Non-uniform excitation input method for numerical simulation analysis of building structure vibration double control

Abstract

This invention discloses a method for non-uniform excitation input analysis in numerical simulation of building structures under dual-control vibration control. The method includes: 1) obtaining the acceleration time histories of each column base using a column base acceleration time history interpolation method based on spectrum analysis; and 2) applying a stiffness-controllable spring-damping system in the acceleration input direction, based on the traditional large-mass method, to form a stiffness-adjustable spring-damping system constrained large-mass method to control nodal displacement deviations. This method can synergistically solve the key challenges of non-uniform excitation simulation and displacement control, significantly improving the accuracy of seismic response analysis under complex soil-structure interactions. It is applicable to building structures with high seismic safety requirements, such as large-span spatial structures, bridge engineering, and underground complexes, as well as to the dual-control vibration simulation analysis of buildings adjacent to urban rail transit systems and factory structures of ultra-large seismic simulation shaking tables.

Description

Technical Field

[0001] This invention relates to the field of building vibration / vibration control technology, and in particular to a non-uniform excitation input method for numerical simulation analysis of building structure vibration and vibration dual control. Background Technology

[0002] Currently, the methods commonly used for numerical simulation analysis of base acceleration input in building structure vibration control generally include uniform excitation input and the traditional large mass method. However, these methods have the following drawbacks:

[0003] 1) Simplified Errors of Uniform Excitation: Traditional uniform excitation methods use the maximum measurement point acceleration as the uniform input to the base. However, the actual propagation of vibration waves is affected by traveling wave effects, local site effects, and coherence losses. In particular, artificially induced vibrations, which are mainly of medium and high frequency, attenuate significantly in the soil, resulting in time differences, amplitude attenuation, and spectral differences in vibrations at adjacent supports. The uniform excitation assumption completely ignores these factors, which will significantly underestimate or overestimate the internal force response of key components.

[0004] 2) Crude interpolation methods: During the propagation of seismic waves or vibration waves, the amplitude attenuation and phase delay of different frequency components are caused by soil damping, scattering, and inelastic deformation. Traditional interpolation techniques are mostly based on linear or polynomial fitting, which do not consider the frequency attenuation characteristics of the soil, resulting in distortion of high-frequency vibration components.

[0005] 3) Limitations of the traditional large mass method. During acceleration input, the traditional large mass method suffers from numerical instability due to the increased number of degrees of freedom, resulting in continuously increasing displacement drift and affecting the reliability of long-duration seismic response and long-term vibration response analysis.

[0006] Therefore, new technological approaches are needed to at least partially overcome the problems existing in the prior art. Summary of the Invention

[0007] To address the issues of overly conservative uniform acceleration field input and insufficient computational accuracy and displacement drift in existing non-uniform excitation input techniques, this invention proposes two core innovations: First, a column base acceleration time history interpolation method based on spectral analysis with corrections for soil attenuation and structural construction effects. This method uses acceleration time history data from key nodes obtained through field testing, combined with soil frequency attenuation characteristics and considering corrections for the impact of building construction, to accurately fit the acceleration time histories of all column bases using an improved windowed four-spectrum interpolation FFT technique. Second, a non-uniform excitation vibration input technique using a stiffness-adjustable spring-damping system constrained mass method is proposed. Based on the traditional mass method, a stiffness-controllable spring-damping system is applied in the acceleration input direction to effectively suppress displacement drift.

[0008] More specifically, according to one aspect of the present invention, a method for non-uniform excitation input analysis of vibration dual-control numerical simulation of building structures is provided, comprising:

[0009] 1) Using a column base acceleration time history interpolation method based on spectrum analysis, the acceleration time histories of each column base are obtained, and

[0010] 2) Based on the traditional large mass method, a spring-damping system with controllable stiffness is applied in the direction of acceleration input to form a large mass method with adjustable stiffness spring-damping system to control the displacement deviation of nodes.

