Method for predicting transverse response of high-rise building under action of multiple external strong impacts

Abstract

The invention relates to the technical field of structural dynamic response prediction, and particularly discloses a transverse response prediction method for a high-rise building under the action of multiple external strong impacts, which comprises the following steps: S1, determining the quality of each floor, the interlayer rigidity, the characteristic quality of each order, the damping ratio, the inherent frequency, the damping frequency and the vibration mode matrix of the high-rise building; s2, determining load characteristic parameters of each point location under multiple strong impact loads; s3, calculating a generalized load peak value of strong impact by utilizing the vibration mode matrix and peak value distribution; s4, calculating generalized static displacement by utilizing the characteristic mass of each order, the damping frequency and the generalized load peak value; s5, calculating the dynamic coefficient and inheritance quantity of each strong impact by using the generalized static displacement; s6, substituting the dynamic coefficient and the inheritance quantity into a prediction formula, and calculating a lateral displacement response; according to the method, the generalized load peak value, the generalized static displacement, the dynamic coefficient and the inheritance quantity are calculated, and the prediction formula is combined, so that the transverse response of the high-rise building under the action of multiple external strong impacts is calculated.

Description

Technical Field

[0001] This invention relates to the field of structural dynamic response prediction technology, and more specifically, to a method for predicting the lateral response of a high-rise building under multiple strong external impacts. Background Technology

[0002] High-rise buildings exhibit lateral dynamic responses under strong external impacts. While the amplitudes of overall displacement, acceleration, and interstory deformation are limited under a single impact, they demonstrate significant cumulative effects under multiple consecutive impacts. The resulting stiffness degradation, damping evolution, and damage accumulation alter the dynamic characteristics of the structure under subsequent impacts, thereby affecting subsequent impact responses and safety margins. In particular, the overall lateral response of high-rise buildings exacerbates the propagation and deterioration of existing structural defects (such as microcracks, loose connections, and local buckling initiation). Therefore, rapid and feasible predictive calculations of the overall lateral response of high-rise buildings under multiple strong impacts are of significant engineering importance.

[0003] Currently, research on the dynamic response of structures under strong impacts largely focuses on single impacts or a few simple, repetitive load scenarios. When the number of impacts increases and the peak value, duration, and time interval of each impact differ (complex impact sequences), common methods typically rely on nonlinear dynamic finite element time history analysis or high-precision numerical integration. These methods are computationally expensive, sensitive to parameter settings, and involve a large workload of repetitive modeling and solving, making it difficult to meet the engineering design stage's need for rapid evaluation and comparison of multiple impact time sequences. Especially when comparing different impact sequences and structural schemes in batches, traditional simulation methods often face the dilemma of "difficult modeling and slow computation" when dealing with large-scale mesh calculations of the entire building structure, making it difficult to form a unified, concise, and engineering-usable rapid prediction method. Furthermore, when considering iterative closed-loop simulation-feedback-update mechanisms for intelligent design and reinforcement learning, simulation time directly limits iteration efficiency and data filtering efficiency.

[0004] In summary, existing methods for predicting the lateral response of high-rise buildings under multiple consecutive strong external impacts still suffer from problems such as difficulty in uniformly handling complex impact sequences with different peak values ​​and durations, high computational costs, and difficulty in supporting rapid comparison and iteration.

[0005] Therefore, it is necessary to study a method for calculating the lateral response of high-rise buildings that can achieve rapid calculation and rapid comparative prediction while taking into account the cumulative effects of multiple impacts, so as to improve the efficiency of engineering evaluation and support rapid design decisions. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the lateral response of high-rise buildings under multiple strong external impacts. By calculating the generalized peak load, generalized static displacement, dynamic coefficient and inherited amount and combining them with the prediction formula, the lateral response of high-rise buildings under multiple strong external impacts can be calculated.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting the lateral response of a high-rise building under multiple strong external impacts includes the following steps: S1. Determine the basic parameters of the high-rise building; among which, the basic parameters include: mass of each story, inter-story stiffness, characteristic mass of each order, damping ratio, natural frequency, damping frequency and mode shape matrix; S2. Determine the load characteristic parameters at different locations of a high-rise building under multiple strong impact loads; among which, the load characteristic parameters include: the peak value distribution, duration, and time interval between two adjacent strong impacts of each strong impact. S3. Using the mode shape matrix and the peak value distribution of each strong impact, calculate the generalized load peak value corresponding to each strong impact; S4. Using the characteristic masses of each order, damping frequency and the peak value of the generalized load corresponding to each strong impact, calculate the generalized static displacement corresponding to each strong impact. S5. Calculate the dynamic coefficient and inherited amount corresponding to each strong impact using the generalized static displacement corresponding to each strong impact. S6. Substitute the dynamic coefficient and inherited amount corresponding to each strong impact into the prediction formula to calculate the lateral displacement response of the high-rise building.

