CN112182688A - Method for calculating vertical fundamental frequency reasonable value of straddle-type monorail beam - Google Patents
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Abstract
The invention belongs to the technical field of rail transit, and provides a method for calculating a reasonable vertical fundamental frequency value of a straddle-type monorail beam, aiming at solving the problem of simplifying and analyzing the reasonable vertical fundamental frequency value of the straddle-type monorail beam with the speed of 120km per hour on the premise of no detailed vehicle parameters and no axle coupling dynamic simulation analysis. According to the invention, firstly, static calculation analysis is carried out to determine the reasonable beam height of the straddle type single-rail simply-supported beam; then, determining a power analysis expression of the straddle type monorail simply-supported beam under the action of the marshalling monorail train; and finally, dynamically solving and determining a reasonable value of the vertical fundamental frequency of the straddle-type single-rail simply-supported beam, facilitating design research on the single-rail beam at the speed of 120 kilometers per hour as early as possible, filling the blank of the design specification of the straddle-type single rail on the requirement of the vertical fundamental frequency, and further facilitating revision and improvement of the design specification of the straddle-type single rail.
Description
Technical Field
The invention belongs to the technical field of rail transit, and particularly relates to a method for calculating a reasonable vertical fundamental frequency value of a straddle-type monorail beam.
Background
At present, the related research of the straddle-type monorail bridge is mainly suitable for a monorail beam with the speed of 80km per hour, and the monorail beam with the speed of 120km per hour becomes a development direction along with the continuous popularization of a monorail technology, wherein the vertical fundamental frequency research of the straddle-type monorail beam with the speed of 120km per hour is still in a blank stage, and cannot meet the actual requirement.
A paper "comparison study of vertical fundamental frequency limits of two simply supported beams of a 400km/h high-altitude railway, xuxin et al, 2019" discloses: in order to avoid excessive vibration and even resonance when a train passes through a bridge, two 33.1m simple-supported beam bridge forms (a concrete simple-supported box beam bridge and a steel-concrete combined simple-supported beam bridge) of a mokew high-speed railway are taken as backgrounds, and the vertical deflection and the fundamental frequency limit value of the simple-supported beam bridge are researched through axle coupling vibration analysis;
the thesis "optimization design of main span 40m straddle type monorail transit continuous steel box track beam, luyanbiao, etc., 2018 discloses: a cloud rail demonstration line-main span 40m continuous steel box rail beam in a certain city is taken as an engineering background, a direct grid search method principle is utilized, a bivariate optimization design method is adopted, and finite element software ANSYS is applied to calculate and analyze the mechanical characteristics of a selected structural system. Optimizing the structure by taking the beam height, the side span and the mid-span ratio as design variables and taking the deflection of a main beam, the vertical fundamental frequency, the corner of a beam end and the stress as constraint conditions, and determining an optimal structure system which minimizes the consumption of structural materials;
the patent "straddle type monorail pier and design method thereof, publication No. CN109344554A, application No. 20181129" discloses: the straddle type single-rail bridge pier is characterized in that a straddle type single-rail beam body can longitudinally and freely deform under the action of temperature load, the longitudinal movement of the beam body is restrained under the action of braking force, the straddle type single-rail bridge piers are connected in series, and braking force is transmitted to the bridge piers in the forward direction of a vehicle; the straddle type monorail bridge pier comprises a fixed support and a longitudinal movable support which are arranged on the bridge pier, wherein the allowable displacement of the longitudinal movable support is larger than the temperature deformation of a beam body, and the allowable deformation and the beam seam width of an expansion joint are larger than the allowable displacement of the longitudinal movable support. The design method solves the strict limitation of the specification on the displacement of the pier top of the pier, ensures that the section size of the pier body can be effectively reduced even if the design method provided by the invention is adopted under the limit value, greatly saves the construction cost, reduces the occupied space of the pier, and improves the landscape effect of the structure.
