Method for calculating natural vibration frequency, vibration mode and pedestrian comfort of assembled integral bidirectional ribbed laminated floor system

Abstract

The invention relates to a method for calculating natural vibration frequency, vibration mode and pedestrian comfort of an assembled integral type bidirectional dense rib laminated floor system, which comprises the following steps of: obtaining a rigidity calculation formula of the floor system on the basis of a full-scale test and an abutted seam load test of the assembled integral type bidirectional dense rib laminated floor system; the natural vibration frequency and vibration mode calculation formula of the assembled integral type bidirectional dense rib laminated floor system is obtained through the free vibration equation of the bidirectional plate; considering the corrected vibration equation and the human-shaped load dynamic model of the assembled integral two-way dense rib laminated floor system, and performing numerical calculation to obtain an acceleration time travel curve of the assembled integral two-way dense rib laminated floor system; based on the numerical calculation method and parameterized analysis, a theoretical calculation formula of the maximum acceleration of the assembled integral type bidirectional dense rib laminated floor system is obtained. The method can effectively predict the natural vibration frequency, the vibration mode and the pedestrian comfort of the assembled integral two-way dense rib laminated floor, is well matched with test comparison, and can further guide the design and calculation of the assembled integral two-way dense rib laminated floor.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering, and in particular to a method for calculating the natural vibration frequency, vibration mode and pedestrian comfort of an assembled integral bidirectional multi-rib composite floor. Background Art

[0002] Floor slabs are a critical component of building structures. In frame structures, floor slab material consumption accounts for 50% to 80% of the entire building, its weight accounts for 50%-60% of the total building weight, and its construction cost accounts for 20%-30% of the total civil engineering cost. This significantly impacts project cost control and the development of prefabricated buildings. To further promote the development of green and prefabricated buildings, the prefabricated, monolithic, bidirectional, multi-ribbed composite floor slab system has emerged. Composed of a precast base plate, reinforced inner formwork, and post-cast composite layers, this system not only combines the advantages of both floor slab systems but also effectively addresses many issues encountered in traditional engineering applications.

[0003] However, due to structural measures such as joints, overlaps, and sleeve connections, the overall performance of prefabricated, two-way multi-rib composite floor systems is affected. Therefore, further verification is needed to analyze the load-bearing performance under design loads and the comfort level under normal use. According to the "Technical Standard for Vibration Comfort of Building Floor Structures" and related specifications, there are requirements for the stiffness, load-bearing capacity, and comfort level of prefabricated, two-way multi-rib composite floor systems. However, there is currently no method for calculating these parameters. Therefore, it is urgent to propose a method for calculating the natural frequency, mode shape, and pedestrian comfort of prefabricated, two-way multi-rib composite floor systems. Summary of the Invention

[0004] Based on this, in order to solve the above technical problems, a method for calculating the natural frequency, vibration mode and pedestrian comfort of an assembled integral two-way multi-ribbed composite floor is provided, which can calculate the natural frequency, vibration mode and pedestrian comfort of an assembled integral two-way multi-ribbed composite floor, and further guide the design and calculation of the assembled integral two-way multi-ribbed composite floor.

[0005] A method for calculating the natural vibration frequency, vibration mode, and pedestrian comfort of an assembled integral bidirectional multi-rib composite floor, the method comprising:

[0006] Obtaining parameters of the assembled integral two-way multi-rib composite floor, determining a correction coefficient for the effect of joints on the assembled integral two-way multi-rib composite floor, and obtaining a floor stiffness calculation formula based on the parameters of the assembled integral two-way multi-rib composite floor and the correction coefficient based on a full-scale test and a joint load test, thereby calculating the floor stiffness;

[0007] Determine floor parameters, obtain a two-way slab free vibration equation and boundary conditions based on the floor parameters, and calculate the natural frequency and mode shape of the floor based on the floor stiffness calculation formula and in combination with the two-way slab free vibration equation and boundary conditions;

[0008] Collecting pedestrian standard weight and single-step cycle, obtaining the acceleration when the floor is deformed, and constructing the floor vibration equation and pedestrian load dynamic model based on the standard weight, single-step cycle, and acceleration;

[0009] Based on the floor vibration equation and the pedestrian load dynamic model, the acceleration time history curve of the assembled integral bidirectional multi-rib composite floor is calculated, and the acceleration time history curve is analytically calculated.

