Calculation method for hydrodynamic coefficient of damping component in tuned liquid damper

Abstract

A method for calculating the hydrodynamic coefficient of a damping component in a tuned liquid damper comprises the following steps that S11, wave height response signals of a TLD free surface are collected through a plurality of wave height meters under the action of random loads; s12, performing parameter identification on the wave height response signal by adopting a data-driven random subspace method to obtain the inherent frequency and the damping ratio of the TLD system; the method comprises the following steps of S11, establishing a TLD equivalent mechanical model, S13, establishing an inherent frequency omega T formula and a damping ratio zeta T formula of the TLD equivalent mechanical model, and S14, substituting the inherent frequency of a TLD system into the inherent frequency omega T formula for calculation to obtain an additional mass coefficient Cm of a TLD internal damping component, and substituting the damping ratio of the TLD system into the damping ratio zeta T formula for calculation to obtain a resistance coefficient Cd of the TLD internal damping component. The hydrodynamic coefficient, obtained through the method, of the damping component can be used for calculating the additional mass and the damping ratio generated by the damping component under the action of the random load and used for dynamic response analysis of an equivalent mechanical model on TLD under the action of the random load; and the method is simple and convenient, easy to implement and suitable for determining the optimal design scheme of the damping component for controlling the wind-induced vibration of the super high-rise building by the TLD.

Description

Technical Field

[0001] The invention relates to the technical field of wind-induced vibration control of high-rise buildings, and in particular to a method for calculating the hydrodynamic coefficient of a damping component inside a tuning liquid damper. Background Art

[0002] Tuned liquid dampers (TLDs) have the advantages of simple structure and low installation and maintenance costs, and have been successfully used in wind-induced vibration control of super high-rise buildings. TLDs are generally composed of a water tank and internal damping components, where the damping components can improve the energy dissipation capacity of the TLD and optimize the vibration reduction performance of the TLD. When wind-induced loads cause super high-rise buildings to vibrate, the TLD uses the inertial force generated by the sloshing liquid to suppress the vibration response of the super high-rise building. In order to study the basic principles of liquid sloshing and to facilitate the design of TLD in actual engineering, TLD is usually expressed as an equivalent mechanical model. However, in the equivalent mechanical model, the calculation of the natural frequency and damping ratio requires the prior determination of the hydrodynamic coefficients of the damping component (including the drag coefficient C d and the additional mass coefficient C m ).

[0003] At present, there are two main methods for obtaining the hydrodynamic coefficient of the internal damping component of TLD: (1) Calculate it using theoretical formulas based on the measured dynamic water pressure on the damping component during a sloshing cycle; (2) Fit the frequency response curve of the equivalent mechanical model with the measured data of TLD and determine it by minimizing the error between the two curves. The above methods are currently only applicable to the case where the external excitation is a periodic load, and cannot be directly applied to the determination of the hydrodynamic coefficient of the internal damping component of TLD of super high-rise buildings under random wind loads. Summary of the invention

[0004] Based on this, the purpose of the present invention is to provide a method for calculating the hydrodynamic coefficient of the internal damping component of a tuned liquid damper, so as to solve the problem of solving the hydrodynamic coefficient of the internal damping component of a super high-rise building TLD under random loads.

[0005] A method for calculating the hydrodynamic coefficient of a damping component inside a tuned liquid damper comprises the following steps:

[0006] Step S11: Under the action of random load, the wave height response signal η(t)=[η 1 (t),η 2 (t),…,η k (t)] Τ , where k is the number of wave height meters, with a minimum value of 1 and a maximum value equal to the TLD mode order;

[0007] Step S12: Identify the parameters of the wave height response signal using the data-driven stochastic subspace method to obtain the natural frequency and damping ratio of the TLD system;

[0008] Step S13: Establish the natural frequency ω T formula and damping ratio ζ T formula, where

[0009]

[0010] ζ T = ζ w + ζ p ;