[0008] Furthermore, in S1, the high-rise building is modeled as a multi-degree-of-freedom lateral dynamic system; The mode shape matrix is ​​determined by the number of stories, mass of each story, and inter-story stiffness of the high-rise building.

[0009] Furthermore, in S3, the calculation formulas for the peak value of the generalized load corresponding to each strong impact are as follows: (1); In the formula, This is the first generalized load peak vector. This is the second generalized load peak vector. This represents the peak vector of the first strong impact. This represents the peak vector of the second strong impact. This is the mode shape matrix.

[0010] Furthermore, in S4, the formula for calculating the generalized static displacement corresponding to each strong impact is: (2); In the formula, Let be the peak component of the first strong impact generalized load corresponding to the i-th vibration mode. This represents the peak component of the second strong impact generalized load corresponding to the i-th vibration mode. This represents the generalized static displacement corresponding to the first strong impact. This represents the generalized static displacement corresponding to the second strong impact. Let be the damping frequency of the i-th mode. Let be the characteristic mass of the i-th mode shape.

[0011] Furthermore, the generalized static displacement is determined by the generalized load peak value, characteristic mass, and damping frequency.

[0012] Furthermore, in S5, the dynamic coefficient is used to characterize the amplification effect of a single strong impact on the lateral response of a high-rise building. The inherited quantity is used to characterize the cumulative effect of a previous strong impact on the response to subsequent strong impacts, and is determined by the dynamic state of the structure at the end of the previous strong impact.

[0013] Furthermore, in S5, the formula for calculating the dynamic coefficient is as follows: (3); In the formula, The dynamic coefficient of the i-th mode shape under the first strong impact. This represents the generalized static displacement corresponding to the first strong impact. This represents the generalized displacement response of the i-th mode shape under the first strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time under the first strong impact. (5); In the formula, This represents the generalized displacement response of the i-th mode shape under the second strong impact. For the generalized static displacement of the second impact, The dynamic coefficient of the i-th mode shape under the second strong impact.

[0014] Furthermore, in S5, the inheritance quantity is: (4); In the formula, The dynamic coefficient of the i-th mode shape at the end of the first strong impact is used as the inherited value for calculating the response to the second strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time is given at the moment the first strong impact ends.

[0015] Furthermore, in step S6, the expression for the prediction formula is: (6); In the formula, Let be the predicted value of the lateral displacement response of the j-th floor of the high-rise building, and n be the total number of floors in the high-rise building. Let i be the mode shape value of the i-th mode shape on the j-th floor. The characteristic length of a high-rise building. Let be the peak component of the first strong impact generalized load corresponding to the i-th vibration mode. For the i-th order characteristic mass, Let be the damping frequency of the i-th mode. The dynamic coefficient of the i-th mode shape under the second strong impact. Let be the damping ratio of the i-th mode. Let be the natural frequency of the i-th mode shape. This represents the peak component of the second strong impact generalized load corresponding to the i-th vibration mode.

[0016] Furthermore, the lateral response prediction method is applicable to rapid prediction and comparative analysis of strong impact conditions with multiple points, multiple cycles, and independently designable load characteristics for each cycle.

[0017] According to specific embodiments provided by the present invention, the present invention has the following technical effects compared to the prior art: This invention integrates the basic physical parameters of high-rise buildings with the time history characteristics of multiple strong impact loads, and realizes the transformation from physical coordinates to modal coordinates based on the mode matrix. Then, by calculating the generalized load peak and generalized static displacement, it accurately solves the dynamic coefficients under each impact and the inherited amount reflecting the residual effect of the previous impact vibration. It makes full use of the decoupling advantage of modal analysis and introduces the inherited amount to quantify the mutual interference and superposition effect of the structural vibration state between adjacent impacts. Thus, it can accurately capture the nonlinear dynamic evolution process of high-rise buildings under the complex condition of multiple strong external impacts, significantly improve the calculation accuracy and efficiency of lateral displacement response, and solve the technical problem that existing methods cannot accurately handle the cumulative effect of multiple consecutive impacts. It provides a reliable calculation basis for the impact-resistant design and safety assessment of high-rise buildings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] The following description, in conjunction with the accompanying drawings, further illustrates the method for predicting the lateral response of a high-rise building under multiple strong external impacts according to the present invention. Figure 1 This is a schematic diagram of the overall process of a method for predicting the lateral response of a high-rise building under multiple strong external impacts according to the present invention. Detailed Implementation

[0020] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0021] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0022] Example 1 like Figure 1 As shown, this invention provides a method for predicting the lateral response of a high-rise building under multiple strong external impacts, comprising the following steps: S1. Determine the basic parameters of the high-rise building; the basic parameters include: the mass of each floor. Interlayer stiffness Characteristic quality M of each order i Damping ratio Natural frequency Damping frequency And mode matrix Use subscripts i Indicates the first i Mode shape, subscript j Indicates the number of high-rise buildings j layer, n This represents the total number of floors.

