Method and system for calculating structural vibration response based on step-by-step integration processing input seismic loading

Abstract

The invention discloses a calculation method and system for inputting seismic loading calculation structure vibration response based on step-by-step integration processing, and the method comprises the steps: importing seismic acceleration time history data, dispersing the seismic acceleration time history data into a time-acceleration pair set, and carrying out the dispersion correction of the seismic acceleration time history data if the discreteness of the inputted seismic oscillation data is large; establishing a frequency equation based on a structural vibration theory, solving a vibration mode coefficient characteristic value, and constructing a normalized vibration mode function; constructing a piecewise linear seismic oscillation excitation function, dividing the discretized seismic wave into n time periods, and simplifying the seismic wave in each time period into a linear relation for calculation; calculating generalized mass and generalized external force, substituting the generalized mass and the generalized external force into the dynamic equation, solving a dynamic function of each time period section by section by adopting an analytical solution, and taking an end value of the time period as an initial value condition of the next time period; and outputting the vibration response in each section, superposing the vibration mode response of each time period, and summarizing the time history curve of the earthquake loading whole process response, thereby improving the calculation precision.

Description

Technical Field

[0001] The present invention relates to a method and system for calculating the vibration response of a seismic loading structure, and in particular to a method and system for calculating the vibration response of a structure based on step-by-step integration to process the input seismic loading. Background Art

[0002] In the design and safety assessment of civil engineering structures, accurately grasping the vibration response of the structure under seismic action is a key link to ensure the reliable seismic performance of the structure. However, the existing technologies have exposed a series of significant defects when dealing with the input seismic loading and calculating the structure vibration. Traditional calculation methods are limited by the insufficient understanding of the complex characteristics of seismic waves and the nonlinear behavior of structures, resulting in a large deviation between the calculation results and the actual situation.

[0003] Taking the seismic wave processing as an example, the discretization processing of seismic waves by some traditional methods is relatively rough, and it is impossible to comprehensively and accurately capture the dynamic changes of seismic waves in the time and space dimensions. This makes it difficult to truly reflect the actual stress state and vibration characteristics of the structure under seismic action when calculating the vibration response of the structure. The final calculation results are difficult to meet the strict requirements of engineering design for high-precision data, and cannot provide a reliable basis for the safety assessment of the structure. In addition, in the face of complex structures, the calculation process of existing methods is usually cumbersome and lengthy, and the calculation efficiency is low, which severely restricts its application and promotion in actual engineering projects. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to propose a method and system for calculating the vibration response of a structure based on step-by-step integration to process the input seismic loading, which can more accurately consider the characteristics of seismic waves and the characteristics of the structure, and improve the calculation accuracy and efficiency.

[0005] Technical Solution: The present invention includes the following steps:

[0006] S1. Import the seismic acceleration time history data, and discretize it into a set of time-acceleration pairs {dz i}, if the discreteness of the input ground motion data is relatively large, then perform scatter correction on the seismic acceleration time history data;

[0007] S2. Based on the structural vibration theory, establish a frequency equation, solve the eigenmode coefficient eigenvalue α, and construct a normalized eigenmode function W norm ;

[0008] S3. Construct a piecewise linear ground motion excitation function P(t), divide the discretized seismic wave into n time periods, and simplify the seismic wave within each time period into a linear relationship PT for calculation;

[0009] S4. Calculate the generalized mass M mn and the generalized external force Pmn , substitute it into the dynamic equation, and use the analytical solution to solve the dynamic function Y(t) for each time period segment by segment, and take the end value of this time period as the initial value condition for the next time period;

[0010] S5. Output the vibration responses in each section, superimpose the mode responses of each time period, and summarize the time history curve of the responses throughout the earthquake loading process.

[0011] The dispersion correction of the seismic acceleration time history data is to invert the medium quality factor Q through the measured seismic wave data and correct the P-wave and S-wave velocities:

[0012]

[0013] In the formula, ω0 is the reference frequency, V P0 , V S0 is the initial wave velocity.

[0014] The medium quality factor Q is determined through the following steps:

[0015] S11. Extract the seismic wave spectrum center frequency offset and calculate the Q value:

[0016]

[0017] In the formula, Δf is the frequency offset and Δt is the propagation time difference;

[0018] S12. Fit the function of Q value varying with frequency through multi-measurement point data:

[0019]

[0020] In the formula, Q0 and γ are fitting parameters.

