein,and->A third optimal stiffness ratio and a third optimal damping ratio of the displacement transfer function respectively,and->The fourth optimal stiffness ratio and the fourth optimal damping ratio of the speed transfer function, respectively.

According to the embodiment, the normalization processing of the root mean square response is carried out on the displacement root mean square response function and the speed root mean square response function, so that the vibration reduction effect of the TID can be considered when the rigidity ratio and the damping ratio are optimized subsequently.

And comparing the vibration reduction effect of the optimal parameter original structure under simple harmonic excitation and white noise random excitation with the four obtained parameter groups. Under simple harmonic excitation, the transfer function obtained by combining the original structure displacement obtained by adopting a fixed point method and the most stable other parameters of the speed transfer function has larger oscillation, namely, the two resonance peaks have larger difference with the minimum value at the fundamental frequency of the SDOF system, so that the SDOF system can have displacement or speed change with different degrees during frequency sweeping. At the same inertial ratio, adoptκ _Vopt,2 Andζ _Vopt,2 the resulting SDOF system has the greatest displacement root mean square response, but the least velocity root mean square response. This means that the SDOF system is in a low-speed sloshing state although the displacement amplitude is large; in contrast, the SDOF system obtained by adopting the displacement condition has smaller displacement response, but has larger speed root mean square response and quicker structure shaking under the same inertial ratio.

Therefore, although the analysis expression of the optimal damping ratio and the optimal stiffness ratio of the TID under the simple harmonic excitation and the white noise random excitation is obtained, the value basis of the optimal inertial ratio is not available. In order to realize the global optimization design of the TID, the structural performance is further defined below, and parameter optimization is performed according to different performance requirements of the TID.

In one embodiment, determining a target parameter set for TID among a parameter set for a first optimal stiffness ratio and a first optimal damping ratio, a parameter set for a second optimal stiffness ratio and a second optimal damping ratio, a parameter set for a third optimal stiffness ratio and a third optimal damping ratio, and a parameter set for a fourth optimal stiffness ratio and a fourth optimal damping ratio, comprises:

determining a displacement vibration reduction coefficient based on the displacement root mean square response function;

and under the condition that the displacement vibration reduction coefficient reaches a first designated threshold value, determining a target parameter set of the TID from the parameter set of the first optimal stiffness ratio and the first optimal damping ratio and the parameter set of the third optimal stiffness ratio and the third optimal damping ratio.

In one embodiment, the method further comprises:

determining an energy reduction coefficient based on the speed root mean square response function;

and determining a target parameter set of the TID from the parameter sets of the second optimal stiffness ratio and the second optimal damping ratio, and the parameter sets of the fourth optimal stiffness ratio and the fourth optimal damping ratio under the condition that the displacement vibration reduction coefficient reaches a first specified threshold and the energy reduction coefficient reaches a second specified threshold.

When selecting TID optimal design parameters, controlling the displacement of the original structure can be considered firstly; meanwhile, the reduction of the shaking speed of the original structure means the reduction of the input kinetic energy. For this purpose, two performance indicators are introduced, namely displacement damping coefficients JAnd an energy reduction coefficientη：

（27）

Wherein,σ _U0 andσ _V0 for uncontrolled system primary structure displacementAnd a speed root mean square value. Displacement damping ratioJThe smaller the TID provides the better the damping effect; coefficient of energy reductionηThe smaller the energy input to the original structure, the less the sloshing speed will be. The earthquake motion is randomly excited, soH ₂ The optimized norm is more accurate as an objective function. According to the primary structural performance (minimizing displacement) requirement, an optimization method using the displacement damping ratio as an objective function can be adopted, as shown in the formula (28):

（28）

wherein,υ _u andυ _l is thatυUpper and lower bounds of the value. Optimal parameters of two groups of displacement control based on TID can obtain a designated target displacement vibration reduction ratioJ _t The following TID optimum design parameters, equation (28) may be written as:

（29）

however, even if the displacement of the structure is controlled to a low level, the energy caused by the high-frequency vibration increases the burden on the structure. For this purpose, an energy reduction factor is introduced on the basis of the formula (28)ηAs a supplemental objective function, equation (28) becomes:

（30）

equation (30) is a double-objective optimization problem, and the objective vibration reduction ratio can be presetJ _t The formula (30) is changed to:

（31）

based on the optimal parameters of two groups of speed control of the TID, the optimal TID design parameters which simultaneously consider the reduction of energy input and the target displacement damping ratio can be obtained, and then the formula (31) can be written as:

（32）

Different target displacement damping ratios can be obtained by the formulas (28) and (31)J _t Tables 1 and 2 below show. As can be seen from tables 1 and 2, whenJ _t When=0.5, the optimized TID nominal damping ratio is smaller than the inherent damping ratioζ ₀ =0.02, i.e. a higher level of damping performance can be achieved with a smaller damping ratioJ _t =0.5 represents a 50% decrease in the root mean square value of the primary structural displacement under random excitation); at the same time, the energy reduction coefficientηSmaller indicates more external energy dissipated by the TID whenJ _t At < 0.7, the TID may dissipate more than 50% of the input kinetic energy.

