Method, device and readable storage medium for quickly calculating bridge pier damping rate

Abstract

The application relates to a quick calculation method of a bridge pier damping ratio, comprising the following steps: determining a bridge anti-seismic basic system, and establishing an anti-seismic stress and calculation model; the bridge comprises a main beam, a bridge pier and a damping and isolation support arranged between the main beam and the bridge pier; the internal force response of the pier bottom of the bridge pier without the damping and isolation support is obtained to obtain a first shear force and a first bending moment; the internal force response of the pier bottom of the bridge pier with the damping and isolation support is obtained to obtain a second shear force and a second bending moment; and the bridge pier damping ratio is calculated. According to the bridge anti-seismic basic system, the anti-seismic stress and calculation model is established, the internal force responses of the pier bottoms of the bridge piers before and after the damping and isolation support is arranged are obtained, and the bridge pier damping ratio is quickly calculated, so that the damping ratio is used to measure the vibration absorption capacity or damping effect of the damping and isolation support applied to the bridge, the damping ratio is used as a quantitative basis for evaluating the structural seismic response and the seismic safety evaluation, the method does not depend on complex finite element software, the calculation time is short, and the calculation efficiency is high.

Description

Technical Field

[0001] This invention relates to the field of bridge seismic design, specifically to a method, device, and readable storage medium for rapidly calculating the vibration reduction rate of bridge piers. Background Technology

[0002] Seismic isolation bearings are the main energy-dissipating components of seismic isolation bridges. They primarily achieve the purpose of dissipating seismic energy and reducing the seismic response of the structure by extending the natural period of vibration and increasing damping. In the early stages of bridge design, when studying the rationality of the bridge's seismic resistance scheme, complex finite element software is often relied upon to calculate the basic parameters that the seismic isolation bearings need to meet, such as stiffness and damping, based on the actual resistance of the bridge substructure. Then, repeated communication is conducted with the seismic isolation bearing manufacturer to determine whether the seismic isolation bearings can be manufactured and implemented.

[0003] However, in related technologies, the stiffness and damping parameters of seismic isolation bearings calculated by complex finite element software cannot be intuitively judged in terms of their relationship with structural seismic response and structural seismic safety performance. They are insufficient as a quantitative basis for evaluating structural seismic response and seismic safety. Moreover, the finite element calculation process is complex and computationally intensive. Summary of the Invention

[0004] This application provides a rapid calculation method, computer equipment, and computer-readable storage medium for the seismic damping rate of bridge piers, solving the technical problems in related technologies where the stiffness and damping parameters of seismic isolation bearings calculated by complex finite element software are insufficient as quantitative basis for evaluating the seismic response and seismic safety of structures, and where the finite element calculation process is complex and computationally intensive.

[0005] In a first aspect, embodiments of this application provide a rapid calculation method for the vibration damping rate of bridge piers, comprising the following steps:

[0006] The basic seismic resistance system of the bridge is determined, and the seismic stress and calculation model of the bridge is established; the bridge includes a main girder, piers, and seismic isolation bearings installed between the main girder and the piers;

[0007] The internal force response at the bottom of the pier is obtained when the seismic isolation bearing is not installed, so as to obtain the first shear force Q0 and the first bending moment M0 at the bottom of the pier.

[0008] Based on the bridge seismic stress and calculation model, the internal force response of the pier bottom when the seismic isolation bearing is installed is obtained, so as to obtain the second shear force Q and the second bending moment M of the pier bottom;

[0009] The damping ratio of the bridge piers is calculated, including the shear damping ratio η determined based on the first shear force Q0 and the second shear force Q. Q and the moment damping ratio η determined based on the first bending moment M0 and the second bending moment M.M .