[0011] According to an embodiment of the present invention, step 1) includes:

[0012] 1.1) Measure the acceleration of key nodes, with the measuring points corresponding to the positions of pile foundations or structural columns, to form a control network covering the structural base;

[0013] 1.2) Calculate frequency domain attenuation;

[0014] 1.3) Calculate the soil attenuation compensation coefficient;

[0015] 1.4) Calculate the structural construction impact correction factor; and

[0016] 1.5) Amplitude spatial interpolation correction, column foot time-domain acceleration synthesis.

[0017] According to an embodiment of the present invention, in 1.1), the distance D between measuring points satisfies the spatial sampling theorem: D≤Vs / (2fs), where Vs is the minimum shear wave velocity, and f s To analyze the highest frequency (≥50Hz).

[0018] According to an embodiment of the present invention, wherein 1.2) includes:

[0019] The measured acceleration time history is windowed using a Hanning window to suppress spectral leakage, and then subjected to an FFT windowing transform.

[0020] Extract four spectral lines k1, k2, k3, and k4 near the peak of the FFT spectrum, where k2 = k1 + 1, k3 = k2 + 1, and k4 = k3 + 1, and calculate the interpolation variables β and α:

[0021] ,

[0022] Where p 11 , p 13 , p 15 The coefficients of the odd-order terms are determined by the window function;

[0023] Calculate the true center frequency f and the corresponding amplitude A for all peaks (m peaks):

[0024]

[0025]

[0026] Where X is the complex spectral value of the spectral line near the peak in the FFT spectrum, N is the number of points of the FFT transform, and P20 and P22 are the even-degree polynomial coefficients related to the window function.

[0027] According to an embodiment of the present invention, wherein 1.3) includes:

[0028] Establish a theoretical frequency-distance dependent decay function: Where f is frequency, d is distance, and the quality factor is... , Q0 is the reference quality factor, V s (f) represents the frequency-dependent shear wave velocity;

[0029] Through exponential polynomial spectral simulation, the formation reflection coefficient R(f) and absorption attenuation effect are separated:

[0030] ,in, Let be the absorption attenuation function, ck be the coefficients of the k-th order polynomial, k be the polynomial order, and f be the frequency variable; separate the attenuation response spectrum from the observed spectrum: , The original vibration signal spectrum;

[0031] After combining the observed attenuation response spectrum with the theoretical attenuation function, the high-frequency attenuation coefficient α is obtained by least-squares fitting. h With low-frequency attenuation coefficient α l ;

[0032] The high-frequency attenuation coefficient α obtained by fitting h and low-frequency attenuation coefficient α l Embedded decay function:

[0033] By correcting Q0 and η in the theoretical attenuation function formula, the corrected frequency-distance dependent attenuation function is obtained.

[0034] Among them, f p f is the dominant frequency of the vibration wave. max To analyze the highest frequency, d represents the wave propagation distance;

[0035] According to an embodiment of the present invention, wherein 1.4) includes:

[0036] Convert the base decay caused by structural construction into acceleration amplitude decay: , where A ratΔdB is the acceleration amplitude attenuation coefficient, and ΔdB is the decibel attenuation (dB), which is determined according to the structural form and floor height.

[0037] Frequency-dependent modeling links the attenuation effect to the structure's natural frequency f. st Related: S st Let f be the structural attenuation coefficient at frequency f. st Let β be the first natural frequency of the structure (Hz). f This is the attenuation bandwidth coefficient.

[0038] According to an embodiment of the present invention, wherein 1.5) includes:

[0039] Frequency domain interpolation synthesizes the acceleration spectrum at point j of the target column base.

