CN115577516A - Method for evaluating vibration reduction performance of super high-rise building structure and MTLD coupling system - Google Patents
Method for evaluating vibration reduction performance of super high-rise building structure and MTLD coupling system Download PDFInfo
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Abstract
A method for evaluating vibration damping performance of a super high-rise building structure and an MTLD coupling system comprises the steps of measuring coupling vibration signals of the super high-rise building structure and the MTLD, and preprocessing the signals; step two, reconstructing a coupling system state matrix; step three, establishing a simplified model motion equation of the super high-rise building structure and the MTLD coupling system, and deducing a state matrix; step four, detecting parameters of the super high-rise building structure and the MTLD; step five, acquiring a frequency response function and a displacement response standard deviation; calculating a frequency response function and a displacement response standard deviation before the super high-rise building structure is controlled; and step seven, evaluating the vibration reduction performance of the super high-rise building structure and the MTLD coupling system. The method solves the technical problems that the traditional TLD parameter detection method cannot acquire the frequency and the damping ratio of each TLD, only can preliminarily judge whether the TLD achieves the optimal control, and cannot accurately evaluate the vibration reduction performance of the structure.
Description
Technical Field
The invention belongs to the field of vibration control of high-rise buildings, and particularly relates to a parameter detection and performance evaluation method of a high-rise building structure MTLD coupling system.
Background
A Tuned Liquid Damper (TLD) is a passive vibration damping and energy dissipation device, is widely applied to the field of wind-induced vibration control of high-rise buildings, and can remarkably reduce the top acceleration of the buildings. The TLD oscillation frequency and the damping ratio are main parameters influencing the TLD vibration reduction performance, and the TLD performance can be objectively evaluated only by accurately detecting the TLD frequency and the damping ratio through a structure and a TLD coupling vibration signal in actual engineering. The conventional TLD parameter detection and performance evaluation method is only used for controlling a single TLD installed in a structure, and the frequency and the damping ratio obtained by detection are compared with the optimal parameters of a linear theory, so that the vibration damping performance of the TLD is evaluated comprehensively.
However, because the effective damping band of a single TLD is narrow and the robustness is poor, the effective damping band is widened by forming a plurality of TLDs (MTLDs for short) by TLDs with different frequency distributions, so as to improve the control effect when the structural frequency changes. The existing parameter detection method for a single TLD cannot acquire the frequency and the damping ratio of each TLD in the MTLD, so that the dynamic characteristic of each TLD cannot be accurately identified, and certain parameters of the TLD are difficult to optimize so as to achieve a better control effect. On the other hand, the existing performance evaluation method only can preliminarily judge whether the TLD achieves the optimal control or not by comparing with the optimal parameter of the linear theory, and the vibration damping performance of the TLD on the structure cannot be accurately and objectively evaluated.
Disclosure of Invention
The invention aims to provide a parameter detection and performance evaluation method for an MTLD coupling system of a high-rise building structure, which aims to solve the technical problems that the conventional TLD parameter detection method cannot acquire the frequency and the damping ratio of each TLD in the MTLD, so that the dynamic characteristic of each TLD cannot be accurately identified and certain parameters of the TLD are difficult to optimize so as to achieve a better control effect, and also aims to solve the technical problems that the conventional performance evaluation method can only preliminarily judge whether the TLD achieves optimal control and cannot accurately and objectively evaluate the vibration reduction performance of the structure.
In order to achieve the purpose, the invention adopts the following technical scheme.
A method for evaluating the vibration damping performance of a super high-rise building structure and an MTLD coupling system comprises the following steps.
Measuring a coupling vibration signal of a super high-rise building structure and an MTLD (maximum transmission level laser diode), and preprocessing the signal; the specific operation method comprises the following steps:
step 1-1, installing TLDs with different frequencies at intervals on the top of a super high-rise building structure, wherein a group of TLDs form an MTLD, and the MTLD and the super high-rise building form a coupling system together;
step 1-2, numbering a group of TLDs, respectively TLD 1 、TLD 2 、TLD 3 、TLD 4 .......TLD n ；
Step 1-3, respectively installing a group of propeller column components at intervals in each TLD, and simultaneously respectively installing a liquid level measuring instrument in each TLD;
step 1-4, installing an accelerometer at the top of the super high-rise building structure, monitoring the acceleration response of the top of the super high-rise building structure, and simultaneously monitoring the liquid level response of each TLD by a liquid level measuring instrument;
step 1-5, preprocessing the monitored acceleration response and the monitored liquid level response to obtain a coupling acceleration response signal; the pretreatment method comprises the following steps:
step A, taking the monitored liquid level response signal of each TLD as a coupling vibration signal, and transmitting the coupling vibration signal back to a central server through the Internet;
step B, removing the mean value of a group of coupled vibration signals, converting the liquid level response signal of each TLD into equivalent horizontal displacement, and converting the liquid level response signal into the equivalent horizontal displacement according to the specific formula:
in the formula u n For the level response of the nth TLD, x n Is the equivalent horizontal displacement of the nth TLD, L n Is the length of the nth TLD, h n Is the liquid depth within the nth TLD;
step C, equivalent horizontal displacement x of a group of TLDs n Respectively solving second derivatives to obtain equivalent horizontal acceleration;
and D, performing low-pass filtering processing on the top acceleration and the equivalent horizontal acceleration of the super high-rise building structure, and filtering out a high-order mode of the coupling system to obtain a coupling acceleration response signal mainly based on a fundamental-order mode.