[0010] In conjunction with the first aspect, in one embodiment, the shear damping ratio η Q The calculation formula is:

[0011]

[0012] The bending moment damping ratio η M The calculation formula is:

[0013]

[0014] Where p0 is the time-domain parameter of the seismic load; γ is the frequency ratio of the seismic isolation bearing to the bridge pier; ψ is the frequency ratio of the seismic vibration to the bridge pier; μ is the equivalent mass ratio of the main beam to the bridge pier; ζ2 is the equivalent damping ratio of the seismic isolation bearing; m b It is the mass of the bridge pier, m a It is the mass of the main beam; λ E ω3 is the frequency of the pier without seismic isolation bearings; L is the pier height; L0 is the equivalent pier height.

[0015] In conjunction with the first aspect, in one implementation method, establishing the seismic stress and calculation model of the bridge includes:

[0016] A seismic stress model of the bridge is established, with the main beam as the superstructure and the piers as the substructure.

[0017] The main beam and the pier are simplified as concentrated loads;

[0018] The seismic isolation bearing is simplified to equivalent stiffness k2 and equivalent damping c2;

[0019] A seismic calculation model for the bridge is established, which is a damped system with two degrees of freedom.

[0020] In conjunction with the first aspect, in one embodiment, simplifying the main beam and the pier into concentrated loads includes:

[0021] Mass m a The main beam is simplified to a first concentrated load with an equivalent mass of m2;

[0022] Mass m b The pier with stiffness EI is simplified to a second concentrated load, with equivalent mass m1, equivalent stiffness k1, and equivalent pier height L0.

[0023] In conjunction with the first aspect, in one embodiment, obtaining the internal force response at the bottom of the pier without the seismic isolation bearing, to obtain the first shear force Q0 and the first bending moment M0 at the bottom of the pier, includes:

[0024] Establish the pier coordinate system for the bridge pier without the aforementioned seismic isolation bearings;

[0025] Based on the aforementioned pier coordinate system, the structural vibration mode function in the direction of seismic stress is obtained as follows:

[0026]

[0027] The frequency ω3 at the bottom of the bridge pier is obtained from the structural vibration mode function as follows:

[0028]

[0029] Calculate the first shear force Q0 at the bottom of the bridge pier;

[0030] The calculation formula is:

[0031] Calculate the first bending moment M0 at the bottom of the bridge pier;

[0032] The calculation formula is:

[0033] coefficient

[0034] Among them, T g K represents the characteristic period in the frequency domain parameters of seismic load. h denoted as the horizontal peak ground acceleration coefficient of the fundamental ground motion in the frequency domain parameters of the seismic load, where g is the gravitational acceleration.

[0035] In conjunction with the first aspect, in one implementation, T in the frequency domain parameters of the seismic load g K h The parameters p0 and ω in the time domain of seismic load are mutually converted through the conversion relationship between response spectrum and power spectrum.

[0036] In conjunction with the first aspect, in one embodiment, obtaining the internal force response at the bottom of the pier when the seismic isolation bearing is installed based on the bridge seismic stress and calculation model, so as to obtain the second shear force Q and the second bending moment M at the bottom of the pier, includes:

[0037] Basic parameters are obtained based on the bridge seismic calculation model.

[0038] Establish the dynamic equation of the seismic calculation model and solve for the displacement amplitude X1 of the main beam;

[0039] Based on the displacement amplitude X1 of the main beam, the internal force response at the bottom of the pier when the seismic isolation support is installed is solved, and the second shear force Q and the second bending moment M at the bottom of the pier are calculated.

[0040] The calculation formula is: Q = k1X1; M = QL0.

[0041] In conjunction with the first aspect, in one implementation, establishing the dynamic equations of the seismic calculation model and solving for the displacement amplitude X1 of the main beam includes:

[0042] Based on the aforementioned seismic calculation model, the seismic load p0sinωt is applied to the pier location, and the motion differential equations of a damped system with two degrees of freedom are established.

[0043] The equation of motion is:

[0044]

[0045] Where p0 and ω are the time-domain parameters of the seismic load;

[0046] The displacement amplitude X1 of the main beam is calculated based on the aforementioned differential equation of motion;

[0047] The calculation formula is:

[0048] Secondly, embodiments of this application provide a computer device, the computer device including a processor, a memory, and a computer program stored in the memory and executable by the processor, wherein when the computer program is executed by the processor, it implements the steps of the rapid calculation method for the pier damping rate as described in any of the above claims.