[0023] The high-rise building was modeled as a multi-degree-of-freedom lateral dynamic system; The mode shape matrix is ​​determined by the number of stories, mass of each story, and inter-story stiffness of the high-rise building.

[0024] S2. Determine the load characteristic parameters at different locations of a high-rise building under multiple strong impact loads; the load characteristic parameters include: the peak value distribution, duration, and time interval between each strong impact; In this embodiment, the peak vector of the first strong impact is set as... The peak vector of the second strong impact is The duration vector of the first strong impact is The duration vector of the second strong impact is The time interval between the two strong impacts is .

[0025] S3. Using the mode shape matrix and the peak value distribution of each strong impact, calculate the generalized load peak value corresponding to each strong impact; In S3, the calculation formulas for the peak value of the generalized load corresponding to each strong impact are as follows: (1); In the formula, This is the first generalized load peak vector. This is the second generalized load peak vector. This represents the peak vector of the first strong impact. This represents the peak vector of the second strong impact. This is the mode shape matrix.

[0026] S4. Using the characteristic masses of each order, damping frequency and the peak value of the generalized load corresponding to each strong impact, calculate the generalized static displacement corresponding to each strong impact. In S4, the formula for calculating the generalized static displacement corresponding to each strong impact is: (2); In the formula, Let be the peak component of the first strong impact generalized load corresponding to the i-th vibration mode. This represents the peak component of the second strong impact generalized load corresponding to the i-th vibration mode. This represents the generalized static displacement corresponding to the first strong impact. This represents the generalized static displacement corresponding to the second strong impact. Let be the damping frequency of the i-th mode. Let be the characteristic mass of the i-th mode shape.

[0027] The generalized static displacement is determined by the generalized load peak value, characteristic mass, and damping frequency.

[0028] S5. Calculate the dynamic coefficient and inherited amount corresponding to each strong impact using the generalized static displacement corresponding to each strong impact. In S5, the dynamic coefficient is used to characterize the amplification effect of a single strong impact on the lateral response of a high-rise building. The inherited quantity is used to characterize the cumulative effect of a previous strong impact on the response to subsequent strong impacts, and is determined by the dynamic state of the structure at the end of the previous strong impact.

[0029] In S5, the formula for calculating the dynamic coefficient is as follows: (3); In the formula, The dynamic coefficient of the i-th mode shape under the first strong impact. This represents the generalized static displacement corresponding to the first strong impact. This represents the generalized displacement response of the i-th mode shape under the first strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time under the first strong impact. In S5, the inheritance amount is: (4); In the formula, The dynamic coefficient of the i-th mode shape at the end of the first strong impact is used as the inherited value for calculating the response to the second strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time is given at the moment the first strong impact ends.

[0030] (5); In the formula, This represents the generalized displacement response of the i-th mode shape under the second strong impact. For the generalized static displacement of the second impact, The dynamic coefficient of the i-th mode shape under the second strong impact.

[0031] In the formula, It can be calculated by the Duhamel integral of the single-degree-of-freedom linearly decaying triangular load response.

[0032] S6. Substitute the dynamic coefficient and inherited amount corresponding to each strong impact into the prediction formula to calculate the lateral displacement response of the high-rise building.

[0033] In step S6, the expression for the prediction formula is: (6); In the formula, Let be the predicted value of the lateral displacement response of the j-th floor of the high-rise building, and n be the total number of floors in the high-rise building. Let i be the mode shape value of the i-th mode shape on the j-th floor. The characteristic length of a high-rise building. Let be the peak component of the first strong impact generalized load corresponding to the i-th vibration mode. For the i-th order characteristic mass, Let be the damping frequency of the i-th mode. The dynamic coefficient of the i-th mode shape under the second strong impact. Let be the damping ratio of the i-th mode. Let be the natural frequency of the i-th mode shape. This represents the peak component of the second strong impact generalized load corresponding to the i-th vibration mode.