[0010] In one embodiment, the parameters of the assembled integral bidirectional multi-rib composite floor include: elastic modulus E of the floor concrete, total height h of the floor, Poisson's ratio of concrete , rib width , rib spacing b, top and bottom plate thickness h s .

[0011] In one embodiment, the floor stiffness calculation formula is: ; ; Wherein, D is the stiffness of the assembled integral two-way multi-rib composite floor; E is the elastic modulus of the floor concrete; h is the total height of the floor; h is the Poisson's ratio of concrete; is the rib width; b is the rib spacing; h s is the thickness of the top and bottom plates; It is the correction coefficient for the influence of joints on assembled integral two-way multi-rib composite floor.

[0012] In one embodiment, the natural frequency and mode shape of the floor are calculated as follows:

[0013] ;

[0014] ;

[0015] Where f is the natural frequency of the assembled integral two-way multi-rib composite floor; F is the vibration mode of the assembled integral two-way multi-rib composite floor; X and Y are the lengths of the short and long sides of the floor, respectively, and x and y are the coordinates of the short and long sides, respectively; is the density of concrete; g is the acceleration of gravity, which is 9.8m / s 2 .

[0016] In one embodiment, the floor vibration equation is:

[0017] ; ;in, is the second derivative of the floor deformation with respect to time, i.e. acceleration; is the second derivative of the floor deformation in the X direction; is the second derivative of the floor deformation in the Y direction; is the fourth derivative of the floor deformation in the X direction; is the fourth derivative of the floor deformation in the Y direction; m is the standard weight of a single person; For a single-step cycle, is the amplitude coefficient of the k-th order harmonic, indicating the contribution ratio of the k-th order sine wave to the total load; k is the harmonic number, indicating the k-th order harmonic component.

[0018] In one embodiment, the pedestrian load dynamic model is:

[0019] .

[0020] In one embodiment, the formula for analytical calculation of the acceleration time history curve is:

[0021] ;in, .

[0022] The above-mentioned calculation method for the natural frequency, mode shape, and pedestrian comfort of prefabricated, two-way multi-ribbed composite slabs is based on full-scale tests and joint load tests of prefabricated, two-way multi-ribbed composite slabs. The stiffness calculation formula for the slab is derived, and the free vibration equation for the two-way slab is used to calculate the natural frequency and mode shape of the prefabricated, two-way multi-ribbed composite slab. The acceleration time history curve of the prefabricated, two-way multi-ribbed composite slab is numerically calculated using the revised vibration equation for the prefabricated, two-way multi-ribbed composite slab and the humanoid load dynamic model. Based on the above numerical calculation method and parametric analysis, a theoretical calculation formula for the maximum acceleration of the prefabricated, two-way multi-ribbed composite slab is obtained. This method can effectively predict the natural frequency, mode shape, and pedestrian comfort of the prefabricated, two-way multi-ribbed composite slab, and the results are in good agreement with the experimental results. This method can further guide the design and calculation of prefabricated, two-way multi-ribbed composite slabs. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 、 Figure 2 This is a diagram of the application environment of a method for calculating the natural vibration frequency, mode shape, and pedestrian comfort of an assembled integral bidirectional multi-rib composite floor in one embodiment;

[0024] Figure 3 Schematic diagram of a flow chart of a method for calculating the natural frequency, mode shape, and pedestrian comfort of an assembled integral bidirectional multi-rib composite floor in one embodiment;

[0025] Figure 4 A schematic diagram of the calculation results of the first-order vibration mode in one embodiment;

[0026] Figure 5 Schematic diagram of the calculation results of the second-order vibration mode in one embodiment;

[0027] Figure 6 Schematic diagram of calculation results of the third-order vibration mode in one embodiment;

[0028] Figure 7 Schematic diagram of calculation results of the fourth-order vibration mode in one embodiment;

[0029] Figure 8 Schematic diagram of the natural frequency test results in one embodiment;

[0030] Figure 9 Schematic diagram of the first-order vibration mode test results in one embodiment;

[0031] Figure 10 Schematic diagram of the second-order vibration mode test results in one embodiment;

[0032] Figure 11 Schematic diagram of the second-order vibration mode test results in one embodiment;

[0033] Figure 12 Schematic diagram of the fourth-order vibration mode test results in one embodiment;

[0034] Figure 13 Schematic diagram of acceleration time history curve calculation results in one embodiment. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0036] The method for calculating the natural frequency, vibration mode and pedestrian comfort of the assembled integral bidirectional multi-rib composite floor provided in the embodiment of the present application can be applied to Figure 1 、 Figure 2 In the application environment shown. Figure 1 、 Figure 2 As shown, the application environment includes assembling an integral two-way multi-ribbed composite floor and assembling a prefabricated ribbed bottom plate of the integral two-way multi-ribbed composite floor.