[0021] The specific content of step S2 is as follows:

[0022] Construct the mode function W:

[0023]

[0024] In the formula,

[0025] The normalization condition of the mode function W is: at the structure center point x = a, y = b, W = 1, and the normalized mode function W norm The calculation formula is:

[0026]

[0027] The calculation formula of the linear relationship PT is:

[0028]

[0029] The generalized mass M mn has the following calculation formula:

[0030]

[0031] The generalized external force P mn has the following calculation formula:

[0032]

[0033] The calculation formula of the dynamic equation is:

[0034]

[0035] In the formula,

[0036] The analytical solution is realized by piecewise recurrence, and the initial condition transfer formula is:

[0037] Y(dz i+1,1 ) = Y i , Y i '(dz i+1,1 ) = Y i '

[0038] In the formula, Y i ' is the derivative of Y i with respect to time t.

[0039] The specific steps of step S5 include:

[0040] S51. The calculation formula for the vibration displacement of the monitoring point with coordinates (a, b) is:

[0041]

[0042] S52. The velocity time history curve is obtained by differentiating the displacement response:

[0043]

[0044] A calculation system for calculating the structural vibration response based on step-by-step integration of the input seismic loading, comprising:

[0045] Seismic acceleration time history data import module: Import the seismic acceleration time history data, discretize it into a set of time-acceleration pairs, and if the input ground motion data has large discreteness, perform scatter correction on the seismic acceleration time history data;

[0046] Normalized mode function construction module: Establish a frequency equation based on the structural vibration theory, solve the eigenvalue of the mode coefficient, and construct a normalized mode function;

[0047] Piecewise linear ground motion excitation function construction module: Construct a piecewise linear ground motion excitation function, divide the discretized seismic wave into n time periods, and simplify the seismic wave within each time period into a linear relationship for calculation;

[0048] Dynamic function solving module: Calculate the generalized mass and generalized external force, substitute them into the dynamic equation, and use the analytical solution to solve the dynamic function of each time period segment by segment, and use the end value of this time period as the initial value condition for the next time period;

[0049] Vibration response output module: Output the vibration response within each section, superimpose the modal responses of each time period, and summarize the time history curve of the response throughout the earthquake loading process.

[0050] Beneficial effects: The present invention constructs a normalized modal function based on the structural vibration theory, supports one-key import of seismic time history data and flexible adjustment of parameters such as structural dimensions and material properties, and combines the output of visual displacement and velocity time history curves, which can quickly adapt to the seismic analysis requirements of complex structures such as bridges and buildings. The operation process has a high degree of automation, can more accurately consider the characteristics of seismic waves and structural features, and improve the calculation accuracy and efficiency. Brief Description of the Drawings

[0051] Figure 1 It is a flow chart of the present invention;

[0052] Figure 2 It is a structural plate vibration diagram of the present invention. Detailed Embodiments

[0053] The present invention will be further described below with reference to the accompanying drawings.

[0054] Embodiment 1

[0055] As Figure 1 shown, the calculation method of the present embodiment for calculating the structural vibration response based on the step-by-step integration of the input earthquake loading adopts the step-by-step integration method to discretize the seismic wave, supports parameter adjustment and visual output, conforms to the engineering reality, has high calculation efficiency and accurate results, and is also applicable to the seismic analysis of complex structures. The specific steps are as follows:

[0056] S1. Import the seismic acceleration time history data and discretize it into a set of time-acceleration pairs {dz i}, if the discreteness of the input ground motion data is large, then perform dispersion correction on the seismic acceleration time history data; the dispersion correction of the seismic acceleration time history data is to invert the medium quality factor Q through the measured seismic wave data and correct the P-wave and S-wave velocities:

[0057]

[0058] In the formula, ω0 is the reference frequency, V P0 、VS0 is the initial wave velocity.

[0059] The medium quality factor Q is determined by the following steps:

[0060] S11. Extract the frequency offset of the seismic wave spectrum and calculate the Q value:

[0061]

[0062] In the formula, Δf is the frequency offset and Δt is the propagation time difference.

[0063] S12. Fit the function of Q value varying with frequency through multi - measurement - point data:

[0064]

[0065] In the formula, Q0 and γ are fitting parameters.

[0066] S2. Based on the structural vibration theory, establish the frequency equation, solve the eigenvalue α of the vibration mode coefficient, and construct the normalized vibration mode function W norm ; specifically:

[0067] Construct the vibration mode function W:

[0068]

[0069] In the formula,

[0070] The normalization condition of the vibration mode function W is: at the center point x = a, y = b of the structure, W = 1, and the normalized vibration mode function W norm The calculation formula is:

[0071]

[0072] S3. Construct the piece - wise linear ground motion excitation function P(t), divide the discretized seismic wave into n time intervals (time periods), and simplify the seismic wave within each time period into a linear relationship PT for calculation.

[0073] The calculation formula for simplifying the seismic wave into the piece - wise linear relationship PT is:

[0074]

[0075] S4. Calculate the generalized mass M mn and the generalized external force P mn , substitute them into the dynamic equation, and use the analytical solution to solve the dynamic function Y(t) of each time period segment by segment, and take the end value of this time period as the initial value condition of the next time period.