Secondly, identifying the characteristic value and the vibration mode of the super high-rise building structure and the MTLD coupling system through the coupling acceleration response signal, and further reconstructing a state matrix A of the coupling system c 。
Step three, establishing a motion equation of a simplified model of the super high-rise building structure and the MTLD coupling system, and deducing a state matrix from the motion equation of the simplified model; the method comprises the following specific operations:
when the super high-rise building structure only considers the fundamental order modal response, the super high-rise building structure can be simplified into a mass-spring-damping structure with single degree of freedom; because TLD mainly relies on fundamental mode response when controlling super high-rise building structure, consequently can simplify every TLD in MTLD as equivalent mechanics model, establish the equation of motion of super high-rise building structure and the simplified model of MTLD coupled system from this, the concrete formula is:
in the formula, x s Displacement for a single degree of freedom structure;
speed for single degree of freedom configurations;
acceleration in a single degree of freedom configuration; x is the number of n Equivalent displacement for the nth TLD;
is the equivalent speed for the nth TLD;
equivalent acceleration for the nth TLD; ζ represents a unit s The fundamental order modal damping ratio of the super high-rise building structure; omega s Is the fundamental mode frequency of the super high-rise building structure; n is the number of TLDs; ζ represents a unit n Fundamental mode damping ratio for the nth TLD; omega n Is the fundamental mode frequency of the nth TLD; m is T,n Actual quality for the nth TLD; m is s Is the fundamental modal quality of the super high-rise building structure; f. of w Generalized wind loads; mu.s n Represents the equivalent mass of the nth TLD to m as the effective mass ratio s The ratio of (A) to (B);
order to
Then further obtaining a state space equation of the simplified model, wherein the specific formula is as follows:
in the formula, A cs To simplify the state matrix of the model, w c Being the sum of the input vector and the noise caused by the processing,superscript symbol-denotes derivation; through simplification, A cs Expressed as:
in the formula, Z l×l ，I l×l ，P l×l ，Q l×l Are all matrices of the ith row and ith column, in which Z l×l And I l×l Respectively a zero matrix and an identity matrix.
Step four, according to the state matrix A of the simplified model cs And detecting parameters of the super high-rise building structure and the MTLD, wherein the detected parameters comprise respective frequency and damping ratio of the super high-rise building structure and the MTLD and effective mass ratio of each TLD in the MTLD.
Step five, obtaining the frequency response function H of the high-rise building structure according to the parameter detection result in the step four s And standard deviation of displacement response σ s 。
Step six, calculating a frequency response function H before the super high-rise building structure is controlled when the super high-rise building structure is not provided with the MTLD for control so And standard deviation of displacement response σ so 。
And step seven, defining a vibration reduction rate eta according to the displacement response standard deviation before and after the super high-rise building structure is controlled, and realizing effective evaluation on the vibration reduction performance of the super high-rise building structure and the MTLD coupling system by calculating the numerical value of the vibration reduction rate eta.