[0040]

[0041] Where, r j Let r be the target interpolation point position vector. i Let A be the position vector of measurement point i. i (f) is the measured acceleration FFT spectrum at measurement point i, W i (r) is the weighting function centered at measurement point i;

[0042]

[0043] Temporal reconstruction: For each column base position A j Perform inverse FFT transformation to obtain the acceleration time history a j (t),

[0044]

[0045] According to an embodiment of the present invention, step 2) includes:

[0046] 2.1) Set a large mass, including adding a large mass M to each column base node. L Satisfying M L ≥1000M struct M struct Given the total mass of the structure, the acceleration time history a(t) of each column base obtained from the interpolation calculation in step 1) is then converted into a force: P(t) = -M L ·a(t);

[0047] 2.2) Apply a spring-damped system, including parallel connection of miniature spring-damped units in the acceleration input directions (X, Y, Z), whose initial stiffness coefficient Ks and damping coefficient Cs can be taken as follows:

[0048] ,

[0049] Where K struct For the overall structural stiffness, The damping ratio;

[0050] 2.3) Stiffness adjustment based on displacement control.

[0051] According to an embodiment of the present invention, wherein 2.3) includes:

[0052] Real-time calculation of nodal displacement u(t) and target displacement u g Deviation of (t): ;

[0053] When Δu(t) is greater than the allowable threshold δ, adaptive stiffness adjustment is performed: Where ε is the convergence factor, K s 0 K s 1 These are the initial stiffness and adjusted stiffness of the spring damping unit, respectively.

[0054] When Δu(t) does not exceed the threshold δ, obtain the response of the structural node.

[0055] This invention addresses the problems of consistent excitation and non-consistent excitation in the numerical simulation analysis of vibration and seismic dual control of building structures. It employs two technologies in synergy to solve the key challenges of displacement control in non-consistent excitation simulation: a column base acceleration time history interpolation method based on spectrum analysis and a proposed non-consistent excitation vibration input technology using a stiffness-adjustable spring-damped system constrained large mass method. This significantly improves the accuracy of vibration and seismic dual control response analysis under complex soil-structure interactions, greatly enhances computational efficiency, and strictly controls displacement errors. It is applicable to building structures with high seismic safety requirements, such as large-span spatial structures, bridge projects, and underground complexes, as well as to the vibration and seismic dual control numerical simulation analysis of buildings adjacent to urban rail transit and ultra-large earthquake simulation shaking table factory structures.

[0056] The above and other objects, advantages and features of the present invention will become more apparent to those skilled in the art from the following detailed description of specific embodiments of the invention in conjunction with the accompanying drawings. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the non-uniform excitation input method for numerical simulation analysis of building structure vibration under dual control according to an embodiment of the present invention. Detailed Implementation

[0058] The present invention can be better understood from the accompanying drawings and the following embodiments. However, those skilled in the art will readily understand that the descriptions in the embodiments are for illustrative purposes only and should not, and will not, limit the scope of the invention.

[0059] Figure 1 This is a flowchart illustrating the non-uniform excitation input method for dual-control numerical simulation analysis of building structure vibration according to an embodiment of the present invention. As shown in the figure, the method of the embodiment includes:

[0060] 1. Time history interpolation method for column base acceleration considering soil spectral attenuation and structural effects.

[0061] 1) Acceleration test at critical nodes

[0062] M key measuring points (M≥3) are arranged on the construction site. These measuring points should correspond as closely as possible to the locations of pile foundations or structural columns, forming a control network covering the structural foundation. The spacing D between the measuring points should satisfy the spatial sampling theorem: D≤Vs / (2fs), where Vs is the minimum shear wave velocity, and f... s To analyze the highest frequency (≥50Hz), time history data can be simultaneously acquired using three-dimensional (X, Y, and vertical) accelerometers.

[0063] 2) Frequency domain attenuation calculation

[0064] The measured acceleration time history was windowed using a Hanning window to suppress spectral leakage, followed by an FFT windowed transform. Four spectral lines (k1, k2, k3, k4) near the peak of the FFT spectrum were extracted (k2=k1+1, k3=k2+1, k4=k3+1), and the interpolation variables β and α were calculated.