In the design specification of a straddle-type monorail beam with the speed of 80km per hour, the limit value or the reasonable value requirement in the aspect of vertical fundamental frequency is not clear, the determination of the vertical rigidity of the straddle-type monorail beam is usually carried out by adopting a monorail axle dynamic coupling analysis method, and the analysis can be completed only by needing related parameters of the bridge and detailed dynamic analysis parameters of a vehicle. For the research of the 120km per hour straddle type monorail beam, the method cannot be adopted for research due to lack of fine dynamic parameters of vehicles, and the reasonable vertical fundamental frequency value of the 120km per hour straddle type monorail beam is a key technical parameter in design, is directly related to success or failure of the design of the monorail beam, and has a research value.
Disclosure of Invention
The invention aims to solve the problem of how to calculate the reasonable value of the vertical fundamental frequency of a straddle-type monorail beam with the speed of 120km per hour on the premise of no detailed vehicle parameters and no axle coupling dynamic simulation analysis, and provides a method for calculating the reasonable value of the vertical fundamental frequency of the straddle-type monorail beam.
In the technical scheme, based on the current situation of rail transit research, the inventor combines the relevant research on the response of the simple supported beam under the action of a series of moving constant force in a high-speed railway bridge, researches the vertical rigidity problem of the 120km per hour monorail beam by a method combining static solution and series moving load column simplification analysis, and provides a reasonable value of the vertical fundamental frequency of the 120km per hour straddle type monorail simple supported beam for reference.
In order to achieve the technical purpose, the following technical scheme is proposed:
a method for calculating a reasonable vertical fundamental frequency value of a straddle-type monorail beam comprises the following steps:
1) determining the reasonable beam height of the straddle type single-rail simply-supported beam through static calculation analysis;
according to the axle weight information, the wheelbase information and the marshalling information of the monorail vehicle with the speed per hour of 120km, combining the design specification of a monorail bridge (for example, the design specification of straddle type monorail traffic, GB 50458-;
here, "reasonable beam height" is a conventional term in the technical field, and is a beam height determined by the inventor in consideration of meeting design specifications in combination with construction convenience and economy;
here, the working conditions of the worst load combination include dead load, live load, additional force, special load, etc., and there may be inconsistency of the worst load combination for different structural parts, such as: for midspans, the worst load combinations include dead weight, vehicle load and centrifugal force; for the pivot position, the worst load combination comprises dead weight, vehicle load and temperature load; and for the upper edge and the lower edge at the same position, the worst load combination comprises bending moment detection and shearing force detection. Therefore, the working condition of the worst load combination is determined according to the actual situation;
2) determining a power analysis expression of the straddle type monorail simply-supported beam under the action of the marshalling monorail train;
simplifying the axle weight of a grouped monorail train into a series of moving load trains, wherein the equal-spacing load is expressed as follows through a dynamic equation of a monorail simple supported beam at a certain speed:
in the formula (1), E is the elastic modulus of the single-track simple supported beam, I is the vertical inertia moment of the cross section of the single-track simple supported beam, c is the structural damping,
and y (x, t) is the displacement of the monorail simple supported beam at the position x away from the beam end along with the change of time, and t is the change of time.