Preferably, the state matrix A of the coupling system is reconstructed in the second step c The specific operation of the method is as follows:
step 2-1: and performing projection calculation on the coupling acceleration response signal, wherein the specific calculation method comprises the following steps: coupling accelerationThe degree response signal is a matrix with l rows and j columns, wherein l is the number of signal output channels, and j is the signal length; since the coupled acceleration response signal includes the super high-rise building structure top acceleration and the equivalent horizontal acceleration of a set of TLDs, assuming the number of TLDs is N, then l = N +1; construction of a matrix Y from coupled acceleration response signals P And matrix Y f The concrete formula is as follows:
in the formula, Y P And Y f Is a matrix of i rows and k columns, i being sized according to the data length of the coupled acceleration response signal, k = j-2i +1, element y in the matrix m A signal indicating the nth time; calculating Y from projection theory f At Y P The specific formula of the projection is as follows:
in the formula, P i Representing a projection matrix, wherein a superscript symbol T represents a matrix transposition, and a superscript symbol + represents a pseudo-inverse of the matrix;
step 2-2: obtaining an observable matrix by singular value decomposition; to P i Singular value decomposition is carried out, and the specific formula is as follows:
in the formula of U 1 And V 1 A matrix of singular vectors, S 1 For the singular value matrix with 0 elements on the off-diagonal, further calculating an observable matrix Q i The concrete formula is as follows:
according to the state space principle, from observable matrix Q i Calculating an original state matrix A and an original output matrix C of the coupling system, wherein the specific formula is as follows:
A＝Q i (1:i-l:) + Q i (l+1:i,:)；
C＝Q i (1:l,:)；
step 2-3: identifying characteristic values and vibration modes of the MTLD coupling system: and (3) carrying out eigenvalue decomposition on the original state matrix A, wherein the specific formula is as follows:
in the formula (I), the compound is shown in the specification,
is an eigenvector matrix, and lambda is a diagonal matrix formed by eigenvalues; further obtaining the vibration mode matrix of the system
The concrete formula is as follows:
step 2-4: reconstructing the state matrix A of the coupled system c : from a diagonal matrix lambda and a eigenvector matrix
Obtaining characteristic value and vibration mode vector corresponding to the coupling system fundamental mode, and then reconstructing the state matrix A of the coupling system c ：
In the formula (I), the compound is shown in the specification,
λ c ＝diag[λ 1 ，λ 2 ，…，λ l ]diag denotes a matrix of elements in a diagonal line, and a superscript symbol denotes a conjugate matrix.
Preferably, the frequency ω of the nth TLD is obtained in the fourth step n And damping ratio ζ n The concrete formula is as follows:
wherein P (x, y) and Q (x, y) each represent P l×l And Q l×l The value of the x-th row and the y-th column;
let p be n = P (1, n + 1)/P (n +1, 1), then the effective mass ratio μ for the nth TLD is calculated n The concrete formula is as follows:
solving the linear equation system of the formula to obtain the effective mass ratio mu of each TLD n (ii) a Then, the value of omega is adjusted n 、ζ n And mu n Are substituted into P (1, 1) and Q (1, 1) to obtain the frequency omega of the super high-rise building structure s And damping ratio ζ s 。
Preferably, the state matrix A of the coupled system is reconstructed in step four c And the state matrix A of the simplified model cs Approximately equal; thus, comparative
due to A c And A cs Calculating out matrixes which are 2l multiplied by 2l and are approximately equal to each other; state matrix A of coupling system is reconstructed c And the state matrix A of the simplified model cs The elements in the super high-rise building structure are equal in one-to-one correspondence, and therefore the parameters of the super high-rise building structure and the parameters of the MTLD are obtained.
Preferably, step five is to solve the motion equation of the simplified model of the super high-rise building structure and the MTLD coupling system according to a frequency domain method, and the equation is expressed by
in the formula, H s Is the frequency response function, H, of a super high-rise building structure n Is the frequency response function of the nth TLD;
will be provided with
Substituted type
To obtain H s And H n The relationship of (1) is:
general formula (II)
Substituted type
Eliminating primordial qi to obtain H s The expression is as follows:
in the formula, the symbol '| · |' represents a modulo operation.
Preferably, in the sixth step, when the very high-rise building structure is not controlled by the MTLD, the frequency response function H of the very high-rise building structure so And standard deviation of displacement response σ so The concrete formula is as follows:
preferably, the damping ratio η is calculated by:
assuming that the excitation is an ideal stationary white noise excitation, i.e. S (ω) is a constant, the damping ratio η is:
in pair type
Compared with the prior art, the invention has the following characteristics and beneficial effects.
1. According to the invention, the frequency and the damping ratio of each TLD can be rapidly and accurately detected through the coupled vibration signal of the super high-rise building structure and the MTLD, and the actual structure frequency is obtained through detection, so that a more reliable basis can be provided for the frequency tuning of the MTLD.
2. The invention obtains the frequency response function of the super high-rise building structure in the coupling system by the super high-rise building structure and the MTLD parameters, thereby objectively evaluating the vibration damping performance of the MTLD on the super high-rise building structure.
3. Firstly, reconstructing a state matrix of a system by using coupling acceleration response signals of a super high-rise building and an MTLD (maximum transmission/loss diode) obtained through monitoring, thereby carrying out parameter detection on the super high-rise building structure and the MTLD, finally obtaining a frequency response function of the super high-rise building structure in the coupling system according to a detection result, and realizing the evaluation of the vibration damping performance of the MTLD; compared with the prior art, the method can quickly and accurately detect the frequency, the damping ratio and the effective mass ratio of each TLD, the frequency and the damping ratio of the super high-rise building structure, and calculate the vibration reduction rate of the MTLD through the frequency response function of the super high-rise building structure; the invention has clear and simple realization form, is convenient for practical engineering application, and can make the frequency tuning and the performance evaluation of the MTLD more objective and reliable.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings.
