CN108763646B - Box-type beam local vibration prediction method based on FE-SEA (enhanced FE-SEA) hybrid method - Google Patents
Box-type beam local vibration prediction method based on FE-SEA (enhanced FE-SEA) hybrid method Download PDFInfo
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Abstract
The invention discloses a box beam local vibration prediction method based on an FE-SEA (enhanced FE-SEA) hybrid method, which comprises the following steps of: dividing the box beam into a plurality of plates, namely a top plate, a bottom plate, a left wing plate, a right wing plate, a left web plate and a right web plate; and according to the bending mode number of the local vibration of each plate on the box-shaped beam, establishing a local vibration simulation model of the box-shaped beam under the action of the vertical force of the wheel rail in a frequency division manner. The invention has the advantages that: establishing a box-shaped beam local vibration model in a frequency division range by adopting an FE-SEA mixing method; according to the model, each plate of the box beam is divided into FE and SEA subsystems in different frequency bands according to the bending mode number of each plate of the box beam, particularly, in a medium-frequency domain, mixed connection of the FE subsystems and the SEA subsystems of different plates is realized in the same model, the defects that the calculation amount of an FE deterministic method in a high-frequency band is large and the precision of the SEA in a low-frequency band is poor are overcome, the contradiction between the calculation efficiency and the calculation precision is solved, and the analysis frequency band of local vibration of the box beam is expanded through research results.
Description
Technical Field
The invention belongs to the technical field of urban rail transit environment vibration and noise, and particularly relates to a box girder local vibration prediction method based on an FE-SEA (finite element isolation-induced transient analysis) hybrid method.
Background
With the rapid development of urban rail transit, multi-layer elevated roads, underground railways and elevated light rail transit increasingly form a three-dimensional space traffic system, and gradually penetrate deep into dense residential sites, commercial centers and industrial areas in cities from underground, ground and air. The viaduct structure has been widely used in various cities because it is superior to underground works in safety, cost and construction. Meanwhile, as the traffic density is increased, the vibration and noise problems become more and more significant. Local high-frequency vibration of a concrete bridge structure can generate low-frequency structure radiation noise. The low-frequency structure noise radiated by the bridge structure has the characteristics of strong penetrability and slow attenuation, and has considerable negative effects on human attention, reaction time, language identification capability and the like. Therefore, the study on the vibration reduction and noise reduction measures of the viaduct structure is urgent.
At present, a deterministic method and an energy method are mainly used for local vibration analysis of urban rail transit bridges. The deterministic method comprises the following steps: finite element method, boundary element method, energy method mainly includes statistical energy analysis method. The finite element method is clear in concept, mature in theory and wide in application in solving the structural vibration problem, but when the finite element method is used for solving the high-frequency vibration of a large-size structure, grids are dense, the analysis freedom degree is large, and therefore large calculation errors are brought, so that the general finite element method is basically only used for analyzing the low-frequency vibration problem of a small-size structure; the boundary element method converts the problem into the solution of the boundary problem, reduces the dimension of the problem, is a semi-analytic method, is also suitable for the low-frequency vibration problem, but the calculated amount of the problem rapidly increases along with the increase of the degree of freedom, and is time-consuming when the analysis frequency is high; the statistical energy analysis method adopts a statistical principle, can quickly and accurately simulate the high-frequency band vibration characteristics, is more effective for the problem of dynamic response of a complex structure randomly excited by high frequency and wide frequency bands, but is difficult to ensure the research, prediction and analysis precision of the low-frequency vibration of the structure. Meanwhile, most of the scholars develop researches on passive control measures such as vibration reduction and isolation of the track structure, and the researches on active control designed by the bridge structure closely related to local vibration of the bridge structure are few. Due to the limitation of a numerical method, the current research on the local vibration of the rail transit viaduct is mainly concentrated in the range of 20Hz to 200Hz, and the research frequency domain range is narrow. Therefore, how to accurately and efficiently predict and analyze the local vibration characteristics of the box beam, and how to explore an optimal active control strategy from the source based on a local vibration generation mechanism to achieve the effects of vibration and noise reduction are technical problems which need to be solved urgently by technical personnel in the field.