[0049] Thirdly, embodiments of this application provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it implements the steps of the rapid calculation method for the pier damping rate as described in any of the preceding claims.

[0050] The beneficial effects of the technical solutions provided in this application include:

[0051] This application provides a rapid calculation method for the vibration reduction rate of bridge piers. Based on the basic seismic system of bridges, a seismic stress and calculation model is established. The internal force response of the pier bottom before and after the installation of seismic isolation bearings is obtained to quickly calculate the vibration reduction rate of the piers. The vibration reduction rate measures the absorption capacity or vibration reduction effect of seismic isolation bearings when applied to bridges. It serves as a quantitative basis for evaluating the seismic response and seismic safety of structures. It intuitively judges the relationship between seismic isolation bearings and structural seismic response and structural seismic safety performance. It does not rely on complex finite element software and has a short calculation time and high calculation efficiency. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart illustrating a method for rapidly calculating the vibration reduction rate of bridge piers in one embodiment of the present invention.

[0054] Figure 2 This is a schematic diagram of the basic seismic resistance system for bridges in one embodiment of the present invention.

[0055] Figure 3 This is a schematic diagram of the seismic stress and calculation model of a bridge when seismic isolation bearings are installed in one embodiment of the present invention.

[0056] Figure 4 This is a schematic diagram of the basic seismic resistance system of a bridge without seismic isolation bearings in one embodiment of the present invention.

[0057] Figure 5 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention.

[0058] In the diagram: 1. Main beam; 2. Pier; 3. Seismic isolation bearing. Detailed Implementation

[0059] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0060] This application provides a rapid calculation method for the seismic damping rate of bridge piers, which can solve the technical problems in related technologies where the stiffness and damping parameters of seismic isolation bearings calculated by complex finite element software are insufficient as quantitative basis for evaluating the seismic response and seismic safety of structures, and the finite element calculation process is complex and computationally intensive.

[0061] Reference Figure 1 and Figure 2 ,in, Figure 1 This is a flowchart illustrating a method for rapidly calculating the vibration reduction rate of bridge piers in one embodiment of the present invention. Figure 2 This is a schematic diagram of the basic seismic resistance system for bridges in one embodiment of the present invention.

[0062] This embodiment provides a rapid calculation method for the vibration reduction rate of bridge piers, including the following steps:

[0063] Step S1: Determine the basic seismic resistance system of the bridge and establish a seismic stress and calculation model for the bridge; the bridge includes main beam 1, pier 2, and seismic isolation bearings 3 located between main beam 1 and pier 2;

[0064] Step S2: Based on the bridge seismic stress and calculation model, obtain the internal force response of the bottom of pier 2 without setting seismic isolation bearing 3, so as to obtain the first shear force Q0 and the first bending moment M0 at the bottom of pier 2.

[0065] Step S3: Based on the bridge seismic stress and calculation model, obtain the internal force response at the bottom of pier 2 when the seismic isolation bearing 3 is set, so as to obtain the second shear force Q and the second bending moment M at the bottom of pier 2.

[0066] Step S4: Calculate the pier damping ratio, which includes the shear damping ratio η determined based on the first shear force Q0 and the second shear force Q. Q and the moment damping ratio η determined based on the first bending moment M0 and the second bending moment M. M .

[0067] This embodiment provides a rapid calculation method for the vibration reduction rate of bridge piers. Based on the basic seismic resistance system of bridges, a seismic stress and calculation model is established. The internal force response at the pier base before and after the installation of seismic isolation bearings is obtained to quickly calculate the vibration reduction rate. The vibration reduction rate measures the absorption capacity or vibration reduction effect of seismic isolation bearings when applied to bridges. A higher vibration reduction rate indicates that the seismic isolation bearings can more effectively absorb seismic energy and reduce the impact of seismic vibrations on the piers. Using the vibration reduction rate as a quantitative basis for evaluating structural seismic response and seismic safety assessment, it intuitively judges the relationship between seismic isolation bearings and structural seismic response and seismic safety performance. It does not rely on complex finite element software, has a short calculation time, and high computational efficiency.