[0037] In one embodiment, Figure 3 As shown, a method for calculating the natural frequency, mode shape and pedestrian comfort of an assembled integral bidirectional multi-rib composite floor is provided, comprising the following steps:

[0038] Step 302: Obtain parameters of the assembled integral two-way multi-ribbed composite floor, determine a correction coefficient for the influence of the joints of the assembled integral two-way multi-ribbed composite floor, and obtain a floor stiffness calculation formula based on the parameters of the assembled integral two-way multi-ribbed composite floor and the correction coefficient based on full-scale tests and joint load tests to calculate the floor stiffness.

[0039] In one embodiment, the parameters of the assembled integral bidirectional multi-rib composite floor may include: elastic modulus E of the floor concrete, total height h of the floor, Poisson's ratio of the concrete , rib width , rib spacing b, top and bottom plate thickness h s .

[0040] In this embodiment, the floor slab stiffness calculation formula can be used to calculate the floor slab stiffness. Specifically, the stiffness calculation formula for a four-side simply supported floor slab can be obtained based on full-scale tests and joint load tests of assembled integral bidirectional multi-ribbed composite floors.

[0041] In one embodiment, the floor stiffness calculation formula is: ; ; Wherein, D is the stiffness of the assembled integral two-way multi-rib composite floor; E is the elastic modulus of the floor concrete; h is the total height of the floor; h is the Poisson's ratio of concrete; is the rib width; b is the rib spacing; h s is the thickness of the top and bottom plates; It is the correction coefficient for the influence of joints on assembled integral two-way multi-rib composite floor.

[0042] Step 304: Determine the floor parameters, obtain the two-way slab free vibration equation and boundary conditions based on the floor parameters, and calculate the natural frequency and mode shape of the floor based on the floor stiffness calculation formula and in combination with the two-way slab free vibration equation and boundary conditions.

[0043] The floor slab parameters may include the lengths of the short and long sides of the floor slab, as well as the coordinates of the short and long sides.

[0044] In one embodiment, the natural frequency and mode shape of the floor are calculated as follows: ; ; Wherein, f is the natural frequency of the assembled integral two-way multi-rib composite floor; F is the vibration mode of the assembled integral two-way multi-rib composite floor; X and Y are the lengths of the short and long sides of the floor, respectively, and x and y are the coordinates in the direction of the short and long sides, respectively; is the density of concrete; g is the acceleration of gravity, which is 9.8m / s 2 .

[0045] Specifically, in this embodiment, based on the stiffness calculation of the assembled integral two-way multi-rib composite floor, combined with the two-way plate free vibration equation and boundary conditions, the first four natural frequencies and mode shapes of the four-side simply supported assembled integral two-way multi-rib composite floor can be calculated. The specific formula is: ;

[0046] ;

[0047] ;

[0048] ;

[0049] ; ;

[0050] ; ;

[0051] Among them, f1, f2, f3, and f4 are the first four natural frequencies of the assembled integral two-way multi-rib composite floor; F1, F2, F3, and F4 are the first four vibration modes of the assembled integral two-way multi-rib composite floor; X and Y are the lengths of the short and long sides of the floor, respectively, and x and y are the coordinates of the short and long sides, respectively; is the density of concrete; g is the acceleration of gravity, which is 9.8m / s 2 .

[0052] In this embodiment, the first four natural frequencies of the assembled integral two-way multi-rib composite floor are shown in the following table:

[0053]

[0054] The calculation results of the first-order vibration mode of the assembled integral two-way multi-rib composite floor are as follows: Figure 4 As shown in the figure; the calculation results of the second-order vibration mode of the assembled integral two-way multi-rib composite floor are shown in the figure. Figure 5 As shown in the figure; the calculation results of the third-order vibration mode of the assembled integral two-way multi-rib composite floor are shown in the figure. Figure 6 As shown in the figure; the calculation results of the fourth-order vibration mode of the assembled integral two-way multi-rib composite floor are shown in the figure. Figure 7 shown.