[0034] The lateral response prediction method is applicable to rapid prediction and comparative analysis of strong impact conditions with multiple points, multiple cycles, and independently designable load characteristics for each cycle.

[0035] This embodiment specifically presents a method for predicting the response of high-rise buildings under multiple impacts, considering multiple points and multiple times of strong impacts, with each load characteristic designed independently. Addressing the multi-degree-of-freedom lateral dynamic system of high-rise buildings, while maintaining engineering comparability, it incorporates key characteristic parameters such as the occurrence time, peak value, and duration of multiple impacts into a unified calculation framework. It establishes dynamic characteristic update rules considering cumulative effects and a fast solution process for regular coordinates, enabling efficient prediction of lateral responses under continuous multiple strong external impacts. This provides technical support for safety assessment, scheme selection, and rapid decision-making of high-rise buildings under multiple strong impact conditions, and is applicable to rapid assessment, rapid comparison, and rapid iteration in the engineering phase.

[0036] Example 2 This embodiment provides a specific implementation for calculating the lateral response of a high-rise building under two different strong impact loadings with a time interval of Δt at four points: Step 1: Determine the basic parameters of the high-rise building in this embodiment 1, including inputting the mass of each floor. Interlayer stiffness Damping ratios of each order Natural frequency With damping frequency Mode shape matrix Y, etc.; subscripts i Indicates the first i Mode shape, subscript j Indicates the building number j layer, n This represents the total number of floors.

[0037] In this embodiment n =4, j =4, L =12 m. Damping ratio is The mass of each layer is kg; interlayer stiffness is N / m.

[0038] The quality matrix is The stiffness matrix is: ; The frequencies of each order are Damping frequency is The vibration modes at each location are as follows: .

[0039] Characteristic quality is .

[0040] Step 2, determine the peak value and duration of the two strong impact loads at each point (the peak value vector of the first strong impact is...). The peak vector of the second strong impact is The duration vector of the first strong impact is The duration vector of the second strong impact is The time interval between the two strong impacts is ).

[0041] ; ; ; Step 3: Calculate the first generalized load peak vector. and the second generalized load peak vector The formula is as follows: (7); Calculations show that the peak vectors of the two generalized loads in this embodiment are... and They are respectively: ; ; Step 4: Calculate the generalized static displacement corresponding to the first strong impact. Generalized static displacement corresponding to the second strong impact The formula is: (8); Calculations show that the two generalized static displacements in Example 1 are... and They are respectively: ; ; Step 5, calculate the dynamic coefficients twice. , The amount of inheritance is calculated using the following formula: (9); In the formula, The dynamic coefficient of the i-th mode shape under the first strong impact; This refers to the generalized static displacement corresponding to the first strong impact. This represents the generalized displacement response of the i-th mode shape under the first strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time under the first strong impact. Get the inheritance amount: (10); In the formula, The i-th mode dynamic coefficient at the end of the first strong impact is used as the inherited value for calculating the response to the second strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time is given at the moment the first strong impact ends.

[0042] Second impact dynamic coefficient: (11); In the formula, The generalized displacement response of the i-th mode under the second strong impact; This refers to the generalized static displacement of the second impact; The dynamic coefficient of the i-th mode shape under the second strong impact.

[0043] Calculations can be obtained in this embodiment The dynamic coefficients under condition s , , They are respectively: ; ; Step 6: Substitute the dynamic coefficients of the two strong impacts into the prediction formula, take j=4, and obtain the lateral displacement response of the highest floor. The prediction formula is: (12); calculate At the highest level, j=4, the value reaches its maximum of 0.004 0.1 seconds after the start of the second strong impact; ; The formula required in step 6 of this embodiment is: The function form (a function of time) is used here, rather than a specific value at a particular moment. The common Duhamel integral form is used instead. (13); The parts of this invention not described in detail are prior art.

[0044] Example 3 The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the lateral response prediction method for high-rise buildings under multiple strong external impacts as described in Embodiment 1.

[0045] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for predicting the lateral response of a high-rise building under multiple strong external impacts as described in Embodiment 1.