[0076] The generalized mass M mn The calculation formula is:

[0077]

[0078] Generalized external force P mn The calculation formula is as follows:

[0079]

[0080] The calculation formula of the dynamic equation is as follows:

[0081]

[0082] Wherein,

[0083] The analytical solution is realized by piecewise recursion, and the initial condition transfer formula is:

[0084] Y(dz i+1,1 ) = Y i , Y i '(dz i+1,1 ) = Y i '

[0085] Wherein, Y i ' is the derivative of Y i with respect to time t.

[0086] S5. Output the vibration response within each interval segment, superimpose the mode shape responses of each time period, and summarize the time history curve corresponding to the entire process of seismic loading, specifically including:

[0087] S51. The calculation formula for the vibration displacement of the monitoring point with coordinates (a, b) is:

[0088]

[0089] S52. The velocity time history curve is obtained by differentiating the displacement response:

[0090]

[0091] Embodiment 2

[0092] The calculation system for calculating the structural vibration response based on step-by-step integration of the input seismic loading in this embodiment includes

[0093] Seismic acceleration time history data import module: Import the seismic acceleration time history data, discretize it into a set of time-acceleration pairs, and if the discreteness of the input ground motion data is large, perform dispersion correction on the seismic acceleration time history data;

[0094] Normalized mode shape function construction module: Establish a frequency equation based on the structural vibration theory, solve the eigenvalue of the mode shape coefficient, and construct a normalized mode shape function;

[0095] Piecewise linear ground motion excitation function construction module: Construct a piecewise linear ground motion excitation function, divide the discretized seismic wave into n time periods, and simplify the seismic wave within each time period into a linear relationship for calculation;

[0096] Dynamic function solving module: Calculate the generalized mass and generalized external force, substitute them into the dynamic equation, and use the analytical solution to solve the dynamic function of each time period segment by segment, and use the end value of this time period as the initial value condition for the next time period;

[0097] Vibration response output module: Output the vibration response within each section, superimpose the modal responses of each time period, and summarize the time history curve of the response during the entire process of seismic loading.

[0098] Example 3

[0099] 1. Data preparation: According to the above technical solution, import the seismic data file "seismic wave.txt". The imported data file

[0100] contains information such as time and seismic acceleration, as shown below:

[0101]

[0102] 2. Parameter setting: Set the structure and material parameters, such as the length a of the structural plate = 3m, the width b of the structural plate = 3m, the plate density ρ = 2500 kg / m3, the plate thickness h = 0.1m, E = 203 GPa, Poisson's ratio ν = 0.3, etc. These parameters are determined according to the material properties and geometric dimensions of the actual structure.

[0103] 3. Frequency equation and mode calculation:

[0104] (1) Calculate the flexural rigidity D and related frequency parameters β m and β 2m .

[0105] (2) Construct the frequency equation, draw the curve, and observe the frequency characteristics. Solve the eigenvalue α of the mode coefficient by the iteration method.

[0106] (3) Find the roots of the frequency equation, and then calculate the mode parameter a m and the mode function W, and obtain the normalized mode function W norm .

[0107] 4. Vibration response calculation:

[0108] (1) Assume that the initial displacement and velocity of the structural plate are 0, and perform parameter initialization.

[0109] (2) Calculate the vibration response at each step through iteration. In the iteration, calculate the seismic excitation P(t) at the current moment according to the time and acceleration data in the data file.

[0110] (3) Calculate the generalized mass M mn and the generalized force P mn , and obtain the displacement response Y(t) by solving the differential equation, update the displacement and velocity, store the calculation results at this moment, and transfer them to the next moment as the initial value for calculation.

[0111] (4) After all the data calculations are completed, use the plotting command to display the calculated structural vibration response data and graphs, as Figure 2 shown.

[0112] Example 4

[0113] 1. Data adjustment: Replace with different seismic data files, which may have different time intervals and seismic acceleration variation laws, and import the data according to the same data import method.

[0114] 2. Parameter fine-tuning: Fine-tune the structural and material parameters according to the actual situation, such as adjusting a to 1.0 m and b to 1.2 m, etc., to simulate the characteristics of different structures.

[0115] 3. Repeat the calculation process: Re-calculate according to the frequency equation and mode shape calculation and vibration response calculation steps in Example 1. By adjusting the parameters and data, observe the changes in the calculation results. For example, under the new parameter settings, the shape of the frequency equation curve and the eigenvalue α of the mode shape coefficient have changed, and the time history curve of the structural vibration response also shows different characteristics, and the values of displacement and velocity also change accordingly. By comparing the results of different examples, the influence of different seismic data and structural parameters on the structural vibration response can be analyzed, providing a richer reference basis for structural design and seismic analysis in practical engineering.