[0068] The following provides a detailed explanation of each step.

[0069] In one embodiment, the shear damping ratio η Q The calculation formula is:

[0070]

[0071] Bending moment damping ratio η M The calculation formula is:

[0072]

[0073] Where p0 is the time-domain parameter of the seismic load; γ is the frequency ratio of the seismic isolation bearing to the bridge pier; ψ is the frequency ratio of the seismic vibration to the bridge pier; μ is the equivalent mass ratio of the main beam to the bridge pier; ζ2 is the equivalent damping ratio of the seismic isolation bearing; mb It is the mass of the bridge pier, m a It is the mass of the main beam; λ E ω3 is the frequency of the pier without seismic isolation bearings; L is the pier height; L0 is the equivalent pier height.

[0074] The above scheme establishes the correlation between the pier damping rate and frequency ratio (frequency ratio of seismic isolation bearings to piers, and frequency ratio of seismic vibration to piers), equivalent mass ratio (equivalent mass ratio of main beams to piers), and equivalent damping ratio of seismic isolation bearings. This allows for the rapid calculation of the pier damping rate, thereby assessing the seismic response and seismic safety of the structure. It effectively reduces the computational workload of structural seismic response, demonstrating strong practicality and effectiveness, and significantly improving computational efficiency.

[0075] like Figure 2 As shown, there are multiple piers 2, which are evenly spaced below the main beam 1. Each pier 2 and the main beam 1 is equipped with a seismic isolation bearing 3, which is a friction pendulum bearing.

[0076] like Figure 3 As shown, Figure 3 This is a schematic diagram of a bridge seismic stress and calculation model according to an embodiment of the present invention. Wherein, Figure 3 (a) is the seismic stress model. Figure 3 (b) is the seismic calculation model, where x represents displacement.

[0077] In one embodiment, step S1, establishing the bridge's seismic stress and calculation model, includes:

[0078] A seismic stress model of the bridge was established, with the main beam 1 as the superstructure and the pier 2 as the substructure.

[0079] The main beam 1 and pier 2 are simplified as concentrated loads.

[0080] Specifically, simplifying the main beam 1 and pier 2 into concentrated loads includes:

[0081] Mass m a The main beam 1 is simplified to the first concentrated load, with an equivalent mass m2;

[0082] Mass m b The pier 2 with stiffness EI is simplified to the second concentrated load, with equivalent mass m1, equivalent stiffness k1, and equivalent pier height L0.

[0083] The seismic isolation bearing 3 is simplified to equivalent stiffness k2 and equivalent damping c2;

[0084] A seismic calculation model for the bridge is established, which is a damped system with two degrees of freedom.

[0085] like Figure 4 As shown, Figure 4 This is a schematic diagram of the basic seismic resistance system of a bridge without seismic isolation bearings in one embodiment of the present invention. Figure 4 (a) The basic seismic system of the bridge without seismic isolation bearings. Figure 4 (b) is the coordinate system of the pier body.

[0086] In one embodiment, step S2, obtaining the internal force response at the bottom of pier 2 without the installation of seismic isolation bearing 3, to obtain the first shear force Q0 and the first bending moment M0 at the bottom of pier 2, includes:

[0087] Based on the basic seismic resistance system of bridges, a coordinate system for pier 2 is established when no seismic isolation bearing 3 is installed.

[0088] The mass of main girder 1 is ma; the stiffness of pier 2 is EI, and its mass is m. b =m(h)L.