[0011] In the formula, ω w and m eq are the natural frequency and equivalent mass of the pure water tank respectively, m p,eq is the additional mass of the damping member, ζ w is the damping ratio caused by the viscosity of water, ζ p is the damping ratio caused by the damping member;

[0012] Step S14: Substitute the natural frequency of the TLD system into the natural frequency ω T formula for calculation to obtain the additional mass coefficient C m of the internal damping member of the TLD. Substitute the damping ratio of the TLD system into the damping ratio ζ T formula for calculation to obtain the drag coefficient C d of the internal damping member of the TLD.

[0013] Preferably, the step S12 includes:

[0014] Step S121: Establish a Hankel matrix based on the wave height response signal;

[0015]

[0016] In the formula, Y 0|2i-1 is a matrix composed of 2i block rows and j columns. "0|2i - 1" are the subscripts of y 0 and y 2i-1 respectively. y i is the response data measured by all wave height gauges at time i. j satisfies 2i + j - 1 < N, where N is the total data length. Y p is the upper half of the Hankel matrix, called the past matrix, and Y f is the lower half of the Hankel matrix, called the future matrix;

[0017] Among them, another expression of Y 0|2i-1 is;

[0018]

[0019] In the formula, Y p Added a row. Y f A block of rows was reduced;

[0020] Step S122, calculate the projection matrix P according to the Hankel matrix i ;

[0021]

[0022] Step S123, introducing Kalman filter sequence and the observable matrix O i , transform the projection matrix;

[0023]

[0024] Step S124, i Perform singular value decomposition to obtain the observable matrix O i and Kalman filter sequence

[0025]

[0026]

[0027]

[0028]

[0029] Where S is a diagonal matrix with singular values ​​arranged from large to small, S 1 is the non-zero part of S, U and V are orthogonal matrices, U 1 , U 2 and V 1 、V 2 They are matrices composed of the internal elements of U and V, which are specifically related to S 2 The number of rows and columns of is related to the number of columns. The superscripts "T" and "+" indicate the transpose and pseudo-inverse of the matrix.

[0030] Step S125, according to the Kalman filter sequence Calculate the TLD system matrix;

[0031]

[0032] Y i|j =[y i y i+1 … y i+j-1 ];

[0033] In the formula, A is the discrete state matrix, C is the output matrix;

[0034] Step S126, calculating the natural frequency and damping ratio of the TLD system according to the TLD system matrix.

[0035] Preferably, the step S126 includes:

[0036] Step S1261, performing eigenvalue decomposition on the discrete state matrix A;

[0037] A=ΨΛΨ -1 ;

[0038] Where Ψ is the discrete system eigenvector matrix, Λ is the diagonal matrix composed of discrete system eigenvalues, Λ=diag(μ i ), μ i is the eigenvalue of the discrete system;

[0039] Step S1262, calculate according to the discrete system eigenvalue and the wave height meter sampling time interval to obtain the continuous system eigenvalue, and at the same time calculate the continuous system eigenvalue to obtain the natural frequency and damping ratio of the TLD system:

[0040]

[0041]

[0042]

[0043] Where Δt is the sampling time interval of the wave height meter, a i is the real part of the eigenvalue of the continuous system, b i is the imaginary part of the eigenvalue of the continuous system.

[0044] Preferably, the step S13 comprises:

[0045] Step S131, calculating the sloshing force f acting on the unit column length at any position of the internal damping component of the TLD;

[0046]

[0047]

[0048] In the formula, C d is the resistance coefficient of the damping component, ρ is the density of water, A 0 is the projected area per unit damping component height, U p is the water particle velocity orthogonal to the damping element, C m is the additional mass coefficient of the damping component, V 0is the displacement volume per unit damping element height, q is the generalized coordinate, x and z are the position coordinates of the damping element, L is the length of the water tank, and h is the static height of the water tank;