Disclosure of Invention
The invention aims to provide a box beam local vibration prediction method based on an FE-SEA hybrid method according to the defects of the prior art, and the prediction method is used for solving the problem of a local vibration simulation model established by mixing a deterministic FE subsystem and a stochastic SEA subsystem of a box beam in a middle-low frequency area by quantitatively analyzing the local vibration of a box beam structure for rail transit in a frequency range of 2.5Hz-500Hz and calculating and predicting the sound contribution and vibration transmission rule of each plate of the box beam.
The purpose of the invention is realized by the following technical scheme:
a box beam local vibration prediction method based on an FE-SEA hybrid method is characterized by comprising the following steps: dividing the box-shaped beam into a plurality of plates, namely a top plate, a bottom plate, a left wing plate, a right wing plate, a left web and a right web; and according to the bending mode number of the local vibration of each plate on the box-shaped beam, establishing a local vibration simulation model of the box-shaped beam under the action of the vertical force of the wheel rail in a frequency division manner.
Determining the type of a subsystem adopted by each corresponding plate according to the bending mode number of local vibration of each plate on the box-shaped beam under different frequency bands, wherein the subsystem can be a deterministic FE subsystem or a stochastic SEA subsystem; and realizing the coupling between the subsystems by calculating the parameters of the coupling loss factor and the damping loss factor so that the local vibration simulation model is formed by coupling one or two of the deterministic FE subsystem or the stochastic SEA subsystem.
The method for determining the subsystem type adopted by each plate comprises the following steps: if the bending mode number of the local vibration of the plate is less than or equal to 5, the plate adopts FEM modeling to form the deterministic FE subsystem; and if the bending mode number of the local vibration of the plate is more than 5, the plate adopts SEA modeling to form the random SEA subsystem.
The box-shaped beam vibration and sound radiation analysis frequency is 2.5Hz-500Hz, and the box-shaped beam vibration and sound radiation analysis frequency is divided into a low-frequency region, a medium-frequency region and a high-frequency region, wherein the frequency domain of the low-frequency region is 2.5 Hz-160 Hz, the frequency domain of the medium-frequency region is 160 Hz-315 Hz, and the frequency domain of the high-frequency region is 315-500 Hz.
In the low-frequency region, the bending mode number of each plate of the box beam is less than 5, and each plate adopts the deterministic FE subsystem;
in the medium frequency region, the bending mode numbers of a top plate, a bottom plate, a left web plate and a right web plate on the box girder are more than 5, and the stochastic SEA subsystem is adopted; the bending mode number of a left wing plate and a right wing plate on the box-shaped beam is less than 5, and the deterministic FE subsystem is adopted; the top plate on the box beam is in mixed connection with the left wing plate and the right wing plate on the two sides;
in the high-frequency region, the bending mode number of each plate of the box girder is more than 5, and each plate adopts the stochastic SEA subsystem.
Obtaining the energy of the stochastic SEA subsystem according to the energy response of the stochastic SEA subsystem, obtaining the displacement response of the deterministic FE subsystem according to the displacement spectrum matrix expression of the deterministic FE subsystem, and further obtaining the speed and acceleration physical quantity of each subsystem; on the basis, the propagation sound pressure of any field point is obtained by the sound radiation theory, and the prediction of the local vibration and the structural noise of the box-shaped beam is realized.
The invention has the advantages that an FE-SEA mixing method is adopted, and a box-type beam local vibration model is established in frequency division; according to the model, each plate of the box beam is divided into FE and SEA subsystems in different frequency bands according to the bending mode number of each plate of the box beam, particularly, in a medium-frequency domain, mixed connection of the FE subsystems and the SEA subsystems of different plates is realized in the same model, the defects that the calculation amount of an FE deterministic method in a high-frequency band is large and the precision of the SEA in a low-frequency band is poor are overcome, the contradiction between the calculation efficiency and the calculation precision is solved, the analysis frequency band of local vibration of the box beam is expanded according to research results, and the prediction precision and the calculation efficiency are improved.