Table 1 TID optimization parameters obtained using equation (29)ζ ₀ =0.02)

TABLE 2 TID optimization parameters obtained by equation (32)ζ ₀ =0.02）

According to the above embodiment, the parameter global optimization can be performed by using different parameter sets according to the target displacement damping ratio and the target energy reduction ratio.

Embodiments of the present disclosure derive based onH _∞ Optimization and optimizationH ₂ The optimal nominal damping ratio and the stiffness ratio of the TID of the optimization theory are optimized, the TID global optimization design is developed based on two performance requirements, and verification analysis is carried out through an optimization example and earthquake vibration excitation. The main conclusion is as follows:

（1）H _∞ the optimized TID optimum parameter combination can be used to suppress the structural peak response, H ₂ The optimized TID optimal parameter combination can be used for reducing the structural root mean square response and the input total energy. NeedleThe optimal parameter combination is more suitable for optimizing the TID system under the random earthquake action by adopting the random response as the objective function.

(2) The optimization method based on performance requirements can realize TID global optimization design, and after the target displacement vibration reduction coefficient is determined, the four groups of TID design parameters provided herein can realize accurate control of the displacement response of the original structure. The optimized parameters obtained by the speed index can exert the deformation enhancement capability of the inertial unit to the greatest extent, and the VD energy consumption capability which is several times can be obtained under the same nominal damping ratio. As the nominal damping ratio increases, the deformation enhancement performance of the TID damping unit decreases. The TID damping ratio deduced based on random response is smaller than that of a fixed-point method, and meanwhile the requirement of deformation synergy of the damping unit is met.

(3) The TID shock absorption structure obtained by adopting the larger nominal damping ratio has the least input energy, but the energy consumption and the energy consumption duty ratio of the TID are also the least; the deformation and synergy advantages of the inertial unit can be fully exerted by adopting a smaller nominal damping ratio and properly increasing the inertial ratio, and better damping and energy consumption effects can be obtained at lower cost.

A damping system formed by topological combination of elements such as inertial volume, rigidity and damping has the characteristics of high damping performance, good robustness and the like, but the traditional optimization design method is difficult to complete global optimization of the inertial volume system. The optimization design method taking the damping performance as the drive can accurately meet various requirements of the main structure, and the inertial capacity element can exert the energy consumption performance to the greatest extent.

FIG. 7 is a block diagram of a damper optimizing apparatus according to an embodiment of the present disclosure.

As shown in fig. 7, the damper optimizing apparatus may include:

a transfer function determining module 710, configured to perform mechanical analysis on a single-degree-of-freedom SDOF system deployed with a tuned inertial damper TID, to obtain a displacement transfer function and a velocity transfer function of the SDOF system;

the first fixed point calculating module 720 is configured to calculate the displacement transfer function and the velocity transfer function based on a principle that the transfer function passes through two fixed points at any damping ratio and the values of the transfer function at the two fixed points are the same, so as to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the velocity transfer function;

A second fixed point calculating module 730, configured to calculate the displacement transfer function and the velocity transfer function based on the principle that the extremum of the transfer function is at the two fixed points, so as to obtain a first optimal damping ratio of the displacement transfer function and a second optimal damping ratio of the velocity transfer function;

the root mean square calculation module 740 is configured to substitute the displacement transfer function and the velocity transfer function into root mean square response functions, respectively, to obtain a displacement root mean square response function and a velocity root mean square response function of the SDOF system;

the random excitation calculation module 750 is configured to take the stiffness ratio and the damping ratio as partial derivatives, and take the derivative result as zero, and perform derivative calculation on the displacement root mean square response function and the velocity root mean square response function, so as to obtain a third optimal stiffness ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal stiffness ratio and a fourth optimal damping ratio of the velocity transfer function;

a target parameter determining module 760, configured to determine a target parameter set of the TID from among the parameter sets of the first optimal stiffness ratio and the first optimal damping ratio, the parameter sets of the second optimal stiffness ratio and the second optimal damping ratio, the parameter sets of the third optimal stiffness ratio and the third optimal damping ratio, and the parameter sets of the fourth optimal stiffness ratio and the fourth optimal damping ratio.