[0049] Step S132, based on the virtual displacement principle, calculate the virtual work generated by all damping components according to the sloshing force;

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] In the formula, ω w and m eq are the natural frequency and equivalent mass of the pure water tank, ζ p and m p,eq are the damping ratio and additional mass of the damping component, Г is the modal participation factor, n p is the number of damping components, B is the width of the water tank, g is the acceleration of gravity, δυ is the virtual horizontal displacement of the damping component, x j is the horizontal distance between the damping member and the side wall of the water tank;

[0056] Step S133, establishing the natural frequency ω of the TLD equivalent mechanical model according to the virtual work T Formula and damping ratio ζ T formula.

[0057] Preferably, when the TLD internal damping component specifically refers to a propeller column, the propeller column damping ratio ζ is obtained by calculation based on the swaying force and the virtual work. p and additional mass m p,eq ;

[0058]

[0059]

[0060] In the formula, a p is 1 / 2 of the propeller length, σ q is the root mean square of the TLD sway response.

[0061] Preferably, the damping ratio ζ caused by the viscosity of water is w for:

[0062]

[0063] Where ν is the kinematic viscosity of the water inside the water tank.

[0064] Preferably, the model of the TLD system is a scaled model or a CFD model.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] (1) This method solves the problem of solving the hydrodynamic coefficient of the internal damping component of the TLD under random loads;

[0067] (2) The hydrodynamic coefficient of the damping component obtained by this method can be used to calculate the additional mass and damping ratio of the damping component under the action of random loads;

[0068] (3) The hydrodynamic coefficients of the damping components obtained by this method can be used to analyze the dynamic response of TLD under random loads using an equivalent mechanical model;

[0069] (4) This method is simple, convenient and easy to implement, and is suitable for TLD to determine the optimal design scheme of damping components for wind-induced vibration control of super-high-rise buildings. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 A schematic flow chart of a method for calculating the hydrodynamic coefficient of an internal damping component of a tuned liquid damper proposed by the present invention;

[0071] Figure 2 It is a schematic diagram of the built-in paddle TLD in the present invention;

[0072] Figure 3 for Figure 2 CFD model diagram of TLD in;

[0073] Figure 4 for Figure 2 Time history graph of random excitation of TLD substrate.

[0074] The following specific implementation manner will further illustrate the present invention in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0075] The following description is used to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are only examples, and those skilled in the art may think of other obvious variations.

[0076] See also Figures 1 to 3 The embodiment of the present invention provides a method for calculating the hydrodynamic coefficient of the internal damping component of a tuned liquid damper, comprising the following steps:

[0077] Step S11: Under the action of random load, the wave height response signal η(t)=[η1 (t), η 2 (t), …, η k (t)] Τ , where k is the number of wave gauges, with a minimum value of 1 and a maximum value equal to the TLD modal order;

[0078] Step S12: Use the data-driven stochastic subspace method to identify the parameters of the wave height response signal to obtain the natural frequency and damping ratio of the TLD system;

[0079] Step S13: Establish the natural frequency ω T formula and damping ratio ζ T formula, where

[0080]

[0081] ζ T = ζ w + ζ p ;

[0082] In the formula, ω w and m eq are respectively the natural frequency and equivalent mass of the pure water tank, m p,eq is the added mass of the damping member, ζ w is the damping ratio caused by the viscosity of water, ζ p is the damping ratio caused by the damping member;

[0083] Step S14: Substitute the natural frequency of the TLD system into the natural frequency ω T formula for calculation to obtain the added mass coefficient C m of the internal damping member of the TLD. Substitute the damping ratio of the TLD system into the damping ratio ζ T formula for calculation to obtain the drag coefficient C d of the internal damping member of the TLD.