Fig. 1 is a schematic numbering diagram of a TLD in an MTLD according to an embodiment of the present invention.
Fig. 2 is a top view of a TLD with a built-in paddle in an embodiment of the present invention.
Fig. 3 is a schematic diagram of a simplified model of a super high-rise building structure and an MTLD according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of the frequency response function before and after the control of the super high-rise building structure in the embodiment of the invention.
Detailed Description
The method for evaluating the vibration reduction performance of the super high-rise building structure and the MTLD coupling system is characterized by comprising the following steps.
Measuring a coupling vibration signal of a super high-rise building structure and an MTLD, and preprocessing the signal; the specific operation method is as follows.
Step 1-1, installing TLDs with different frequencies at intervals on the top of a super high-rise building structure, wherein a group of TLDs form an MTLD, and the MTLD and the super high-rise building form a coupling system together; in this embodiment, a total of 4 TLDs with different frequencies are installed on the top floor of the super high-rise building structure, and an MTLD is composed of 4 TLDs with different frequencies.
Step 1-2, numbering a group of TLDs, respectively TLD 1 、TLD 2 、TLD 3 、TLD 4 .......TLD n 。
And 1-3, respectively installing a group of propeller column components at intervals in each TLD, and simultaneously respectively installing a liquid level measuring instrument in each TLD.
And 1-4, installing an accelerometer at the top of the super high-rise building structure, monitoring the acceleration response of the top of the super high-rise building structure, and simultaneously monitoring the liquid level response of each TLD by a liquid level measuring instrument.
Step 1-5, preprocessing the monitored acceleration response and the monitored liquid level response to obtain a coupling acceleration response signal; the pretreatment method comprises the following steps.
And step A, taking the monitored liquid level response signal of each TLD as a coupling vibration signal, and transmitting the coupling vibration signal back to the central server through the Internet.
And step B, removing the mean value of a group of coupled vibration signals, converting the liquid level response signal of each TLD into equivalent horizontal displacement, and converting the liquid level response signal into the equivalent horizontal displacement according to a specific formula.
In the formula u n For the level response of the nth TLD, x n Is the equivalent horizontal displacement of the nth TLD, L n Is the length of the nth TLD, h n Is the liquid depth within the nth TLD;
step C, equivalent horizontal displacement x of a group of TLDs n Respectively solving second derivatives to obtain equivalent horizontal acceleration;
d, performing low-pass filtering processing on the top acceleration and the equivalent horizontal acceleration of the super high-rise building structure, and filtering out a high-order mode of the coupling system to obtain a coupling acceleration response signal mainly based on a fundamental-order mode;
identifying characteristic values and vibration modes of the super high-rise building structure and the MTLD coupling system by the coupling acceleration response signal, and further reconstructing a state matrix A of the coupling system c ；
Step three, establishing a motion equation of a simplified model of the super high-rise building structure and the MTLD coupling system, and deducing a state matrix from the motion equation of the simplified model; the specific operation is as follows:
when the super high-rise building structure only considers the fundamental order modal response, the super high-rise building structure can be simplified into a mass-spring-damping structure with single degree of freedom; because TLD mainly relies on fundamental mode response when controlling super high-rise building structure, consequently can simplify every TLD in MTLD as equivalent mechanics model, establish the equation of motion of super high-rise building structure and the simplified model of MTLD coupled system from this, the concrete formula is:
in the formula, x s Displacement for a single degree of freedom structure;
speed for single degree of freedom configurations;
acceleration in a single degree of freedom configuration; x is the number of n Equivalent displacement for the nth TLD;
is the equivalent speed for the nth TLD;
equivalent acceleration for the nth TLD; ζ represents a unit s The fundamental order modal damping ratio of the super high-rise building structure; omega s Is the fundamental mode frequency of the super high-rise building structure; n is the number of TLDs; zeta n Fundamental mode damping ratio for the nth TLD; omega n Is the fundamental mode frequency of the nth TLD; m is T,n Actual quality for the nth TLD; m is a unit of s Is the fundamental modal quality of the super high-rise building structure; f. of w Generalized wind loads; mu.s n Represents the equivalent mass of the nth TLD to m as the effective mass ratio s The ratio of (A) to (B);
order to
Then further obtaining a state space equation of the simplified model, wherein the specific formula is as follows:
in the formula, A cs To simplify the state matrix of the model, w c For the sum of input vectors and noise due to processingThe superscript symbol represents the derivation; through simplification, A cs Expressed as:
in the formula, Z l×l ，I l×l ，P l×l ，Q l×l Are all matrices of the ith row and ith column, in which Z l×l And I l×l Respectively a zero matrix and an identity matrix;
step four, according to the state matrix A of the simplified model cs Detecting parameters of the super high-rise building structure and the MTLD, wherein the detected parameters comprise respective frequency and damping ratio of the super high-rise building structure and the MTLD and effective mass ratio of each TLD in the MTLD;
step five, obtaining the frequency response function H of the high-rise building structure according to the parameter detection result in the step four s And standard deviation of displacement response σ s ；
Step six, calculating a frequency response function H before the super high-rise building structure is controlled when the super high-rise building structure is not provided with the MTLD for control so And standard deviation of displacement response σ so ；
And seventhly, defining a vibration reduction rate eta according to the displacement response standard deviation before and after the control of the super high-rise building structure, and realizing effective evaluation on the vibration reduction performance of the super high-rise building structure and the MTLD coupling system by calculating the numerical value of the vibration reduction rate eta.