[0089] Based on the pier coordinate system, the structural vibration mode function in the direction of seismic stress is obtained as follows:

[0090]

[0091] The frequency ω3 at the bottom of pier 2 is obtained from the structural vibration mode function as follows:

[0092]

[0093] Calculate the first shear force Q0 at the bottom of pier 2;

[0094] The calculation formula is:

[0095] Calculate the first bending moment M0 at the bottom of pier 2;

[0096] The calculation formula is:

[0097] coefficient

[0098] Among them, T g K represents the characteristic period in the frequency domain parameters of seismic load. h denoted as the horizontal peak ground acceleration coefficient of the fundamental ground motion in the frequency domain parameters of the seismic load, where g is the gravitational acceleration.

[0099] In one embodiment, T in the frequency domain parameters of seismic load g K h The parameters p0 and ω in the time domain of seismic load are mutually converted through the conversion relationship between response spectrum and power spectrum.

[0100] T g K hThese are two parameters in the frequency domain (response spectrum) of the seismic load, and p0 and ω are two parameters in the time domain (power spectrum) of the seismic load. Given the known frequency domain parameters T of the seismic load... g K h When the response spectrum and power spectrum are converted, the response spectrum can be converted into the power spectrum, and then the time-domain parameters p0 and ω of the seismic load can be obtained, and vice versa.

[0101] The specific process is as follows:

[0102] First, the target reaction spectrum S a (ω) is converted into the power spectrum of the response S(ω).

[0103] The calculation formula is:

[0104] S a (ω)=λ E ω;

[0105]

[0106]

[0107] Where T is the duration of the seismic load, ω is the frequency of the seismic load, ε is the damping ratio of the bridge pier, and r is the probability of exceeding the response spectrum value.

[0108] Then, using the trigonometric series superposition method, a stationary Gaussian process with zero mean is generated.

[0109] The calculation formula is:

[0110]

[0111]

[0112]

[0113] Take ω that is close to the fundamental frequency of the structure i Then the time-domain parameters of the seismic load

[0114] like Figure 2 and Figure 3 As shown, in one embodiment, step S3, obtaining the internal force response at the bottom of pier 2 when the seismic isolation bearing 3 is installed based on the bridge seismic stress and calculation model, to obtain the second shear force Q and the second bending moment M at the bottom of pier 2, includes:

[0115] Step S31: Obtain basic parameters based on the bridge seismic stress and calculation model;

[0116] Specifically, the basic parameters include: the equivalent mass m2 of the main beam 1; the equivalent stiffness k2, natural frequency ω2, equivalent damping ratio ζ2, and equivalent damping c2 of the seismic isolation bearing 3; and the natural frequency ω1, equivalent height L0, equivalent stiffness k1, and equivalent mass m1 of the pier 2.

[0117] Wherein, the equivalent mass of main beam 1 is m2 = m a ;

[0118] Equivalent stiffness of seismic isolation bearing 3

[0119] W is the support reaction force under constant load; H is the equivalent distance between the centers of the spheres on the sliding surface of the support; D d It is the horizontal displacement of the support design; μ is the dynamic friction coefficient of the support, with a value between 0.02 and 0.05.

[0120] The natural frequency of the seismic isolation bearing 3

[0121] The equivalent damping ratio of seismic isolation bearing 3

[0122] The equivalent damping of the seismic isolation bearing 3 is c2 = 2m2ξ2ω2;

[0123] The natural frequency of pier 2

[0124] Equivalent height of pier 2 (constant cross-section pier)

[0125] Equivalent stiffness of pier 2 (constant cross-section pier)

[0126] Equivalent mass of pier 2 (constant cross-section pier)

[0127] Step S32: Establish the dynamic equation of the seismic calculation model and solve for the displacement amplitude X1 of the main beam 1.

[0128] Specifically, in one embodiment, step S32, establishing the dynamic equation of the seismic calculation model and solving for the displacement amplitude X1 of the main beam 1, includes:

[0129] Based on the seismic calculation model, the seismic load p0sinωt is applied to the bridge pier m1 position, and the motion differential equation of the damped system with two degrees of freedom is established.

[0130] The differential equation of motion is:

[0131]

[0132] Where p0 and ω are the time-domain parameters of the seismic load;

[0133] The displacement amplitude X1 of the main beam 1 is calculated based on the equation of motion.