[0055] Step 306 , collect the standard weight and single-step cycle of pedestrians, obtain the acceleration when the floor is deformed, and construct the floor vibration equation and pedestrian load dynamic model based on the standard weight, single-step cycle, and acceleration.

[0056] The weight of a single person is m, and the standard weight can be 60 kg; the single-step cycle is The step frequency can be 1.5-2.2Hz, and the single step period is 0.45-0.67s.

[0057] In one embodiment, the floor vibration equation is: ; ;in, is the second derivative of the floor deformation with respect to time, i.e. acceleration; is the second derivative of the floor deformation in the X direction; is the second derivative of the floor deformation in the Y direction; is the fourth derivative of the floor deformation in the X direction; is the fourth derivative of the floor deformation in the Y direction; m is the standard weight of a single person; For a single-step cycle, is the amplitude coefficient of the k-th order harmonic, indicating the contribution ratio of the k-th order sine wave to the total load; k is the harmonic number, indicating the k-th order harmonic component.

[0058] In one embodiment, the pedestrian load dynamic model is: .

[0059] Specifically, considering the revised vibration equation for prefabricated, bidirectional, multi-ribbed composite floors and the pedestrian load dynamic model, the acceleration time history curve of the prefabricated, bidirectional, multi-ribbed composite floor can be calculated. The vibration equation can be discretized using the central difference method, Gengeralized-alpha, or Newmark-β method. In the floor vibration equation and the pedestrian load dynamic model, a damping ratio of 3% is used.

[0060] Step 308 : Based on the floor vibration equation and the pedestrian load dynamic model, the acceleration time history curve of the assembled integral bidirectional multi-rib composite floor is calculated, and the acceleration time history curve is analytically calculated.

[0061] A method for calculating the natural frequency, mode shape, and pedestrian comfort of prefabricated, bidirectional, multi-ribbed composite floors is provided. This method also includes an analytical method for calculating the acceleration time history of the floor under human-shaped loads. Based on numerical analytical algorithms and parametric analysis, the effects of different parameters on maximum acceleration are explored, resulting in an analytical calculation method for prefabricated, bidirectional, multi-ribbed composite floors.

[0062] In one embodiment, the formula for analytically calculating the acceleration time history curve is: ;in, Indicates the maximum acceleration; .

[0063] In one embodiment, the method also includes verifying the calculation method of the natural vibration frequency, vibration mode and pedestrian comfort of the assembled integral two-way multi-rib composite floor.

[0064] Specifically, the acceleration response of the new assembled integral bidirectional multi-rib composite floor under pedestrian load can be obtained through dynamic measurement methods, and the natural vibration characteristics of the new floor are studied in the frequency domain by using the random subspace method (SSI), and the first four modes are obtained. Among them, the experimental results of the natural frequency are as follows Figure 8 The experimental results of the first four vibration modes are shown in Figure 9 、 10 As shown in Figures 11 and 12, in order to obtain multiple vibration mode results in the test, multiple sensors need to be placed. By performing Fourier analysis on multiple sensors, their common vibration frequency can be obtained, which is the natural frequency of the structure. The vibration mode is obtained by the amplitude and phase angle difference (the phase difference is 180, that is, the vibration direction is opposite), which corresponds to a three-dimensional diagram as shown in Figure 11 and 12. Figure 9 、 10 , 11, and 12. Among them, the mode shape refers to the characteristic deformation shape of the structure under free vibration. Each mode shape corresponds to a natural frequency, and the plate will perform sinusoidal periodic vibrations at this frequency. The object in this embodiment is a bidirectional plate, which means that there will be sinusoidal periodic vibrations in both directions. After the two directions are synthesized, it will become a three-dimensional graph, which is the mode shape diagram of the plate. By comparing the two, the error between the experimental dynamic measurement frequency and the method of this application is less than 5%, which verifies the effectiveness of this method in predicting the natural frequency of the new assembled integral bidirectional multi-rib composite floor.