[0084] Preferably, the step S12 includes:

[0085] Step S121: Establish a Hankel matrix based on the wave height response signal;

[0086]

[0087] In the formula, Y 0|2i-1 is a matrix composed of 2i block rows and j columns. "0|2i - 1" are respectively the subscripts of y 0 and y 2i-1 . y i is the response data measured by all wave gauges at time i. j satisfies 2i + j - 1 < N, where N is the total data length, and Y pis the upper part of the Hankel matrix, called the past matrix, Y f is the lower half of the Hankel matrix, called the future matrix;

[0088] Among them, Y 0|2i-1 Another expression of is;

[0089]

[0090] In the formula, Y p Added a row. Y f A block of rows was reduced;

[0091] Step S122, calculate the projection matrix P according to the Hankel matrix i ;

[0092]

[0093] Step S123, introducing Kalman filter sequence and the observable matrix O i , transform the projection matrix;

[0094]

[0095] Step S124, i Perform singular value decomposition to obtain the observable matrix O i and Kalman filter sequence

[0096]

[0097]

[0098]

[0099]

[0100] Where S is a diagonal matrix with singular values ​​arranged from large to small, S 1 is the non-zero part of S, U and V are orthogonal matrices, U 1 , U 2 and V 1 、V 2 They are matrices composed of the internal elements of U and V, which are specifically related to S 2 The number of rows and columns of is related to the number of columns. The superscripts "T" and "+" indicate the transpose and pseudo-inverse of the matrix.

[0101] Step S125, according to the Kalman filter sequence Calculate the TLD system matrix;

[0102]

[0103] Y i|j =[y i y i+1 … y i+j-1 ];

[0104] In the formula, A is the discrete state matrix, C is the output matrix;

[0105] Step S126, calculating the natural frequency and damping ratio of the TLD system according to the TLD system matrix.

[0106] Preferably, the step S126 includes:

[0107] Step S1261, performing eigenvalue decomposition on the discrete state matrix A;

[0108] A=ΨΛΨ -1 ;

[0109] Where Ψ is the discrete system eigenvector matrix, Λ is the diagonal matrix composed of discrete system eigenvalues, Λ=diag(μ i ), μ i is the eigenvalue of the discrete system;

[0110] Step S1262, calculate according to the discrete system eigenvalue and the wave height meter sampling time interval to obtain the continuous system eigenvalue, and at the same time calculate the continuous system eigenvalue to obtain the natural frequency and damping ratio of the TLD system:

[0111]

[0112]

[0113]

[0114] Where Δt is the sampling time interval of the wave height meter, a i is the real part of the eigenvalue of the continuous system, b i is the imaginary part of the eigenvalue of the continuous system.

[0115] Preferably, the step S13 comprises:

[0116] Step S131, calculating the sloshing force f acting on the unit column length at any position of the internal damping component of the TLD;

[0117]

[0118]

[0119] In the formula, Cd is the resistance coefficient of the damping component, ρ is the density of water, A 0 is the projected area per unit damping component height, U p is the water particle velocity orthogonal to the damping element, C m is the additional mass coefficient of the damping component, V 0 is the displacement volume per unit damping element height, q is the generalized coordinate, x and z are the position coordinates of the damping element, L is the length of the water tank, and h is the static height of the water tank;

[0120] Step S132, based on the virtual displacement principle, calculate the virtual work generated by all damping components according to the sloshing force;

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] In the formula, ω w and m eq are the natural frequency and equivalent mass of the pure water tank, ζ p and m p,eq are the damping ratio and additional mass of the damping component, Г is the modal participation factor, n p is the number of damping components, B is the width of the water tank, g is the acceleration of gravity, δυ is the virtual horizontal displacement of the damping component, x j is the horizontal distance between the damping member and the side wall of the water tank;

[0127] Step S133, establishing the natural frequency ω of the TLD equivalent mechanical model according to the virtual work T Formula and damping ratio ζ T formula.

[0128] Preferably, when the TLD internal damping component specifically refers to a propeller column, the propeller column damping ratio ζ is obtained by calculation based on the swaying force and the virtual work. p and additional mass m p,eq ;

[0129]

[0130]

[0131] In the formula, a p is 1 / 2 of the propeller length, σ q is the root mean square of the TLD sway response.