[0065] ,

[0066] Where p 11 , p 13 , p 15 The coefficients of the odd-order terms are determined by the window function.

[0067] Then, calculate the true center frequency f and the corresponding amplitude A for all peaks (m peaks):

[0068]

[0069]

[0070] Where X is the complex spectral value of the spectral line near the peak in the FFT spectrum, N is the number of points in the FFT transform, and P20 and P22 are the even-degree polynomial coefficients related to the window function.

[0071] 3) Calculate soil attenuation compensation to correct for energy loss and waveform distortion of vibration waves as they pass through real soil, thereby obtaining a more realistic vibration response in structural vibration analysis.

[0072] Establish a theoretical frequency-distance dependent decay function:

[0073]

[0074] Where f is the frequency, d is the distance, and the quality factor is... V s (f) represents the frequency-dependent shear wave velocity, and Q0 is the reference quality factor.

[0075] Through exponential polynomial spectral simulation, the formation reflection coefficient R(f) and absorption attenuation effect are separated: ,in, Let be the absorption attenuation function, ck be the coefficients of the k-th order polynomial, k be the polynomial order, and f be the frequency; separate the attenuation response spectrum from the observed spectrum: , The original vibration signal spectrum;

[0076] After combining the observed attenuation response spectrum with the theoretical attenuation function, the high-frequency attenuation coefficient α is obtained by least-squares fitting. h With low-frequency attenuation coefficient α l .

[0077] The high-frequency attenuation coefficient α obtained by fitting h and low-frequency attenuation coefficient α l Revisions based on embedded decay function:

[0078]

[0079] For Q0 and in the theoretical decay function formula After correction, the corrected frequency-distance dependent decay function is obtained; where f p f is the dominant frequency of the vibration wave. max To analyze the highest frequency, d represents the distance.

[0080] 4) After completing the soil frequency attenuation compensation, the additional impact on the base acceleration after the structure is built should be further considered. According to the measured study, after the structure is built, due to the soil-structure interaction and the change in site stiffness caused by the structure's self-weight, the base vibration response will experience a systematic attenuation of 3~5dB.

[0081] Convert the base decay caused by the structure's construction into acceleration amplitude decay: , where A rat ΔdB is the acceleration amplitude attenuation coefficient, and ΔdB is the decibel attenuation (dB), which is determined according to the structural form and floor height.

[0082] Frequency-dependent modeling links the acceleration decay effect to the structure's natural frequency f. st Related: Sst β is the structural attenuation coefficient at frequency f, fst is the first natural frequency of the structure (Hz), and β f This is the attenuation bandwidth coefficient.

[0083] 5) Spatial interpolation synthesis

[0084] Frequency domain interpolation synthesis: Acceleration spectrum at point j of the target column base.

[0085]

[0086] Where rj is the target interpolation point position vector, r i Let i be the position vector of measurement point i, Ai(f) be the FFT spectrum of the measured acceleration at measurement point i, and W be the position vector of measurement point i. i (r) is the weighting function centered at measurement point i;

[0087]

[0088] Temporal reconstruction: For each column base position A j Perform inverse FFT transformation to obtain the acceleration time history a j (t),

[0089]

[0090] 2. Stiffness-adjustable spring-damped system constrained by large mass method

[0091] 1) Set large mass

[0092] Add a large mass M to each column base node L Satisfying M L ≥1000M struct M struct The total mass of the structure. The interpolated acceleration time histories a(t) of each column base are converted into forces: P(t) = -M L ·a(t).

[0093] 2) Applying a spring-damped system

[0094] A miniature spring-damped unit is connected in parallel in the acceleration input direction (X, Y, Z). Its initial stiffness coefficient Ks and damping coefficient Cs can be taken as follows:

[0095] ,

[0096] Where K struct For the overall structural stiffness, The damping ratio is denoted as .