[0116] Example 5

[0117] 1. Simulation of complex structures: Assume that the structure has a more complex geometric shape and mechanical properties, and accordingly adjust the structural parameters a, b and material parameters E, ν, etc. to reflect this complexity.

[0118] 2. Calculation process: According to the calculation process in the above technical solution, start from data import and gradually perform frequency equation and mode shape calculation and vibration response calculation. During the calculation process, due to the increased structural complexity, the solution of the frequency equation and the calculation of the mode shape function may be more complex, but the method of the present invention can still effectively handle it. For example, when calculating the mode shape W and the generalized mass M mn and the generalized force P mnWhen it is necessary, integral calculations need to be performed according to the parameters of the complex structure, and finally the vibration response data and graphs of the structure under the complex structure are obtained. By comparing with the calculation results of the simple structure, the influence of the complex structure on the structural vibration response can be seen, further verifying the effectiveness and accuracy of the method of the present invention when dealing with different structures.

Claims

1. A method for calculating the vibration response of a structure based on step-by-step integration of input seismic loading, characterized in that: The following steps are involved: S1. Import earthquake acceleration time history data and discretize it into a set of time-acceleration pairs {dz i }, if the input seismic motion data is highly discrete, the earthquake acceleration time history data is corrected; S2. Establish the frequency equation based on the structural vibration theory, solve the characteristic value α of the vibration mode coefficient, and construct the normalized vibration mode function W norm ; S3, construct a piecewise linear earthquake excitation function P(t), divide the discretized earthquake wave into n time periods, and simplify the earthquake wave in each time period into a linear relationship PT for calculation; S4. Calculation of generalized mass M mn and the generalized external force P mn , bring it into the dynamic equation, use the analytical solution to solve the dynamic function Y(t) of each period step by step, and use the end value of the period as the initial value condition of the next period; S5. Output the vibration response in each section, superimpose the vibration response of each time period, and summarize the time history curve of the whole process of earthquake loading response.

2. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 1 is characterized in that: The dispersion correction of the seismic acceleration time history data is performed by inverting the medium quality factor Q through the measured seismic wave data to correct the P-wave and S-wave velocities: Where ω0 is the reference frequency, V P0 、V S0 is the initial wave velocity.

3. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 2, characterized in that: The medium quality factor Q is determined by the following steps: S11. Extract the center frequency offset of the seismic wave spectrum and calculate the Q value: Where Δf is the frequency offset and Δt is the propagation time difference; S12. Fit the Q value with frequency function through multiple measurement point data: Where Q0 and γ are fitting parameters.

4. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 1, characterized in that: The step S2 is specifically as follows: Construct the vibration mode function W: In the formula, The normalization condition of the vibration mode function W is: at the center point of the structure x = a, y = b, W = 1, and the normalized vibration mode function W norm The calculation formula is:

5. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 4, characterized in that: The calculation formula of the linear relationship PT is:

6. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 5, characterized in that: The generalized mass M mn The calculation formula is:

7. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 6, characterized in that: The generalized external force P mn The calculation formula is:

8. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 7, characterized in that: The calculation formula of the dynamic equation is: In the formula, The analytical solution is achieved through piecewise recursion, and the initial condition transfer formula is: And(dz) i+1,1 )=And i ,AND i '(dz i+1,1 )=And i ' Where Y i 'It's Y i The derivative with respect to time t.

9. The method for calculating the vibration response of a structure based on step-by-step integration processing of input earthquake loading according to claim 8, characterized in that: The step S5 specifically includes: S51. The calculation formula for the vibration displacement of the monitoring point with coordinates (a, b) is: S52, the velocity time history curve is obtained by differential displacement response:

10. A computing system for calculating the vibration response of a structure based on step-by-step integration processing of input seismic loading, characterized in that: include: Earthquake acceleration time history data import module: import earthquake acceleration time history data and discretize it into a set of time-acceleration pairs. If the input seismic motion data is highly discrete, the earthquake acceleration time history data will be corrected. Normalized vibration mode function construction module: establishes the frequency equation based on the structural vibration theory, solves the vibration mode coefficient eigenvalue, and constructs the normalized vibration mode function; Piecewise linear seismic excitation function construction module: constructs a piecewise linear seismic excitation function, divides the discretized seismic wave into n time periods, and simplifies the seismic wave in each time period into a linear relationship for calculation; Dynamic function solving module: calculates generalized mass and generalized external force, brings them into the dynamic equation, uses analytical solution to solve the dynamic function of each period step by step, and uses the end value of the period as the initial value condition of the next period; Vibration response output module: outputs the vibration response in each section, superimposes the vibration response of each time period, and summarizes the time history curve of the whole process response of earthquake loading.

Images