In this embodiment, the state matrix a of the coupling system is reconstructed in the second step c The specific operation is as follows:
step 2-1: and performing projection calculation on the coupling acceleration response signal, wherein the specific calculation method comprises the following steps: coupling ofThe acceleration response signal is a matrix with l rows and j columns, wherein l is the number of signal output channels, and j is the signal length; since the coupled acceleration response signal includes the super high-rise building structure top acceleration and the equivalent horizontal acceleration of a set of TLDs, assuming the number of TLDs is N, then l = N +1; construction of a matrix Y from coupled acceleration response signals P And matrix Y f The concrete formula is as follows:
in the formula, Y P And Y f Is a matrix of i rows and k columns, the size of i is determined according to the data length of the coupled acceleration response signal, k = j-2i +1, the element y in the matrix m A signal indicating the m-th time; calculating Y from projection theory f At Y P The specific formula of the projection is as follows:
in the formula, P i Representing a projection matrix, wherein a superscript symbol T represents a matrix transposition, and a superscript symbol + represents a pseudo-inverse of the matrix;
step 2-2: obtaining an observable matrix by singular value decomposition; to P i Singular value decomposition is carried out, and the specific formula is as follows:
in the formula of U 1 And V 1 A matrix of singular vectors, S 1 For the singular value matrix with 0 elements on the off-diagonal, further calculating an observable matrix Q i The concrete formula is as follows:
according to the state space principle, from observable matrix Q i Calculating an original state matrix A and an original output matrix C of the coupling system, wherein the specific formula is as follows:
A＝Q i (1:i-l:) + Q i (l+1:i,:)；
C＝Q i (1:l,:)；
step 2-3: identifying characteristic values and vibration modes of the MTLD coupling system: and (3) carrying out eigenvalue decomposition on the original state matrix A, wherein the specific formula is as follows:
in the formula (I), the compound is shown in the specification,
is an eigenvector matrix, and lambda is a diagonal matrix formed by eigenvalues; further obtaining the vibration mode matrix of the system
The concrete formula is as follows:
step 2-4: reconstructing the state matrix A of the coupled system c : from a diagonal matrix lambda and a eigenvector matrix
Obtaining characteristic value and vibration mode vector corresponding to the coupling system fundamental mode, and then reconstructing the state matrix A of the coupling system c ：
In the formula (I), the compound is shown in the specification,
λ c ＝diag[λ 1 ，λ 2 ，…，λ l ]the diag represents a matrix of elements in diagonal lines, and the superscript symbol denotes a conjugate matrix.
In this embodiment, the frequency ω of the nth TLD is obtained in the fourth step n And damping ratio ζ n The concrete formula is as follows:
wherein P (x, y) and Q (x, y) each represent P l×l And Q l×l The value of the x row and the y column;
let p be n = P (1, n + 1)/P (n +1, 1), and then the effective mass ratio ζ of the nth TLD is calculated n The concrete formula is as follows:
solving the linear equation system of the formula to obtain the effective mass ratio mu of each TLD n (ii) a Then, the value of omega is adjusted n 、ζ n And mu n Are substituted into P (1, 1) and Q (1, 1) to obtain the frequency omega of the super high-rise building structure s And damping ratio ζ s 。
In this embodiment, the state matrix A of the coupled system is reconstructed in step four c And the state matrix A of the simplified model cs Approximately equal; thus, comparative
since n is c And A cs Calculating out matrixes which are 2l multiplied by 2l and are approximately equal to each other; state matrix A of coupling system is reconstructed c And the state matrix A of the simplified model cs Are equal to each other because of A c The data are obtained by real monitoring data identification and are specific numerical values; a. The cs Is derived theoretically, and the elements of the method are expressions composed of various parameters; and the two parameters are equal, so that the actual values corresponding to the parameters for detecting the super high-rise building structure and the MTLD are obtained, and the parameters for detecting the super high-rise building structure and the MTLD are detected.