[0134] The calculation formula is:

[0135] Among them, the natural frequency of the seismic isolation bearing 3

[0136] The natural frequency of pier 2

[0137] The frequency ratio of seismic isolation bearing 3 to pier 2

[0138] The frequency ratio of earthquake vibration to that of pier 2

[0139] Equivalent mass ratio of main girder 1 to pier 2

[0140] Step S33: Based on the displacement amplitude X1 of the main beam 1, solve for the internal force response at the bottom of pier 2 when the seismic isolation support 3 is installed, and calculate the second shear force Q and the second bending moment M at the bottom of pier 2.

[0141] The calculation formula is: Q = k1X1; M = QL0.

[0142] Of course, in other embodiments, the displacement amplitude of pier 2 can also be calculated based on the motion differential equation, thereby calculating the second shear force Q at the bottom of the pier.

[0143] Secondly, embodiments of this application provide a computer device, which may be a personal computer (PC), a laptop computer, a server, or other device with data processing capabilities.

[0144] Reference Figure 5 , Figure 5 This is a schematic diagram of the hardware structure of a computer device according to one embodiment of the present invention. In one embodiment, the computer device includes a processor, a memory, a communication interface, and a communication bus.

[0145] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.

[0146] Communication interfaces include input / output (I / O) interfaces, physical interfaces, and logical interfaces used to interconnect components within a computer device, as well as interfaces used to interconnect the computer device with other devices (such as other computing devices or user equipment). Physical interfaces can be Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user equipment can be displays, keyboards, etc.

[0147] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0148] The processor can be a general-purpose processor, which can call a computer program stored in memory and execute the fast calculation method for the pier damping rate provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the computer program is called can be referred to the embodiments of this application, and will not be repeated here.

[0149] Those skilled in the art will understand that Figure 5 The hardware structure shown does not constitute a limitation of this application and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0150] Thirdly, embodiments of this application also provide a computer-readable storage medium.

[0151] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the rapid calculation method for the vibration reduction rate of bridge piers as described above. Specific details can be found in the embodiments of this application, and will not be repeated here.

[0152] It should be noted that the sequence numbers of the embodiments in this application are merely for descriptive purposes and do not represent the superiority or inferiority of the embodiments. The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not represent a sequential order, nor do they limit "first," "second," and "third" to different types.

[0153] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0154] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0155] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish the different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0156] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0157] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A rapid calculation method for the vibration damping rate of bridge piers, characterized in that, Includes the following steps: The basic seismic resistance system of the bridge is determined, and the seismic stress and calculation model of the bridge is established. The bridge includes a main beam (1), a pier (2), and a seismic isolation bearing (3) located between the main beam (1) and the pier (2). Obtain the internal force response at the bottom of the pier (2) without the vibration damping and isolation bearing (3) to obtain the first shear force at the bottom of the pier (2). Q 0. First bending moment M 0; Based on the bridge seismic stress and calculation model, the internal force response at the bottom of the pier (2) when the seismic isolation bearing (3) is installed is obtained, so as to obtain the second shear force at the bottom of the pier (2). Q Second bending moment M ; Calculate the damping ratio of the bridge piers, the damping ratio including the damping ratio based on the first shear force. Q 0. Second shear force Q Determined shear damping rate and based on the first bending moment M 0. Second bending moment M Determined bending moment damping rate ; The shear damping rate The calculation formula is: ； The bending moment damping rate The calculation formula is: ； in, p 0 represents the time-domain parameter of the seismic load; It is the frequency ratio of the seismic isolation bearing to the bridge pier; It is the ratio of the earthquake vibration frequency to the frequency of the bridge pier; It is the ratio of the equivalent mass of the main beam to the pier; It is the equivalent damping ratio of the seismic isolation bearing; m b It's the quality of the bridge piers. m a It refers to the quality of the main beam; It is a coefficient; This refers to the frequency of the bridge piers when no seismic isolation bearings are installed. L It refers to the height of the bridge pier; L 0 is the equivalent pier height of the bridge pier.