In one embodiment, the first fixed point calculating module 720 includes:

a first normalization unit configured to determine a displacement transfer function that ignores an inherent damping ratio of the SDOF system and a velocity transfer function that ignores an inherent damping ratio of the SDOF system, respectively, based on the displacement transfer function and the velocity transfer function;

the second normalization unit is used for carrying out modular square calculation on the displacement transfer function neglecting the inherent damping ratio of the SDOF system to obtain a normalized displacement transfer function;

the module square calculation unit is used for carrying out module square calculation on the speed transfer function neglecting the inherent damping ratio of the SDOF system to obtain a normalized speed transfer function;

and the fixed point optimization unit is used for respectively calculating the normalized displacement transfer function and the normalized speed transfer function based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, so as to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the speed transfer function.

In one embodiment, the function optimizing unit is specifically configured to:

Under the principle that the normalized displacement transfer function passes through a first fixed point and a second fixed point under any damping ratio, respectively inputting the normalized displacement transfer function with the damping ratio of 0 and the damping ratio of infinity, and making two results output by the normalized displacement transfer function equal to each other to obtain a first equation;

respectively inputting the square of the relative excitation frequency of the first fixed point and the square of the relative excitation frequency of the second fixed point into the normalized displacement transfer function, and making the two results output by the normalized displacement transfer function equal to obtain a second equation;

solving an equation set consisting of the first equation and the second equation to obtain a first optimal stiffness ratio of the displacement transfer function;

under the principle that the normalized speed transfer function passes through a third fixed point and a fourth fixed point under any damping ratio, respectively inputting the normalized speed transfer function with the damping ratio of 0 and the damping ratio of infinity, and making two results output by the normalized speed transfer function equal to obtain a third equation;

respectively inputting the square of the relative excitation frequency of the third fixed point and the square of the relative excitation frequency of the fourth fixed point into the normalized speed transfer function, and making the two results output by the normalized speed transfer function equal to obtain a fourth equation;

In one embodiment, the second fixed point computing module 730 includes:

a first damping ratio determining unit, configured to input and derive a square of a relative excitation frequency of the first fixed point and a square of a relative excitation frequency of the second fixed point into the normalized displacement transfer function respectively, and solve an equation that makes both derived results zero, to obtain an optimal damping ratio of the normalized displacement transfer function at the first fixed point and an optimal damping ratio at the second fixed point, under a principle that an extremum of the normalized displacement transfer function is located at the first fixed point and the second fixed point;

A second damping ratio determining unit, configured to solve a square root for a mean value of a sum of squares of the optimal damping ratio at the first fixed point and the optimal damping ratio at the second fixed point, to obtain the first optimal damping ratio;

a third damping ratio determining unit, configured to input and derive a square of a relative excitation frequency of the third fixed point and a square of a relative excitation frequency of the fourth fixed point into the normalized speed transfer function respectively, and solve an equation that makes both derived results zero, to obtain an optimal damping ratio of the normalized speed transfer function at the third fixed point and an optimal damping ratio at the fourth fixed point, under a principle that an extremum of the normalized speed transfer function is located at the third fixed point and the fourth fixed point;

and a fourth damping ratio determining unit, configured to solve a square root for a mean value of a sum of squares of the optimal damping ratio at the third fixed point and the optimal damping ratio at the fourth fixed point, to obtain the second optimal damping ratio.

In one embodiment, the random excitation calculation module 750 includes:

the third normalization unit is used for respectively carrying out normalization processing on the displacement root mean square response function and the velocity root mean square response function to obtain a normalized displacement root mean square response function and a normalized velocity root mean square response function;

And the root mean square response optimization unit is used for taking the rigidity ratio and the damping ratio as partial derivatives respectively, taking the derivative result as zero, and respectively carrying out derivative calculation on the normalized displacement root mean square response function and the normalized velocity root mean square response function to obtain a third optimal rigidity ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal rigidity ratio and a fourth optimal damping ratio of the velocity transfer function.

In one embodiment, the target parameter determination module 760 includes:

a displacement vibration reduction coefficient determining unit for determining a displacement vibration reduction coefficient based on the displacement root mean square response function;

and the first parameter set determining unit is used for determining a target parameter set of the TID from the parameter sets of the first optimal stiffness ratio and the first optimal damping ratio and the parameter sets of the third optimal stiffness ratio and the third optimal damping ratio under the condition that the displacement vibration reduction coefficient reaches a first specified threshold value.