In this embodiment, step five is to solve the equation of motion of the simplified model of the super high-rise building structure and the MTLD coupled system according to a frequency domain method, and order the formula
in the formula, H s Is the frequency response function, H, of the super high-rise building structure n Is the frequency response function of the nth TLD;
will be provided with
Substituted type
To obtain H s And H n The relationship of (c) is:
general formula
Substituted type
Eliminating primordial qi to obtain H s The expression is as follows:
assuming that the power spectral density function of the excitation is S (omega), the standard deviation sigma of the displacement response of the super high-rise building structure is obtained s The concrete formula is as follows:
in the formula, the symbol '| · |' represents a modulo operation.
In this embodiment, in the sixth step, when the MTLD is not installed in the super high-rise building structure for control, the frequency response function H of the super high-rise building structure so And standard deviation of displacement response σ so The concrete formula is as follows:
in this embodiment, the calculation formula of the vibration damping rate η is:
assuming that the excitation is an ideal stationary white noise excitation, i.e. S (ω) is a constant, the damping ratio η is:
in pair type
In this embodiment, the level response in steps 1-4 is the wave height of the instrument at a certain point on the measured water surface, and is given in m.
In this embodiment, the monitored acceleration response of the top of the super high-rise building structure is the acceleration of the top of the super high-rise building structure.
In this embodiment, each TLD has a length of 11m and a width of 4.45m, and the water storage heights are 1.69m, 1.96m, 2.18m, and 2.63m, and 4 TLDs are numbered as TLD1, TLD2, TLD3, and TLD4, as shown in fig. 1. Six column members are mounted inside each TLD, each column width a p At 0.45m, the top view of the paddle column arrangement is shown in figure 2. The acceleration response of the super high-rise building structure is monitored by an accelerometer, meanwhile, the liquid level response of 4 TLDs is respectively monitored by a liquid level measuring instrument, and then the acceleration response signal of the super high-rise building structure and the liquid level response signals of the 4 TLDs are preprocessed to obtain a coupling acceleration response signal.
In the embodiment, the super high-rise building structure is simplified into a single-degree-of-freedom structure, namely, a fundamental-order modal mass m s 20802.52 tons, with actual masses of 4 TLDs being 82.73 tons, 95.94 tons, 106.71 tons and 128.74 tons, respectively. Since l is 5, P and Q are both 5 rows and 5 columns of the matrix, A cs Is 10A matrix of rows and 10 columns.
In this embodiment, first, parameters of 4 TLDs are detected, and the frequencies are: omega 1 ＝1.12rad/s、ω 2 ＝1.19rad/s、ω 3 ＝1.24rad/s、ω 4 =1.33rad/s, damping ratio: zeta 1 ＝3.57％、ζ 2 ＝3.49％、ζ 3 ＝3.33％、ζ 4 =3.02%. Then the actual quality of each TLD, the structural fundamental order modal quality and the elements of the P matrix are substituted into
In this embodiment, the specific method in step seven includes: the frequency response functions of the super high-rise building structure before and after control are obtained by using the detected super high-rise building structure and MTLD parameters are shown in FIG. 4, and it can be known that the super high-rise building structure under the control action of MTLD, | H s The | is significantly reduced; and the damping rate eta is 0.286 through numerical integration, so that the MTLD is evaluated to have good damping performance, and a remarkable control effect on structural wind vibration response can be achieved.
The above embodiments are not intended to be exhaustive or to limit the invention to other embodiments, and the above embodiments are intended to illustrate the invention and not to limit the scope of the invention, and all applications that can be modified from the invention are within the scope of the invention.