2. The rapid calculation method for the vibration reduction rate of bridge piers as described in claim 1, characterized in that, The establishment of the seismic stress and calculation model of the bridge includes: A seismic stress model of the bridge is established, with the main beam (1) as the superstructure and the pier (2) as the substructure. The main beam (1) and the pier (2) are simplified as concentrated loads; The seismic isolation bearing (3) is simplified to an equivalent stiffness. k 2. Equivalent Damping c 2; A seismic calculation model for the bridge is established, which is a damped system with two degrees of freedom.

3. The rapid calculation method for the vibration reduction rate of bridge piers as described in claim 2, characterized in that, The simplification of the main beam (1) and the pier (2) into concentrated loads includes: quality m a The main beam (1) is simplified to the first concentrated load, with an equivalent mass m 2; quality m b Stiffness EI The bridge pier (2) is simplified to the second concentrated load, with an equivalent mass m 1. Equivalent stiffness k 1. Equivalent pier height L 0.

4. The rapid calculation method for the vibration reduction rate of bridge piers as described in claim 3, characterized in that, The internal force response at the bottom of the pier (2) without the seismic isolation bearing (3) is obtained to obtain the first shear force at the bottom of the pier (2). Q 0. First bending moment M 0 includes: Establish the pier coordinate system of the bridge pier (2) without the vibration isolation bearing (3); Based on the aforementioned pier coordinate system, the structural vibration mode function in the direction of seismic stress is obtained as follows: ； The frequency of the bridge pier base is obtained based on the structural vibration mode function. for: ； Calculate the first shear force at the bottom of the pier (2). Q 0; The calculation formula is: ; Calculate the first bending moment at the bottom of the pier (2). M 0; The calculation formula is: ; coefficient ; in, T g The characteristic period in the frequency domain parameters of seismic load. K h The horizontal peak ground acceleration coefficient of the fundamental ground motion in the frequency domain parameters of seismic load. g This is the acceleration due to gravity.

5. The rapid calculation method for the vibration reduction rate of bridge piers as described in claim 4, characterized in that, The frequency domain parameters of the earthquake load shown T g , K h With the time-domain parameters of seismic load p 0、 They can be converted to each other through the conversion relationship between reaction spectrum and power spectrum.

6. The rapid calculation method for the vibration reduction rate of bridge piers as described in claim 3, characterized in that, The internal force response at the bottom of the pier (2) when the seismic isolation bearing (3) is installed is obtained based on the bridge seismic stress and calculation model, so as to obtain the second shear force at the bottom of the pier (2). Q Second bending moment M include: Basic parameters are obtained based on the bridge seismic calculation model. Establish the dynamic equations of the seismic calculation model and solve for the displacement amplitude of the main beam (1). X 1; According to the displacement amplitude of the main beam (1) X 1. Solve for the internal force response at the bottom of the pier (2) when the seismic isolation bearing (3) is installed, and calculate the second shear force at the bottom of the pier (2). Q Second bending moment M ; The calculation formula is: ; .

7. The rapid calculation method for the vibration reduction rate of bridge piers as described in claim 6, characterized in that, The dynamic equations of the seismic calculation model are established to solve for the displacement amplitude of the main beam (1). X 1 includes: Based on the aforementioned seismic calculation model, the seismic load... Acting on the position of the bridge pier (2), establish the motion differential equations of a damped system with two degrees of freedom; The equation of motion is: ； p 0、 These are the time-domain parameters of the seismic load; The displacement amplitude of the main beam (1) is calculated based on the aforementioned differential equation of motion. X 1; The calculation formula is: .

8. A computer device, characterized in that, The computer device includes a processor, a memory, and a computer program stored in the memory and executable by the processor, wherein when the computer program is executed by the processor, it implements the steps of the rapid calculation method for the pier damping rate as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, wherein when the computer program is executed by a processor, it implements the steps of the rapid calculation method for the pier damping rate as described in any one of claims 1 to 7.

Images