In one embodiment, the method further comprises:

an energy reduction coefficient determination unit for determining an energy reduction coefficient based on the speed root mean square response function;

and a second parameter set determining unit configured to determine, when the displacement vibration reduction coefficient reaches the first specified threshold and the energy reduction coefficient reaches the second specified threshold, a target parameter set of the TID from among parameter sets of the second optimal stiffness ratio and the second optimal damping ratio, and parameter sets of the fourth optimal stiffness ratio and the fourth optimal damping ratio.

For descriptions of specific functions and examples of each module and sub-module of the apparatus in the embodiments of the present disclosure, reference may be made to the related descriptions of corresponding steps in the foregoing method embodiments, which are not repeated herein.

In the technical scheme of the disclosure, the acquisition, storage, application and the like of the related user personal information all conform to the regulations of related laws and regulations, and the public sequence is not violated.

According to embodiments of the present disclosure, the present disclosure also provides an electronic device, a readable storage medium and a computer program product.

Fig. 8 illustrates a schematic block diagram of an example electronic device 600 that can be used to implement embodiments of the present disclosure. Electronic devices are intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device may also represent various forms of mobile apparatuses, such as personal digital assistants, cellular telephones, smartphones, wearable devices, and other similar computing apparatuses. The components shown herein, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the disclosure described and/or claimed herein.

As shown in fig. 8, the apparatus 600 includes a computing unit 601 that can perform various appropriate actions and processes according to a computer program stored in a Read Only Memory (ROM) 602 or a computer program loaded from a storage unit 608 into a Random Access Memory (RAM) 603. In the RAM 603, various programs and data required for the operation of the device 600 may also be stored. The computing unit 601, ROM 602, and RAM 603 are connected to each other by a bus 604. An input/output (I/O) interface 605 is also connected to bus 604.

Various components in the device 600 are connected to the I/O interface 605, including: an input unit 606 such as a keyboard, mouse, etc.; an output unit 607 such as various types of displays, speakers, and the like; a storage unit 608, such as a magnetic disk, optical disk, or the like; and a communication unit 609 such as a network card, modem, wireless communication transceiver, etc. The communication unit 609 allows the device 600 to exchange information/data with other devices via a computer network, such as the internet, and/or various telecommunication networks.

The computing unit 601 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of computing unit 601 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various specialized Artificial Intelligence (AI) computing chips, various computing units running machine learning model algorithms, a Digital Signal Processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 601 performs the various methods and processes described above, such as a damper optimization method. For example, in some embodiments, a damper optimization method may be implemented as a computer software program tangibly embodied on a machine-readable medium, such as storage unit 608. In some embodiments, part or all of the computer program may be loaded and/or installed onto the device 600 via the ROM 602 and/or the communication unit 609. When a computer program is loaded into RAM 603 and executed by the computing unit 601, one or more steps of one damper optimization method described above may be performed. Alternatively, in other embodiments, the computing unit 601 may be configured to perform a damper optimization method by any other suitable means (e.g., by means of firmware).

Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuit systems, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), systems On Chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs, the one or more computer programs may be executed and/or interpreted on a programmable system including at least one programmable processor, which may be a special purpose or general-purpose programmable processor, that may receive data and instructions from, and transmit data and instructions to, a storage system, at least one input device, and at least one output device.

Program code for carrying out methods of the present disclosure may be written in any combination of one or more programming languages. These program code may be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus such that the program code, when executed by the processor or controller, causes the functions/operations specified in the flowchart and/or block diagram to be implemented. The program code may execute entirely on the machine, partly on the machine, as a stand-alone software package, partly on the machine and partly on a remote machine or entirely on the remote machine or server.

In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. The machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and pointing device (e.g., a mouse or trackball) by which a user can provide input to the computer. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic input, speech input, or tactile input.

The systems and techniques described here can be implemented in a computing system that includes a background component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such background, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), wide Area Networks (WANs), and the internet.

The computer system may include a client and a server. The client and server are typically remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server may be a cloud server, a server of a distributed system, or a server incorporating a blockchain.

It should be appreciated that various forms of the flows shown above may be used to reorder, add, or delete steps. For example, the steps recited in the present disclosure may be performed in parallel, sequentially, or in a different order, provided that the desired results of the disclosed aspects are achieved, and are not limited herein.