Claims (7)
1. A method for evaluating vibration reduction performance of a super high-rise building structure and an MTLD coupling system is characterized by comprising the following steps:
measuring a coupling vibration signal of a super high-rise building structure and an MTLD, and preprocessing the signal; the specific operation method comprises the following steps:
step 1-1, installing TLDs with different frequencies at intervals on the top of a super high-rise building structure, wherein a group of TLDs form an MTLD, and the MTLD and the super high-rise building form a coupling system together;
step 1-2, numbering a group of TLDs, respectively TLD 1 、TLD 2 、TLD 3 、TLD 4 .......TLD n ；
1-3, respectively installing a group of propeller column members at intervals in each TLD, and simultaneously respectively installing a liquid level measuring instrument in each TLD;
step 1-4, installing an accelerometer at the top of the super high-rise building structure, monitoring acceleration response of the top of the super high-rise building structure, and monitoring liquid level response of each TLD by a liquid level measuring instrument;
step 1-5, preprocessing the monitored acceleration response and the monitored liquid level response to obtain a coupling acceleration response signal; the pretreatment method comprises the following steps:
step A, taking the monitored liquid level response signal of each TLD as a coupling vibration signal, and transmitting the coupling vibration signal back to a central server through the Internet;
step B, removing the mean value of a group of coupled vibration signals, converting the liquid level response signal of each TLD into equivalent horizontal displacement, and converting the liquid level response signal into the equivalent horizontal displacement by the specific formula:
in the formula u n For the level response of the nth TLD, x n Is the equivalent horizontal displacement of the nth TLD, L n Is the length of the nth TLD, h n Is the liquid depth within the nth TLD;
step C, equivalent horizontal displacement x of a group of TLDs n Respectively solving second derivatives to obtain equivalent horizontal acceleration;
d, performing low-pass filtering processing on the top acceleration and the equivalent horizontal acceleration of the super high-rise building structure, and filtering out a high-order mode of the coupling system to obtain a coupling acceleration response signal mainly based on a fundamental-order mode;
identifying characteristic values and vibration modes of the super high-rise building structure and the MTLD coupling system by the coupling acceleration response signal, and further reconstructing a state matrix A of the coupling system c ；
Step three, establishing a motion equation of a simplified model of the super high-rise building structure and the MTLD coupling system, and deducing a state matrix from the motion equation of the simplified model; the method comprises the following specific operations:
when the super high-rise building structure only considers the fundamental order modal response, the super high-rise building structure can be simplified into a mass-spring-damping structure with single degree of freedom; because TLD mainly relies on fundamental mode response when controlling super high-rise building structure, consequently can simplify every TLD in MTLD as equivalent mechanics model, establish the equation of motion of super high-rise building structure and the simplified model of MTLD coupled system from this, the concrete formula is:
in the formula, x s Displacement for a single degree of freedom structure;
speed for single degree of freedom configurations;
acceleration in a single degree of freedom configuration; x is a radical of a fluorine atom n Equivalent displacement for the nth TLD;
is the equivalent speed for the nth TLD;
equivalent acceleration for the nth TLD; zeta s The fundamental order modal damping ratio of the super high-rise building structure; omega s Is the fundamental mode frequency of the super high-rise building structure; n is the number of TLDs; ζ represents a unit n A fundamental modal damping ratio for the nth TLD; omega n Fundamental mode frequency for the nth TLD; m is a unit of T,n Actual quality for the nth TLD; m is a unit of s Is the fundamental modal mass of the super high-rise building structure; f. of w Generalized wind loads; mu.s n Represents the equivalent mass of the nth TLD to m as the effective mass ratio s The ratio of (A) to (B);
order to
Then further obtaining a state space equation of the simplified model, wherein the specific formula is as follows:
in the formula, A cs To simplify the state matrix of the model, w c The superscript symbol, which is the sum of the input vector and the noise caused by the processing, represents the derivation; through simplification, A cs Expressed as:
in the formula, Z l×l ，I l×l ，P l×l ，Q l×l Are all in the l row and l columnMatrix of which Z l×l And I l×l Respectively a zero matrix and an identity matrix;
step four, according to the state matrix A of the simplified model cs Detecting parameters of the super high-rise building structure and the MTLD, wherein the detected parameters comprise respective frequency and damping ratio of the super high-rise building structure and the MTLD and effective mass ratio of each TLD in the MTLD;
step five, obtaining the frequency response function H of the high-rise building structure according to the parameter detection result in the step four s And standard deviation of displacement response σ s ；
Step six, calculating a frequency response function H before the super high-rise building structure is controlled when the super high-rise building structure is not provided with the MTLD for control so And standard deviation of displacement response σ so ；
And step seven, defining a vibration reduction rate eta according to the displacement response standard deviation before and after the super high-rise building structure is controlled, and realizing effective evaluation on the vibration reduction performance of the super high-rise building structure and the MTLD coupling system by calculating the numerical value of the vibration reduction rate eta.