Drawings
FIG. 1 is a schematic view of a rail coupling model according to the present invention;
FIG. 2 is a schematic diagram of effective amplitude of wheel-rail force corresponding to the center frequency of 1/3 octave in the present invention;
FIG. 3 is a cross-sectional view of the midspan of the box beam of the present invention;
FIG. 4 shows the bending mode number of each plate of the box beam under the center frequency of 1/3 octave;
FIG. 5 is a schematic view of the wheel-rail force position loading of the present invention;
FIG. 6 is a schematic diagram of the arrangement of the acceleration level and sound pressure level prediction points of the box beam according to the present invention;
FIG. 7 is a graph of the vibration acceleration level of the midpoint of each plate in the span of the box girder;
FIG. 8 is a graph showing sound pressure level at 0.3m from each plate in the span of the box beam according to the present invention;
FIG. 9 is a graph of sound pressure level of the far field points M1, M2, M3 of the box beam of the present invention;
FIG. 10 is a graph of the vibration power level loss of the box beam of the present invention;
FIG. 11 is a graph showing vibration energy levels of the plates of the box beam according to the present invention;
FIG. 12 is a comparison graph of predicted sound pressure levels and associated actual measurements in accordance with the present invention;
FIG. 13 is a schematic flow chart of a box beam local vibration prediction method based on an FE-SEA hybrid method in the present invention.
Detailed Description
The features of the present invention and other related features are described in further detail below by way of example in conjunction with the following drawings to facilitate understanding by those skilled in the art:
referring to fig. 1-13, the symbols in the drawings are: the vehicle comprises a vehicle 1, a track 2, a top plate 3, a left wing plate 4, a right wing plate 5, a left web plate 6, a right web plate 7, a bottom plate 8, a box-shaped beam 9, a wheel pair 10 and a bogie 11.
Example (b): as shown in fig. 1 to 13, the embodiment specifically relates to a box beam local vibration prediction method based on an FE-SEA hybrid method, which performs quantitative analysis on local vibration of a rail transit box beam 9 structure in a frequency domain of 2.5 to 500Hz, and solves noise of the box beam structure according to an acoustic radiation principle. Each plate of the box-shaped beam 9 is divided into a deterministic FE subsystem and a stochastic SEA subsystem, the number of the subsystem modes is less than or equal to 5, an FE model is built, the number of the subsystem modes is more than 5, an SEA model is built, the defects that the FE deterministic method is large in calculation amount in a high frequency band and the SEA energy method is poor in accuracy in a low frequency band are overcome, the contradiction between calculation efficiency and calculation accuracy is solved, the analysis frequency band of local vibration of the box-shaped beam 9 is expanded through research results, and prediction accuracy and calculation efficiency are improved.
As shown in fig. 1 and 2, in the embodiment, a CRH2 type vehicle is selected as a vehicle model, a german high-interference rugged track spectrum is adopted for track irregularity, the sampling frequency is 1250Hz, the wavelength is 0.25m to 30m, and the vehicle speed is 140km/h, and the specific parameters are shown in table 1 below. For example, as shown in fig. 1, the time domain vertical wheel-rail force of the vehicle-rail coupling is obtained by defining the wheel-rail contact geometric relationship, the articulation of the subsystems, the setting of the force element and other parameters. The hinge joint of the bogie adopts the hinge joint with 6 degrees of freedom, and the hinge joint of the vehicle body adopts the hinge joint with 5 degrees of freedom. The steel rail 2 is UIC60 in type, and the wheel rail is in single-point rigid contact. In order to accurately describe the wheel-rail contact relationship, 6 coordinate systems of a rail, a wheel tread, a rail surface, a wheel contact and a rail contact are introduced in the wheel-rail modeling, so as to describe the relative motion relationship of each rigid body of the rail 2 and the vehicle 1. And (3) performing fast Fourier transform and 1/3 octave conversion on the wheel-rail vertical force in the time domain to obtain the wheel-rail vertical force in the frequency domain, as shown in fig. 2.
TABLE 1 CRH2-TYPE VEHICLE CONSTRUCTION PARAMETERS
As shown in fig. 3, in the model of the box girder 9 in this embodiment, a certain rail transit overhead bridge is selected as the model, and specific parameters are as shown in table 2 below, and the model is divided into a plurality of plates, which are respectively a top plate 3, a left wing plate 4, a right wing plate 5, a left web 6, a right web 7, and a bottom plate 8. The vibration and sound radiation analysis frequency of the box-shaped beam 9 is 2.5Hz-500Hz, and in order to consider the calculation accuracy and the calculation efficiency, a plate-shell type unit is adopted to divide the frequency range of 2.5Hz-500Hz into a low-frequency region, a medium-frequency region and a high-frequency region, wherein the frequency domain of the low-frequency region is 2.5 Hz-160 Hz, the frequency domain of the medium-frequency region is 160 Hz-315 Hz, and the frequency domain of the high-frequency region is 315-500 Hz.