[0046] The above description of the disclosed embodiments enables those skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the lateral response of a high-rise building under multiple strong external impacts, characterized in that, Includes the following steps: S1. Determine the basic parameters of the high-rise building; among which, the basic parameters include: mass of each story, inter-story stiffness, characteristic mass of each order, damping ratio, natural frequency, damping frequency and mode shape matrix; S2. Determine the load characteristic parameters at different locations of a high-rise building under multiple strong impact loads; among which, the load characteristic parameters include: the peak value distribution, duration, and time interval between two adjacent strong impacts of each strong impact. S3. Using the mode shape matrix and the peak value distribution of each strong impact, calculate the generalized load peak value corresponding to each strong impact; S4. Using the characteristic masses of each order, damping frequency and the peak value of the generalized load corresponding to each strong impact, calculate the generalized static displacement corresponding to each strong impact. S5. Calculate the dynamic coefficient and inherited amount corresponding to each strong impact using the generalized static displacement corresponding to each strong impact. S6. Substitute the dynamic coefficient and inherited amount corresponding to each strong impact into the prediction formula to calculate the lateral displacement response of the high-rise building.

2. The method for predicting the lateral response of high-rise buildings under multiple strong external impacts according to claim 1, characterized in that, In S1, the high-rise building is modeled as a multi-degree-of-freedom lateral dynamic system; The mode shape matrix is ​​determined by the number of stories, mass of each story, and inter-story stiffness of the high-rise building.

3. The method for predicting the lateral response of high-rise buildings under multiple strong external impacts according to claim 1, characterized in that, In S3, the calculation formulas for the peak value of the generalized load corresponding to each strong impact are as follows: (1)； In the formula, This is the first generalized load peak vector. This is the second generalized load peak vector. This represents the peak vector of the first strong impact. This represents the peak vector of the second strong impact. This is the mode shape matrix.

4. The method for predicting the lateral response of high-rise buildings under multiple strong external impacts according to claim 1, characterized in that, In S4, the formula for calculating the generalized static displacement corresponding to each strong impact is: (2)； In the formula, Let be the peak component of the first strong impact generalized load corresponding to the i-th vibration mode. This represents the peak component of the second strong impact generalized load corresponding to the i-th vibration mode. This represents the generalized static displacement corresponding to the first strong impact. This represents the generalized static displacement corresponding to the second strong impact. Let be the damping frequency of the i-th mode. Let be the characteristic mass of the i-th mode shape.

5. The method for predicting the lateral response of high-rise buildings under multiple strong external impacts according to claim 4, characterized in that, The generalized static displacement is determined by the generalized load peak value, characteristic mass, and damping frequency.

6. The method for predicting the lateral response of high-rise buildings under multiple strong external impacts according to claim 1, characterized in that, In S5, the dynamic coefficient is used to characterize the amplification effect of a single strong impact on the lateral response of a high-rise building. The inherited quantity is used to characterize the cumulative effect of a previous strong impact on the response to subsequent strong impacts, and is determined by the dynamic state of the structure at the end of the previous strong impact.

7. The method for predicting the lateral response of high-rise buildings under multiple strong external impacts according to claim 1, characterized in that, In S5, the formula for calculating the dynamic coefficient is as follows: (3)； In the formula, The dynamic coefficient of the i-th mode shape under the first strong impact. This represents the generalized static displacement corresponding to the first strong impact. This represents the generalized displacement response of the i-th mode shape under the first strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time under the first strong impact. (5)； In the formula, This represents the generalized displacement response of the i-th mode shape under the second strong impact. For the generalized static displacement of the second impact, The dynamic coefficient of the i-th mode shape under the second strong impact.

8. The method for predicting the lateral response of high-rise buildings under multiple strong external impacts according to claim 1, characterized in that, In S5, the inheritance amount is: (4)； In the formula, The dynamic coefficient of the i-th mode shape at the end of the first strong impact is used as the inherited value for calculating the response to the second strong impact. The first derivative of the dynamic coefficient of the i-th mode shape with respect to time is given at the moment the first strong impact ends.

9. The method for predicting the lateral response of a high-rise building under multiple strong external impacts according to claim 1, characterized in that, In step S6, the expression for the prediction formula is: (6)； In the formula, Let be the predicted value of the lateral displacement response of the j-th floor of the high-rise building, and n be the total number of floors in the high-rise building. Let i be the mode shape value of the i-th mode shape on the j-th floor. The characteristic length of a high-rise building. Let be the peak component of the first strong impact generalized load corresponding to the i-th vibration mode. For the i-th order characteristic mass, Let be the damping frequency of the i-th mode. The dynamic coefficient of the i-th mode shape under the second strong impact. Let be the damping ratio of the i-th mode. Let be the natural frequency of the i-th mode shape. This represents the peak component of the second strong impact generalized load corresponding to the i-th vibration mode.

10. The method for predicting the lateral response of a high-rise building under multiple strong external impacts according to claim 1, characterized in that, The lateral response prediction method is applicable to rapid prediction and comparative analysis of strong impact conditions with multiple points, multiple cycles, and independently designable load characteristics for each cycle.

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