Is the fourth partial differential of y (x, t) over x,
and
first and second partial differentials, respectively, of y (x, t) over time t; wherein, F (t) can be expressed as follows:
in the formula (2), p is the axle weight of the monorail vehicle; wherein A iskThe expression is as follows:
Ak(t，v，L)＝[x-v(t-tk)]·[H(t-tk)-H(t-tk-Δt)] (3)
in the formula (3), the function is a Dirac function, H (·) is a unit order function, x is a coordinate point on the beam, v is the train running speed, tkFor the kth load arriving on the beam, tkD is the distance between the axle weights of the vehicles, n is the total number of the moving loads, and delta t is L/v;
solving the formula (1) by adopting a modal superposition method to obtain:
in formula (4), n is the number of modes:
in the formula (5), tcFor a single-track vehicle front-rear wheel spacing D1Ratio to vehicle speed v, tc＝D1/v：
In formula (6):
in formulae (7) and (8), ω isdnDamped nth order natural frequency, omega, for a monorail beamnIs the nth order natural frequency, omega, of the monorail beamnFor a single load with an n-th order excitation frequency, SnIs the ratio of the excitation frequency to the natural frequency; are expressed as follows:
Ωn＝nπv/L (11)
in the formula (5), Fn(v, t) and Fn(v, t-tc) expression forms are consistent, and only the difference tc exists in time, wherein tc is the distance between the front wheel and the rear wheel of the monorail vehicleThe ratio to the vehicle speed v;
3) dynamically solving and determining a reasonable value of the vertical fundamental frequency of the straddle-type single-rail simply-supported beam;
A. considering the complexity of the vertical displacement analytic solution in the step 2), performing solution calculation by using a computer programming program based on the equations (4) - (12);
B. comparing and verifying a solving calculation result obtained according to the computer programming with a result of modeling by adopting dynamic analysis software;
or setting the moving speed of the moving load row as low speed, performing the solving calculation of the computer programming procedure, and comparing and verifying the obtained result with the result of modeling by using static analysis software;
the adopted comparison verification method comprises the following steps: respectively carrying out static force solution and dynamic solution on the mid-span displacement of the straddle-type single-track simply supported beam under the same load working condition, wherein the static force solution is carried out by adopting bridge structure calculation software, and the dynamic solution is carried out by adopting a computer programming program based on the expressions (4) - (12); in the dynamic solution, the moving speed of the moving load column is set to be low (for example, 5km/h, the load is moved slowly, the dynamic effect is small, or 1km/h, but the period of the whole dynamic analysis is prolonged.) and the correctness of the programming result can be verified if the static solution result and the dynamic solution result are equal or close to each other;
C. determining general parameters of dynamic analysis, wherein the general parameters comprise damping ratio and modal orders participating in dynamic solution;
damping ratio: the safety can be ensured according to the conventional dynamic analysis, the value of the steel beam is set to be 0.005, and the value of the concrete beam is set to be 0.01;
the modal order participating in dynamic solution is as follows: generally speaking, the solution of the mid-span displacement of the straddle-type single-track simply-supported beam has enough precision by taking the first 1-order mode, and the precision can reach 99.2%; the first 5-order mode is selected, the precision is as high as 100%, therefore, the first 5-order mode can be optimized and used for solving the midspan dynamic displacement;
the selection of the modal order is mainly based on the structural form, the vehicle speed, the vehicle axle distance and the like;
D. according to the analysis and solution of general parameters, the reasonable vertical fundamental frequency value of the single-rail simply-supported beam is determined
The method comprises the steps that the running speed of a train and the vertical fundamental frequency of a single-rail simply-supported beam are taken as analysis parameters, the vertical dynamic displacement and the impact coefficient of a structural span are taken as research objects, and the reasonable vertical fundamental frequency limit value of the 120 km-per-hour span-type single-rail beam is comprehensively analyzed and determined by combining the regulations of the bending span ratio and the impact coefficient in the design specification of the single-rail bridge (for example, the design specification of the straddle-type single-rail traffic, GB 50458-;
to obtain: the reasonable value of the vertical fundamental frequency of the 120km straddle-type single-rail simply-supported beam is 100/L.
In the technical scheme, the involved dynamic analysis software and static analysis software are common structural analysis software in the technical field, so that no specific version requirement exists.