TABLE 2 Box Beam construction parameters
Under different frequency bands, determining the subsystem type adopted by each corresponding plate according to the bending mode number of local vibration of each plate on the box-shaped beam 9 according to the following determination principle: if the bending mode number of the local vibration of the plate is less than or equal to 5, the plate adopts FEM modeling to form a deterministic FE subsystem; and if the bending mode number of the local vibration of the plate is more than 5, the plate adopts SEA modeling to form the stochastic SEA subsystem. Obtaining the relationship between the bending mode number and the frequency of the box beam 9 under the action of the wheel-rail force, which is specifically shown in fig. 4 and the following table 3;
TABLE 3 relation between bending mode number and frequency of box girder under wheel-rail force
In the frequency domain of 2.5 Hz-160 Hz in the low-frequency region, all plates of the box-shaped beam 9 do not meet the requirement for establishing an SEA model, so that a full FE structure is established in the frequency domain range, namely all the plates adopt deterministic FE subsystems, the unit side length is uniformly taken as 0.2m, and the precision requirement is met;
in the frequency domain of 160Hz to 315Hz in the intermediate frequency region, the bending mode number of only the left wing plate 4 and the right wing plate 5 is less than 5, so that a deterministic FE subsystem is established, the top plate 3, the left web plate 6, the right web plate 7 and the bottom plate 8 are established into a stochastic SEA subsystem, and the top plate 3 is in mixed connection with the left wing plate 4 and the right wing plate 5;
in the high-frequency region 315-500 Hz, the bending mode number of each plate is more than 5, so that the random SEA subsystem is established.
The sub-system classification of each plate of the box beam in different frequency bands is given as shown in the following table 4. The coupling between the subsystems is realized by calculating the parameters of the coupling loss factor and the damping loss factor, so that the local vibration simulation model is formed by coupling one or two of a deterministic FE subsystem or a stochastic SEA subsystem.
TABLE 4 subsystem Classification
In this embodiment, the steps of modeling a box-beam local vibration simulation model based on an FE-SEA hybrid method and solving a sound pressure level based on a sound radiation theory are as follows: theoretical derivation analysis of a hybrid method, namely defining a boundary with known physical properties in an FE-SEA hybrid model as a deterministic boundary, and otherwise, defining the boundary as a stochastic boundary; and the displacement field at the boundary is divided into a direct field and a reverberation field according to different boundary conditions. For the FE-SEA hybrid model, the elastic wave will generate a reflection at the coupling boundary of the deterministic FE subsystem, which will be subjected to the additional force of the reverberant field, and the stochastic SEA subsystem.
Thus, for the displacement response of the deterministic FE subsystem:
in the formula:
The reciprocal relation of the diffusion field can be used to obtain:
in the formula:
h represents conjugate transpose;
The expression of the displacement cross-spectrum matrix obtained by the above two formulas is as follows:
wherein:
For stochastic SEA subsystem energy responses there are:
After the energy of the stochastic subsystem is obtained by the formula (4), the displacement response of the deterministic subsystem can be obtained by the formula (3), and further the physical quantities such as the speed, the acceleration and the like of the subsystem can be obtained. On the basis, the propagation sound pressure of any field point can be obtained by the acoustic radiation theory.
According to the theory related to the hybrid method, parameters such as coupling factors and bending mode density are determined by combining the relevant parameters of the urban rail transit box girder in the embodiment, and a box girder FE and FE-SEA hybrid model is established in a frequency division mode. By applying frequency domain wheel-track force of 1/3 octave of vertical direction, the midpoint displacement, vibration acceleration level and the like of each plate are obtained, the sound pressure level near each plate and the sound pressure level, contribution amount, vibration power and the like of the under-bridge field point and the far field point are obtained by combining the sound radiation theory, the relevant rules are summarized, and verification and comparison are carried out on the relevant rules and the existing actual measurement contents.