[0132] Preferably, the damping ratio ζ caused by the viscosity of water is w for:

[0133]

[0134] Where ν is the kinematic viscosity of the water inside the water tank.

[0135] In a preferred embodiment of the present invention, the model of the TLD system is a scaled model or a CFD model.

[0136] The method of the present invention is described in detail below with specific embodiments:

[0137] See also Figure 2 and Figure 3 , take a built-in propeller TLD, the length, width and height of the water tank are 2.1m, 0.64m and 0.9m respectively, and the hydrostatic height is 0.44m. Nine propellers are arranged at equal intervals inside the water tank, and the line connecting the center points of the propellers divides the length and width of the water tank equally, and the length of each propeller is 0.077m.

[0138] See also Figure 3 and Figure 4 The computational fluid dynamics (CFD) method is used to simulate the sloshing response of the TLD under random excitation of Gaussian white noise. Four wave height meters are installed at 0.1m, 0.78m, 1.3m, and 2m from the side wall of the water tank to record the TLD free surface wave height response data η(t)=[η 1 (t),η 2 (t),η 3 (t),η 4 (t)] T After the wave height data is collected, the data-driven random subspace method is used to identify the modal parameters. Since the TLD equivalent mechanical model is a first-order sloshing model, when i = 1, the first-order modal parameter results of the TLD system are the required parameters for solving the hydrodynamic coefficient of the damping component, and finally the first-order natural frequency of the TLD system is obtained as ω 1 =2.834rad / s, the first-order damping ratio of the TLD system is ζ 1 =3.09%. The first-order modal parameter identification results (first-order natural frequency and first-order damping ratio) are further substituted into the natural frequency ω of the TLD equivalent mechanical model. T Formula and damping ratio ζ T In the formula, the additional mass coefficient C of the propeller column is obtained m =1.52, drag coefficient C d =8.54.

[0139] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for calculating the hydrodynamic coefficient of the internal damping component of a tuned liquid damper, characterized in that: The following steps are involved: Step S11, under the action of random load, the wave height response signals η(t)=[η1(t),η2(t),…,η k (t)] Τ , where k is the number of wave height meters, with a minimum value of 1 and a maximum value equal to the TLD mode order; Step S12, using a data-driven random subspace method to perform parameter identification on the wave height response signal to obtain the natural frequency and damping ratio of the TLD system; Step S13, establishing the natural frequency ω of the TLD equivalent mechanical model T Formula and damping ratio ζ T Formula, where g T =ζ w +g p ; In the formula, ω w and m eq are the natural frequency and equivalent mass of the pure water tank, m p,eq is the additional mass of the damping component, ζ w is the damping ratio caused by the viscosity of water, ζ p is the damping ratio caused by the damping element; Step S14, substitute the natural frequency of the TLD system into the natural frequency ω T The additional mass coefficient C of the internal damping component of TLD is calculated by the formula m , substitute the damping ratio of the TLD system into the damping ratio ζ T The drag coefficient C of the internal damping component of TLD is calculated by the formula d .