[0065] The average maximum acceleration measured in the test is 0.006m / s 2 The error between the calculated result and the acceleration time history curve is about 5%. Figure 13 As shown in the figure, the effectiveness of this method in predicting the pedestrian comfort of the new assembled integral two-way multi-rib composite floor is also verified.

[0066] It should be understood that, although the various steps in the above flow chart are shown in sequence as indicated by the arrows, these steps are not necessarily performed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be performed in other orders. Moreover, at least a portion of the steps in the above flow chart may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily to be performed in sequence, but can be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

[0067] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0068] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A method for calculating the natural frequency, mode shape and pedestrian comfort of an assembled integral bidirectional multi-rib composite floor, characterized in that: The method comprises: Obtaining parameters of the assembled integral two-way multi-rib composite floor, determining a correction coefficient for the effect of joints on the assembled integral two-way multi-rib composite floor, and obtaining a floor stiffness calculation formula based on the parameters of the assembled integral two-way multi-rib composite floor and the correction coefficient based on a full-scale test and a joint load test, thereby calculating the floor stiffness; Determine floor parameters, obtain a two-way slab free vibration equation and boundary conditions based on the floor parameters, and calculate the natural frequency and mode shape of the floor based on the floor stiffness calculation formula and in combination with the two-way slab free vibration equation and boundary conditions; Collecting pedestrian standard weight and single-step cycle, obtaining the acceleration when the floor is deformed, and constructing the floor vibration equation and pedestrian load dynamic model based on the standard weight, single-step cycle, and acceleration; Based on the floor vibration equation and the pedestrian load dynamic model, the acceleration time history curve of the assembled integral bidirectional multi-rib composite floor is calculated, and the acceleration time history curve is analytically calculated.

2. The method for calculating the natural frequency, mode shape and pedestrian comfort of the assembled integral bidirectional multi-rib composite floor according to claim 1 is characterized in that: The parameters of the assembled integral bidirectional multi-rib composite floor include: elastic modulus E of the floor slab concrete, total height h of the floor slab, concrete Poisson's ratio , rib width , rib spacing b, top and bottom plate thickness h s .

3. The method for calculating the natural frequency, mode shape and pedestrian comfort of the assembled integral bidirectional multi-rib composite floor according to claim 2 is characterized in that: The floor stiffness calculation formula is: ; ; Wherein, D is the stiffness of the assembled integral two-way multi-rib composite floor; E is the elastic modulus of the floor concrete; h is the total height of the floor; h is the Poisson's ratio of concrete; is the rib width; b is the rib spacing; h s is the thickness of the top and bottom plates; It is the correction coefficient for the influence of joints on assembled integral two-way multi-rib composite floor.

4. The method for calculating the natural frequency, mode shape and pedestrian comfort of the assembled integral bidirectional multi-rib composite floor according to claim 3 is characterized in that: The calculation formula of the natural frequency and mode shape of the floor is: ； ； Where f is the natural frequency of the assembled integral two-way multi-rib composite floor; F is the vibration mode of the assembled integral two-way multi-rib composite floor; X and Y are the lengths of the short and long sides of the floor, respectively, and x and y are the coordinates of the short and long sides, respectively; is the density of concrete; g is the acceleration of gravity, which is 9.8m / s 2 .

5. The method for calculating the natural frequency, mode shape and pedestrian comfort of the assembled integral bidirectional multi-rib composite floor according to claim 4 is characterized in that: The floor vibration equation is: ; ;in, is the second derivative of the floor deformation with respect to time, i.e. acceleration; is the second derivative of the floor deformation in the X direction; is the second derivative of the floor deformation in the Y direction; is the fourth derivative of the floor deformation in the X direction; is the fourth derivative of the floor deformation in the Y direction; m is the standard weight of a single person; For a single-step cycle, is the amplitude coefficient of the k-th order harmonic, indicating the contribution ratio of the k-th order sine wave to the total load; k is the harmonic number, indicating the k-th order harmonic component.

6. The method for calculating the natural frequency, mode shape and pedestrian comfort of the assembled integral bidirectional multi-rib composite floor according to claim 5 is characterized in that: The pedestrian load dynamic model is: 。 7. The method for calculating the natural frequency, mode shape and pedestrian comfort of the assembled integral bidirectional multi-rib composite floor according to claim 6 is characterized in that: The formula for analytical calculation of the acceleration time history curve is: ;in, Indicates the maximum acceleration; .

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