By adopting the technical scheme, the beneficial technical effects brought are as follows:
the method can determine the reasonable vertical fundamental frequency value of the 120-kilometer-per-hour straddle-type single-rail simply-supported beam without the detailed parameters of the single-rail vehicle, is convenient for developing the design research of the 120-kilometer-per-hour single-rail beam as early as possible, fills the blank of the design specification of the straddle-type single rail on the requirement of the vertical fundamental frequency, and is further convenient for revising and perfecting the specification of the straddle-type single rail.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic diagram of a monorail car consist in accordance with the present invention;
FIG. 2 is a simplified model of the moving load train of the present invention;
FIG. 3 is a schematic sectional view of a 1800mm beam in example 2;
FIG. 4 is a graph showing the variation of the motion displacement with time across 120 km/h in example 2;
in the figure, 1, a monorail simple supported beam, 2, a monorail vehicle marshalling and 3, monorail vertical axle load are shown.
Detailed Description
Exemplary embodiments will be described in detail herein. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the exemplary embodiments below are not intended to represent all implementations consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as detailed in the appended claims.
Example 1
A method for calculating a reasonable vertical fundamental frequency value of a straddle-type monorail beam comprises the following steps:
1) determining the reasonable beam height of the straddle type single-rail simply-supported beam through static calculation analysis;
according to the axle weight information, the wheelbase information and the marshalling information of the monorail vehicle with the speed per hour of 120km, combining the design specification of a monorail bridge (for example, the design specification of straddle type monorail traffic, GB 50458-;
2) determining a power analysis expression of the straddle type monorail simply-supported beam under the action of the marshalling monorail train;
simplifying the axle weight of a grouped monorail train into a series of moving load trains (as shown in figures 1-2), wherein the equal-spacing load is expressed by a kinetic equation of a monorail simple beam at a certain speed as follows:
in the formula (1), E is the elastic modulus of the single-track simple supported beam, I is the vertical inertia moment of the cross section of the single-track simple supported beam, c is the structural damping,
and y (x, t) is the displacement of the monorail simple supported beam at the position x away from the beam end along with the change of time, and t is the change of time.
Is the fourth partial differential of y (x, t) over x,
and
first and second partial differentials, respectively, of y (x, t) over time t; wherein, F (t) can be expressed as follows:
in the formula (2), p is the axle weight of the monorail vehicle; wherein, Ak is expressed as follows:
Ak(t，v，L)＝[x-v)t-tk)]·[H(t-tk)-H(t-tk-Δt)] (3)
in the formula (3), the function is a Dirac function, H (·) is a unit order function, x is a coordinate point on the beam, v is the train running speed, tkFor the kth load arriving on the beam, tkD is the distance between the axle weights of the vehicles, n is the total number of the moving loads, and delta t is L/v;
solving the formula (1) by adopting a modal superposition method to obtain:
in formula (4), n is the number of modes:
in the formula (5), tcFor a single-track vehicle front-rear wheel spacing D1Ratio to vehicle speed v, tc＝D1/v：
In formula (6):
in formulae (7) and (8), ω isdnDamped nth order natural frequency, omega, for a monorail beamnIs the nth order natural frequency, omega, of the monorail beamnFor a single load with an n-th order excitation frequency, SnIs the ratio of the excitation frequency to the natural frequency; are expressed as follows:
Ωn＝nπv/L (11)
in the formula (5), Fn(v, t) and Fn(v, t-tc) expression forms are consistent, and only the difference tc exists in time, wherein tc is the ratio of the distance between the front wheels and the rear wheels of the monorail vehicle to the vehicle speed v;
3) dynamically solving and determining a reasonable value of the vertical fundamental frequency of the straddle-type single-rail simply-supported beam;
A. considering the complexity of the vertical displacement analytic solution in the step 2), performing solution calculation by using a computer programming program based on the equations (4) - (12);
B. comparing and verifying a solving calculation result obtained according to the computer programming with a result of modeling by adopting dynamic analysis software;
or setting the moving speed of the moving load row as low speed, performing the solving calculation of the computer programming procedure, and comparing and verifying the obtained result with the result of modeling by using static analysis software;
the kinetic analysis software may be ANSYS and the like, and the static analysis software may be MIDAS, bridge doctor and the like.