2. The method for calculating the hydrodynamic coefficient of the internal damping component of the tuned liquid damper according to claim 1, characterized in that: The step S12 comprises: Step S121, establishing a Hankel matrix according to the wave height response signal; where Y 0|2i-1 is a matrix composed of 2i block rows and j columns, and "0|2i - 1" are the subscripts of y0 and y 2i-1 respectively, y i is the response data measured by all wave gauges at time i, j satisfies 2i + j - 1 < N, N is the total data length, Y p is the upper half of the Hankel matrix, which is called the past matrix, Y f is the lower half of the Hankel matrix, which is called the future matrix; Among them, Y 0|2i-1 Another expression of is; In the formula, Y p Added a row. Y f A block of rows was reduced; Step S122, calculate the projection matrix P according to the Hankel matrix i ; Step S123, introducing Kalman filter sequence and the observable matrix O i , transform the projection matrix; Step S124, P i Perform singular value decomposition to obtain the observable matrix O i and Kalman filter sequence Where S is a diagonal matrix with singular values ​​arranged from large to small, S1 is the non-zero part of S, U and V are orthogonal matrices, U1, U2 and V1, V2 are matrices composed of the internal elements of U and V respectively, which is related to the number of rows and columns of S2, and the superscript " T " and "+" represent the transpose and pseudo-inverse of the matrix; Step S125, according to the Kalman filter sequence Calculate the TLD system matrix; AND i|i =[and i and i+1 … and i+j-1 ]; In the formula, A is the discrete state matrix, C is the output matrix; Step S126, calculating the natural frequency and damping ratio of the TLD system according to the TLD system matrix.

3. The method for calculating the hydrodynamic coefficient of the internal damping component of the tuned liquid damper according to claim 2, characterized in that: The step S126 comprises: Step S1261, performing eigenvalue decomposition on the discrete state matrix A; A=ΨΛΨ -1 ; Where Ψ is the eigenvector matrix of the discrete system, Λ is the diagonal matrix composed of the eigenvalues ​​of the discrete system, Λ=diag(μi), μi is the eigenvalue of the discrete system; Step S1262, calculate according to the discrete system eigenvalue and the wave height meter sampling time interval to obtain the continuous system eigenvalue, and at the same time calculate the continuous system eigenvalue to obtain the natural frequency and damping ratio of the TLD system: Where Δt is the sampling time interval of the wave height meter, a i is the real part of the eigenvalue of the continuous system, b i is the imaginary part of the eigenvalue of the continuous system.

4. The method for calculating the hydrodynamic coefficient of the internal damping component of the tuned liquid damper according to claim 3, characterized in that: The step S13 comprises: Step S131, calculating the sloshing force f acting on the unit column length at any position of the internal damping component of the TLD; In the formula, C d is the resistance coefficient of the damping component, ρ is the density of water, A0 is the projected area per unit height of the damping component, U p is the water particle velocity orthogonal to the damping element, C m is the additional mass coefficient of the damping element, V0 is the displacement volume per unit height of the damping element, q is the generalized coordinate, x and z are the position coordinates of the damping element, L is the length of the water tank, and h is the static height of the water tank; Step S132, based on the virtual displacement principle, calculate the virtual work generated by all damping components according to the sloshing force; In the formula, ω w and m eq are the natural frequency and equivalent mass of the pure water tank, ζ p and m p,eq are the damping ratio and additional mass of the damping component, Г is the modal participation factor, n p is the number of damping components, B is the width of the water tank, g is the acceleration of gravity, δυ is the virtual horizontal displacement of the damping component, x j is the horizontal distance between the damping member and the side wall of the water tank; Step S133, establishing the natural frequency ω of the TLD equivalent mechanical model according to the virtual work T Formula and damping ratio ζ T formula.

5. The method for calculating the hydrodynamic coefficient of the internal damping component of the tuned liquid damper according to claim 4, characterized in that: When the internal damping component of the TLD is specifically a propeller column, the propeller column damping ratio ζ is obtained by calculation based on the swaying force and virtual work. p and additional mass m p,eq ; In the formula, a p is 1 / 2 of the propeller length, σ q is the root mean square of the TLD sway response.

6. The method for calculating the hydrodynamic coefficient of the internal damping component of the tuned liquid damper according to claim 1, characterized in that: The damping ratio ζ caused by the viscosity of water w for: Where ν is the kinematic viscosity of the water inside the water tank.

7. The method for calculating the hydrodynamic coefficient of the internal damping component of a tuned liquid damper according to any one of claims 1 to 6, characterized in that: The model of the TLD system is a scaled model or a CFD model.

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