The above detailed description should not be taken as limiting the scope of the present disclosure. It will be apparent to those skilled in the art that various modifications, combinations, sub-combinations and alternatives are possible, depending on design requirements and other factors. Any modifications, equivalent substitutions, improvements, etc. that are within the principles of the present disclosure are intended to be included within the scope of the present disclosure.

Claims

1. A method of optimizing a damper, comprising:

2. The method according to claim 1, wherein the calculating the displacement transfer function and the velocity transfer function based on the principle that the transfer function passes through two fixed points at any damping ratio and the values of the transfer function at the two fixed points are the same, respectively, to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the velocity transfer function includes:

determining a displacement transfer function ignoring an inherent damping ratio of the SDOF system and a velocity transfer function ignoring an inherent damping ratio of the SDOF system, respectively, based on the displacement transfer function and the velocity transfer function;

performing modular square calculation on the displacement transfer function neglecting the inherent damping ratio of the SDOF system to obtain a normalized displacement transfer function;

performing modular square calculation on the speed transfer function neglecting the inherent damping ratio of the SDOF system to obtain a normalized speed transfer function;

based on the principle that the transfer function passes through two fixed points under any damping ratio and the values of the transfer function at the two fixed points are the same, the normalized displacement transfer function and the normalized speed transfer function are respectively calculated to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the speed transfer function.

3. The method according to claim 2, wherein the calculating the normalized displacement transfer function and the normalized velocity transfer function based on the principle that the transfer function passes through two fixed points at any damping ratio and the values of the transfer function at the two fixed points are the same, respectively, to obtain a first optimal stiffness ratio of the displacement transfer function and a second optimal stiffness ratio of the velocity transfer function includes:

4. A method according to claim 3, wherein the calculating the displacement transfer function and the velocity transfer function based on the principle that the extremum of the transfer function is located at the two points, respectively, results in a first optimal damping ratio of the displacement transfer function and a second optimal damping ratio of the velocity transfer function, comprises:

solving a square root of a mean value of a sum of squares of the optimal damping ratio at the first fixed point and the optimal damping ratio at the second fixed point to obtain the first optimal damping ratio;

under the principle that the extreme value of the normalized speed transfer function is positioned at the third fixed point and the fourth fixed point, respectively inputting the square of the relative excitation frequency of the third fixed point and the square of the relative excitation frequency of the fourth fixed point into the normalized speed transfer function, deriving the normalized speed transfer function, and solving an equation enabling the two derived results to be zero to obtain the optimal damping ratio of the normalized speed transfer function at the third fixed point and the optimal damping ratio at the fourth fixed point;

And solving a square root of a mean value of a sum of squares of the optimal damping ratio at the third fixed point and the optimal damping ratio at the fourth fixed point to obtain the second optimal damping ratio.

5. The method of claim 1, wherein deriving the displacement root mean square response function and the velocity root mean square response function with the stiffness ratio and the damping ratio as partial derivatives, respectively, and with the derivation result as zero, respectively, to obtain a third optimal stiffness ratio and a third optimal damping ratio of the displacement transfer function, and a fourth optimal stiffness ratio and a fourth optimal damping ratio of the velocity transfer function, comprises:

6. The method of claim 1, wherein the determining the target parameter set for the TID from among the parameter sets for the first optimal stiffness ratio and the first optimal damping ratio, the parameter sets for the second optimal stiffness ratio and the second optimal damping ratio, the parameter sets for the third optimal stiffness ratio and the third optimal damping ratio, and the parameter sets for the fourth optimal stiffness ratio and the fourth optimal damping ratio comprises:

and under the condition that the displacement vibration reduction coefficient reaches a first designated threshold value, determining a target parameter set of the TID from the parameter sets of the first optimal stiffness ratio and the first optimal damping ratio and the parameter sets of the third optimal stiffness ratio and the third optimal damping ratio.

7. The method as recited in claim 6, further comprising:

and determining a target parameter set of the TID from the parameter sets of the second optimal stiffness ratio and the second optimal damping ratio, and the parameter sets of the fourth optimal stiffness ratio and the fourth optimal damping ratio under the condition that the displacement vibration reduction coefficient reaches the first specified threshold and the energy reduction coefficient reaches the second specified threshold.

8. A damper optimizing apparatus, comprising:

9. An electronic device, comprising: at least one processor, and a memory communicatively coupled to the at least one processor;

wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-7.

10. A non-transitory computer readable storage medium storing computer instructions for causing the computer to perform the method of any one of claims 1-7.