The adopted comparison verification method comprises the following steps: respectively carrying out static force solution and dynamic solution on the mid-span displacement of the straddle-type single-track simply supported beam under the same load working condition, wherein the static force solution is carried out by adopting bridge structure calculation software, and the dynamic solution is carried out by adopting a computer programming program based on the expressions (4) - (12); in the dynamic solution, the moving speed of the moving load column is set to be low (for example, 5km/h, the load is moved slowly, the dynamic effect is small, or 1km/h, but the period of the whole dynamic analysis is prolonged.) and the correctness of the programming result can be verified if the static solution result and the dynamic solution result are equal or close to each other;
C. determining general parameters of dynamic analysis, wherein the general parameters comprise damping ratio and modal orders participating in dynamic solution;
damping ratio: the safety can be ensured according to the conventional dynamic analysis, the value of the steel beam is set to be 0.005, and the value of the concrete beam is set to be 0.01;
the modal order participating in dynamic solution is as follows: generally speaking, the mid-span displacement of the straddle-type single-track simply-supported beam is solved by taking the first 5-order mode, the precision is as high as 100 percent, and the method is used for solving the mid-span dynamic displacement;
the selection of the modal order is mainly based on the structural form, the vehicle speed, the vehicle axle distance and the like;
D. according to the analysis and solution of general parameters, the reasonable vertical fundamental frequency value of the single-rail simply-supported beam is determined
The method comprises the steps that the running speed of a train and the vertical fundamental frequency of a single-rail simply-supported beam are taken as analysis parameters, the vertical dynamic displacement and the impact coefficient of a structural span are taken as research objects, and the reasonable vertical fundamental frequency limit value of the 120 km-per-hour span-type single-rail beam is comprehensively analyzed and determined by combining the regulations of the bending span ratio and the impact coefficient in the design specification of the single-rail bridge (for example, the design specification of the straddle-type single-rail traffic, GB 50458-;
to obtain: the reasonable value of the vertical fundamental frequency of the 120km straddle type single-rail simply-supported beam is 100/L, wherein the value is obtained by analyzing the static power and the dynamic power of the 120km straddle type single-rail simply-supported beam with different spans and comprehensively comparing the values, and the method has universal significance.
Example 2
Based on embodiment 1, this embodiment further describes the present invention by taking a method for calculating a reasonable value of a vertical fundamental frequency of a straddle-type monorail beam with a speed per hour of 120 kilometers and a span of 30m as an example.
The specific setting comprises: the vehicle adopts 6 marshalling, wherein the axle weight is 138kN, the axle distance is 9120mm, and the distance between the front axle of the rear vehicle and the rear axle of the front vehicle is 2725 mm; in fig. 1-2, D1 is 9120mm, D2 is 2725mm, D1+ D2 is 9120+2725 mm, and L is 30 m.
Firstly, static force calculation is carried out, and reasonable beam height is determined.
Preliminarily determining three sections of the monorail beam, wherein the beam heights are 1800mm, 1900mm and 2000mm respectively; wherein, the 1800mm beam height section form is as shown in fig. 3 (wherein, a is 1800mm, b is 225m, c is 240mm, d is 225mm, e is 210mm, f is 1380mm, g is 210mm, h is 690mm), the beam section web height of 1900mm and 2000mm beam height section form is 1480mm and 1580mm respectively, and other parameters are the same as the 1800mm beam height section.
According to the design specification of straddle type monorail traffic (GB 50458 + 2008), structural static calculation is carried out, the static design and the check calculation of the main beam are carried out, the three beam heights obtained through the check calculation meet the specification requirements, and the 1800mm beam height is preliminarily selected as the reasonable beam height in consideration of economy.
Secondly, solving the span neutral motion displacement of the single-track simple beam structure is carried out according to the programming of the formulas (4) to (12) in the embodiment 1.