[0097] 3) Stiffness adjustment based on displacement control

[0098] Real-time calculation of nodal displacement u(t) and target displacement u g Deviation of (t): ;when When the allowable threshold (which can be 1 mm) is reached, adaptive stiffness adjustment is triggered. , where ε is the convergence factor (ranging from 0.01 to 0.1), and K s 0 K s 1 These represent the initial stiffness and the adjusted stiffness of the spring-damped unit, respectively.

[0099] When Δu(t) does not exceed the threshold δ, the responses of important nodes in the structure are obtained.

[0100] Compared to existing technologies, the structural features and benefits of this invention are:

[0101] 1) A time-history interpolation method for column base acceleration considering soil spectral attenuation and structural construction effects. Human-induced vibrations, primarily of medium to high frequencies, such as those from urban road surfaces, rail transit operations, and fans and pumps, exhibit significant attenuation in the soil, leading to time differences, amplitude attenuation, and spectral variations at adjacent supports. This time-history interpolation method for column base acceleration, considering soil spectral attenuation and structural construction effects, fully accounts for the frequency attenuation characteristics of vibration waves in the soil and the additional impact of soil-structure interaction and structural weight-related changes in site stiffness on the base acceleration after structural construction. Compared to traditional interpolation methods, this method can more accurately simulate the acceleration time histories at different column bases, improving the accuracy of structural response simulation.

[0102] 2) Stiffness-adjustable spring-damping system constrained large mass method. Based on the traditional large mass method, an adjustable stiffness spring element (stiffness coefficient Ks≤10) is added. -6 K struct (damping coefficient), forming a "mass-spring" coupled system, which will significantly reduce displacement drift while retaining the computational efficiency advantage of the large mass method.

[0103] 3) Collaborative control based on real-time error feedback. A displacement error threshold control system is established. When the nodal displacement exceeds the allowable range, the stiffness coefficient Ks is automatically dynamically adjusted to ensure computational stability. Furthermore, this method supports three-dimensional six-degree-of-freedom vibration input, and can simultaneously simulate the coupling effect of seismic wave spatial variability and fault slippage, as well as three-dimensional man-made vibrations from railway tracks, ground transportation, and equipment such as fans and pumps.

[0104] The embodiments of the present invention have been described above by way of example, but the present invention is not limited to the embodiments described above. The basic idea of ​​the present invention lies in the above basic scheme. For those skilled in the art, designing various modified models, formulas, and parameters based on the teachings of the present invention does not require creative effort. Changes, modifications, substitutions, and variations made to the embodiments without departing from the principles and spirit of the present invention still fall within the protection scope of the present invention.

Claims

1. A method for non-uniform excitation input analysis of vibration dual-control numerical simulation of building structures, characterized in that, include: 1) Using a column base acceleration time history interpolation method based on spectrum analysis, the acceleration time histories of each column base are obtained, and 2) Based on the traditional large mass method, a spring-damping system with controllable stiffness is applied in the direction of acceleration input to form a large mass method with adjustable stiffness spring-damping system to control the displacement deviation of nodes.

2. The method according to claim 1, characterized in that, Step 1) includes: 1.1) Measure the acceleration of key nodes, with the measuring points corresponding to the positions of pile foundations or structural columns, to form a control network covering the structural base; 1.2) Calculate frequency domain attenuation; 1.3) Calculate the soil attenuation compensation coefficient; 1.4) Calculate the structural construction impact correction factor; and 1.5) Amplitude spatial interpolation correction, column foot time-domain acceleration synthesis.

3. The method according to claim 2, characterized in that, In 1.1), the distance D between measuring points satisfies the spatial sampling theorem: D≤V s0 / (2fs), where V s0 For the minimum shear wave velocity, f s To analyze the highest frequency (≥50Hz).