2. The method for evaluating the vibration damping performance of a super high-rise building structure and an MTLD coupling system according to claim 1, wherein: reconstructing the state matrix A of the coupling system in the second step c The specific operation is as follows:
step 2-1: and performing projection calculation on the coupling acceleration response signal, wherein the specific calculation method comprises the following steps: the coupled acceleration response signal is a matrix with l rows and j columns, wherein l is the number of signal output channels, and j is the signal length; since the coupled acceleration response signal comprises the super high-rise building structure top acceleration and the equivalent horizontal acceleration of a set of TLDs, assuming the number of TLDs is N, then l = N +1; construction of a matrix Y from coupled acceleration response signals P And matrix Y f The concrete formula is as follows:
in the formula, Y P And Y f Is a matrix of i rows and k columns, i being sized according to the data length of the coupled acceleration response signal, k = j-2i +1, element y in the matrix m A signal indicating the m-th time; calculating Y from projection theory f At Y P The specific formula of the projection is as follows:
in the formula, P i Representing a projection matrix, wherein a superscript symbol T represents a matrix transposition, and a superscript symbol + represents a pseudo-inverse of the matrix;
step 2-2: obtaining an observable matrix by singular value decomposition; to P i Singular value decomposition is carried out, and the specific formula is as follows:
in the formula of U 1 And V 1 A matrix of singular vectors, S 1 For the singular value matrix with 0 elements on the off diagonal, an observable matrix Q is further calculated i The concrete formula is as follows:
according to the state space principle, from observable matrix Q i Calculating an original state matrix A and an original output matrix C of the coupling system, wherein the specific formula is as follows:
A＝Q i (1:i-l:) + Q i (l+1:i,:)；
C＝Q i (1:l,:)；
step 2-3: identifying characteristic values and vibration modes of the MTLD coupling system: and (3) carrying out eigenvalue decomposition on the original state matrix A, wherein the specific formula is as follows:
in the formula (I), the compound is shown in the specification,
is an eigenvector matrix, and lambda is a diagonal matrix formed by eigenvalues; further obtaining the vibration mode matrix of the system
The concrete formula is as follows:
step 2-4: reconstructing the state matrix A of the coupled system c : from a diagonal matrix lambda and a eigenvector matrix
Obtaining the characteristic value and the vibration mode vector corresponding to the fundamental mode of the coupled system, and then reconstructing the state matrix A of the coupled system c ：
In the formula (I), the compound is shown in the specification,
λ c ＝diag[λ 1 ，λ 2 ，…，λ l ]the diag represents a matrix of elements in diagonal lines, and the superscript symbol denotes a conjugate matrix.
3. The method for evaluating the vibration damping performance of the super high-rise building structure and MTLD coupling system according to claim 2, wherein: step four, the frequency omega of the nth TLD is obtained n And damping ratio ζ n The concrete formula is as follows:
wherein P (x, y) and Q (x, y) each represent P l×l And Q l×l The value of the x row and the y column;
let p be n = P (1, n + 1)/P (n +1, 1), then the effective mass ratio μ for the nth TLD is calculated n The concrete formula is as follows:
solving the linear equation system of the formula to obtain the effective mass ratio mu of each TLD n (ii) a Then, the value of omega is adjusted n 、ζ n And mu n Are substituted into P (1, 1) and Q (1, 1) to obtain the frequency omega of the super high-rise building structure s And damping ratio ζ s 。
4. The method for evaluating the vibration damping performance of the super high-rise building structure and MTLD coupling system according to claim 3, wherein:
state matrix A of coupled system by reconstruction in step four c And the state matrix A of the simplified model cs Approximately equal; thus, comparative
due to A c And A cs Calculating out matrixes which are 2l multiplied by 2l and are approximately equal to each other; state matrix A of coupling system is reconstructed c And the state matrix A of the simplified model cs The elements in (1) are equal in one-to-one correspondence, so that the parameters of the super high-rise building structure and the MTLD are detected.
5. The method for evaluating the vibration damping performance of the super high-rise building structure and MTLD coupling system according to claim 1, wherein: step five, solving the motion equation of the simplified model of the super high-rise building structure and the MTLD coupling system according to a frequency domain method
Load term f w /m s Is equal to e iωt The frequency response function of the coupled system can then be expressed as:
in the formula, H s Is the frequency response function, H, of a super high-rise building structure n Is the frequency response function of the nth TLD;
will be provided with
Substituted type
To obtain H s And H n The relationship of (c) is:
general formula (II)
Substituted type
Eliminating primordial qi to obtain H s The expression is as follows:
assuming that the power spectral density function of the excitation is S (omega), the standard deviation sigma of the displacement response of the super high-rise building structure is obtained s The concrete formula is as follows:
in the formula, the symbol '| · |' represents a modulo operation.
6. The method for evaluating the vibration damping performance of the super high-rise building structure and MTLD coupling system according to claim 5, wherein: and sixthly, when the super high-rise building structure is not provided with the MTLD for control, the frequency response function H of the super high-rise building structure so And standard deviation of displacement response σ so The concrete formula is as follows:
7. the method for evaluating the vibration damping performance of the super high-rise building structure and MTLD coupling system according to claim 6, wherein: the calculation formula of the damping rate eta is as follows:
assuming that the excitation is an ideal stationary white noise excitation, i.e. S (ω) is a constant, the damping ratio η is:
in pair type
And when the vibration reduction rate eta is more than or equal to 0.2, the MTLD can be evaluated to have good vibration reduction performance, and a remarkable control effect can be achieved on the wind vibration response of the super high-rise building structure.
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| CN117556556B (en) * | 2023-10-11 | 2024-05-10 | 华南理工大学 | MTLD optimal design method considering time-varying characteristics of structural dynamic characteristic parameters |
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