Selecting concrete beams, and determining general calculation parameters as the following table 1:
table 1 shows general calculation parameters of a simply supported monorail girder with a span of 30m
According to the formulas (4) to (12), corresponding parameters are substituted, and the vehicle speed v is used as a variable to obtain: at various vehicle speeds, the time course curves of different beam height midspan dynamic displacements are shown in a typical curve in FIG. 4.
The static displacement, the dynamic displacement, the power amplification coefficient, the mid-span power position time course of different beam heights and the like of three beam heights of 1800mm, 1900mm and 2000mm at different vehicle speeds are shown in the following table 2, and it can be known that: compared with the existing design, the 1900mm beam height has the advantages that the dynamic displacement of the beam is reduced to a certain extent within the range of 80-120 kilometers under all calculated vehicle speeds, the impact coefficient is slightly increased at 80 kilometers per hour, and the dynamic displacement of the beam is reduced to a greater extent under other vehicle speeds; the impact coefficient of a 2000mm beam is larger when the speed per hour is 80 kilometers, and the impact coefficient is obviously reduced at other vehicle speeds, so that the 1900mm beam height is more suitable in general.
Table 2 shows the dynamic displacement and amplification factor of a simply supported monorail beam with a span of 30m and different beam heights
Thirdly, analyzing and comparing the parameters to determine a reasonable value of the vertical fundamental frequency.
The span is set to be 30m, the reasonable beam height is 1900mm, the product of the frequency and the span corresponding to the straddle-type monorail beam with the span of 30m is about 103 by referring to the expression form of the high-speed railway about the vertical fundamental frequency according to the track beam fundamental frequency and the span under the corresponding beam height, and the reasonable value of the vertical fundamental frequency of the straddle-type monorail simply-supported concrete beam is determined to be 100/L (the fundamental frequency value is a more reasonable vertical fundamental frequency value judged according to the power calculation result on the basis of reasonable static calculation, and is not the minimum limit value of the vertical rigidity) by comprehensively considering.
Table 3 shows the reasonable vertical frequency expression
Claims (9)
1. A method for calculating a reasonable vertical fundamental frequency value of a straddle-type monorail beam is characterized by comprising the following steps:
determining the reasonable beam height of the straddle type single-rail simply-supported beam through static calculation analysis;
determining a power analysis expression of the straddle type monorail simply-supported beam under the action of the marshalling monorail train;
and (5) dynamically solving and determining a reasonable value of the vertical fundamental frequency of the straddle type single-rail simply-supported beam.
2. The method for calculating the reasonable vertical fundamental frequency value of the straddle-type monorail beam according to claim 1, wherein the step of determining the reasonable beam height of the straddle-type monorail simply-supported beam comprises the following steps:
and designing by adopting an allowable stress method according to the axle weight information, the wheel base information and the marshalling information of the monorail vehicle with the speed per hour of 120km, and setting the beam height.
3. The method for calculating the reasonable vertical fundamental frequency value of the straddle-type monorail beam according to claim 2, wherein the step of determining the reasonable beam height of the straddle-type monorail simply-supported beam further comprises the following steps:
when the reasonable beam height is determined, the design specification of the monorail bridge is combined, the worst load combination working condition is considered, an allowable stress method is adopted for design, and the beam height is planned.