4. The method according to claim 2, characterized in that, 1.2) Includes: The measured acceleration time history is windowed using a Hanning window to suppress spectral leakage, and then subjected to an FFT windowing transform. List all peaks from the FFT spectral analysis, extract four spectral lines k1, k2, k3, and k4 near each peak, where k2 = k1 + 1, k3 = k2 + 1, and k4 = k3 + 1, and calculate the interpolation variables β and α: , Where p 11 , p 13 , p 15 The coefficients of the odd-order terms are determined by the window function; Calculate the true center frequency f of all peak values ​​and the corresponding amplitude A: Where X is the complex spectral value of the spectral line near the peak in the FFT spectrum, N is the number of points in the FFT transform, and P20 and P22 are the even-degree polynomial coefficients related to the window function.

5. The method according to claim 2, characterized in that, 1.3) Includes: Establish a theoretical frequency-distance dependent decay function: Where f is frequency, d is distance, and the quality factor is... , V s (f) represents the frequency-dependent shear wave velocity, and Q0 is the reference quality factor; Through exponential polynomial spectral simulation, the formation reflection coefficient R(f) and absorption attenuation effect are separated: ,in, For absorption attenuation function, c k Here are the coefficients of the k-th order polynomial, where k is the polynomial order and f is the frequency variable; the decay response spectrum is separated from the observed spectrum: , To test the vibration signal spectrum; After combining the observed attenuation response spectrum with the theoretical attenuation function, the high-frequency attenuation coefficient α is obtained by least-squares fitting. h With low-frequency attenuation coefficient α l The obtained coefficient α h With α l Embedded decay function: For Q0 and in the theoretical decay function formula After correction, the frequency-distance dependent decay function is obtained; where f p f is the dominant frequency of the vibration wave. max To analyze the highest frequency, d represents the distance.

6. The method according to claim 2, characterized in that, 1.4) Includes: Convert the base decay caused by the structure's construction into acceleration amplitude decay: A rat ΔdB is the acceleration amplitude attenuation coefficient, and ΔdB is the decibel attenuation (dB), which is determined according to the structural form and floor height. Frequency-dependent modeling links the attenuation effect to the structure's natural frequency f. st Related: S st Let f be the structural attenuation coefficient at frequency f. st β is the first natural frequency (Hz) of the building structure. f This is the attenuation bandwidth coefficient.

7. The method according to claim 1, characterized in that, 1.5) includes: Frequency domain interpolation synthesizes the acceleration spectrum at point j of the target column base. Where rj is the target interpolation point position vector, r i Let A be the position vector of measurement point i. i (f) is the measured acceleration FFT spectrum at measurement point i, W i (r) is the weighting function centered at measurement point i; Temporal reconstruction: For each column base position A j Perform inverse FFT transformation to obtain the acceleration time history a j (t), 8. The method according to claim 1, characterized in that, Step 2) includes: 2.1) Set a large mass, including adding a large mass M to each column base node. L Satisfying M L ≥1000M struct M struct Given the total mass of the structure, the acceleration time history a(t) of each column base obtained from the interpolation calculation in step 1) is then converted into a force: P(t) = -M L ·a(t); 2.2) Apply a spring-damped system, including miniature spring-damped units connected in parallel in the acceleration input directions (X, Y, Z), with initial stiffness coefficient Ks and damping coefficient Cs values ​​as follows: , Where K struct For the overall structural stiffness, The damping ratio; 2.3) Stiffness adjustment based on displacement control.

9. The method according to claim 8, characterized in that, 2.3) Includes: Real-time calculation of nodal displacement u(t) and target displacement u g Deviation of (t): ; When Δu(t) is greater than the allowable threshold δ, adaptive stiffness adjustment is performed: Where ε is the convergence factor, K s 0 K s 1 These are the initial stiffness and adjusted stiffness of the spring damping unit, respectively. When Δu(t) does not exceed the threshold δ, obtain the response of the structural node.

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