4. The method for calculating the reasonable vertical fundamental frequency value of the straddle-type monorail beam according to claim 1, 2 or 3, wherein the step of determining the power analysis expression of the straddle-type monorail simple beam under the action of the marshalling monorail train comprises the following steps:
simplifying the axle weight of the marshalling monorail train into a series of movable load trains; wherein, equidistant load passes through the kinetic equation expression of single track simple beam with certain speed, includes:
in the formula (1), E is the elastic modulus of the single-track simple supported beam, I is the vertical inertia moment of the cross section of the single-track simple supported beam, c is the structural damping,
the mass per unit length is y (x, t) is the displacement of the position x away from the beam end on the single-rail simple beam along with the change of time, and t is the time variable; wherein, F (t) can be expressed as follows:
in the formula (2), p is the axle weight of the monorail vehicle; wherein A iskThe expression is as follows:
Ak(t，v，L)＝[x-v(t-tk)]·[H(t-tk)-H(t-tk-Δt)] (3)
in the formula (3), the function is a Dirac function, H (·) is a unit order function, x is a coordinate point on the beam, v is the train running speed, tkFor the kth load arriving on the beam, tkD is the distance between the axle weights of the vehicles, n is the total number of the moving loads, and delta t is L/v;
solving the formula (1) by adopting a modal superposition method to obtain:
in formula (4), n is the number of modes:
in the formula (5), tcFor a single-track vehicle front-rear wheel spacing D1Ratio to vehicle speed v, tc＝D1/v：
In formula (6):
in formulae (7) and (8), ω isdnDamped nth order natural frequency, omega, for a single-track simple beamnThe nth order natural frequency, omega, of the single-track simple supported beamnFor a single load with an n-th order excitation frequency, SnIs the ratio of the excitation frequency to the natural frequency; are expressed as follows:
Ωn＝nπv/L (11)
5. the method for calculating the reasonable value of the vertical fundamental frequency of the straddle-type monorail beam according to claim 4, wherein the dynamically solving and determining the reasonable value of the vertical fundamental frequency of the straddle-type monorail simply-supported beam comprises the following steps:
performing dynamic solution calculation on the dynamic equation based on the formulas (4) to (12);
solving a calculation result according to the obtained power, and comparing and verifying the calculation result with a result of modeling by adopting power analysis software;
or setting the moving speed of the moving load line as low speed, performing dynamic solution calculation, and comparing and verifying the obtained result with the result of modeling by static analysis software;
determining general parameters of dynamic analysis, wherein the general parameters comprise damping ratio and modal orders participating in dynamic solution;
and (5) according to the analysis and solution of the general parameters, determining a reasonable value of the vertical fundamental frequency of the single-rail simply-supported beam.
6. The method for calculating the reasonable vertical fundamental frequency value of the straddle-type monorail beam according to claim 5, wherein the comparison verification comprises the following steps:
respectively carrying out static solution and dynamic solution on the mid-span displacement of the straddle type single-track simply-supported beam under the same load working condition, wherein the static solution is carried out by adopting conventional bridge calculation software such as MIDAS (MIDAS), bridge doctor and the like, and the dynamic solution is carried out by adopting the formulas (4) - (12); in the dynamic solving, the moving speed of the moving load column is set to be low, and the static solving result and the dynamic solving result are equal or close to each other, so that the correctness of the dynamic solving result can be verified.
7. The method for calculating the reasonable vertical fundamental frequency value of the straddle-type monorail beam according to claim 5, wherein in the general parameters, a steel beam damping ratio is set to be 0.005, and a concrete beam damping ratio is set to be 0.01;
the modal order participating in the dynamic solution is set to be the first 5-order mode or the first 1-order mode, and is used for solving the mid-span displacement of the straddle type monorail beam.
8. The method for calculating the reasonable value of the vertical fundamental frequency of the straddle-type monorail beam according to claim 5, wherein in the determination of the reasonable value of the vertical fundamental frequency of the monorail simple-supported beam, the running speed of a train and the vertical fundamental frequency of the monorail simple-supported beam are used as analysis parameters, the vertical dynamic displacement and the impact coefficient of a structural straddle are used as research objects, and the reasonable value of the vertical fundamental frequency of the straddle-type monorail beam with the speed of 120km per hour is comprehensively analyzed and determined by combining the regulations on the bending-span ratio and the impact coefficient in the design specification of the monorail bridge.
9. The method for calculating the reasonable vertical fundamental frequency value of the straddle-type monorail beam according to claim 8, wherein the reasonable vertical fundamental frequency value of the 120km straddle-type monorail simply-supported beam is 100/L.
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