As shown in fig. 3 and 5, which are respectively a midspan section view and a loading schematic view of the box girder 9, the wheel pair 10 on the same bogie 11 of the CRH2 vehicle has a wheel base of 2.5m, the minimum wheel base between adjacent cars is 4.5m, and the loading is in the most unfavorable form, i.e. the connection position of two sections of cars is located at the middle position of the bridge. The arrangement of the acceleration and sound pressure level prediction field points of each point on the bridge is shown in fig. 6, wherein M1, M2, M3 are the sound pressure measurement points, respectively, and N1-N6 are the acceleration level measurement points, respectively.
As shown in fig. 7, it can be seen that the local vibration response amplitude of the 32m two-wire simple supported box beam 9 is the largest at the frequency of 50 Hz. The main acceleration frequencies are centered around 40Hz to 100 Hz. The left wing panel 4 and the right wing panel 5 have the largest vibration response at both low and high frequencies.
It can be seen from fig. 8 and 9 that the maximum amplitude frequency of the structural noise is 50Hz, the top plate sound pressure contribution amount is the largest at the near field point and the far field point, the top plate 3 and the bottom plate 8 sound pressure contribution amount is larger than other plates in the frequency band of 2.5-20 Hz, and the frequency band plays a main control role as a main noise reduction object, the sound pressure contribution amount of each plate is almost the same in the frequency band of 50-200 Hz, and the top plate 3 sound pressure contribution amount is the largest and the bottom plate 8 is the smallest in the frequency band of 200-500 Hz. Under the action of the wheel rail force, the dominant frequencies of the vibration acceleration level, the near field point structure noise and the far field point structure noise of the box-shaped beam 9 are mainly concentrated between 40Hz and 100Hz and are the same as the dominant frequencies of the wheel rail force, so the main vibration and noise reduction frequency band of the box-shaped beam 9 is the dominant frequency band of the wheel rail force acting on the box-shaped beam.
It can be seen from fig. 10 that the vibration power level loss of the box beam 9 is about 12.9dB to 18.4dB, and the power level loss increases with the frequency increase and increases with the frequency increase at the time of the whole vibration, and the peak frequency is above 50 Hz. As can be seen from fig. 11, the vibration energy level law of each plate of the box beam 9 is that the top plate 3> left and right wing plates 4/5> left and right webs 6/7> bottom plate 8. The vibration energy has peak values at fundamental frequencies of 4 Hz-5 Hz, 16 Hz-25 Hz and 40 Hz-80 Hz, and has the maximum peak value at 40 Hz-80 Hz.
As shown in fig. 12, the predicted sound pressure result and the actually measured comparison result of the present embodiment both agree well, indicating that the calculation accuracy of the present embodiment can meet the requirement. Meanwhile, as shown in table 5, the calculation efficiency of the present embodiment is also greatly improved.
TABLE 5 calculation method vs. efficiency
The beneficial effect of this embodiment and prior art comparison is: for a complex spring structure of the box beam type, it is almost impossible to obtain an analytical solution due to local high frequency vibrations. At present, a numerical method for analyzing local vibration of an urban rail transit bridge structure mainly comprises the following steps: finite Element Method (FEM), boundary Element Method (BEM), statistical energy method (SEA). The FEM is suitable for structural vibration response analysis of a low frequency band, but the method has low calculation efficiency for a complex dynamic system; the BEM calculation amount is rapidly increased along with the increase of the degree of freedom, and the analysis is time-consuming when the frequency is high; and when the SEA is used for analyzing low frequency, the prediction accuracy may be greatly reduced due to insufficient structural vibration mode number. In the embodiment, an FE-SEA mixing method is adopted, and a box-type beam local vibration model is established in a frequency division mode. The local vibration simulation model divides each plate of the box beam into a deterministic FE subsystem and a stochastic SEA subsystem in different frequency bands according to the bending mode number of each plate of the box beam, particularly realizes the mixed connection of the FE subsystems and the SEA subsystems of different plates in the same model in a medium-frequency domain, avoids the defects of large calculation amount of an FE deterministic method in a high-frequency band and poor precision of the SEA in a low-frequency band, solves the contradiction between calculation efficiency and calculation precision, expands the analysis frequency band of the local vibration of the box beam according to research results, and improves the prediction precision and the calculation efficiency.
Claims (1)
1. A box beam local vibration prediction method based on an FE-SEA hybrid method is characterized by comprising the following steps: dividing the box beam into a plurality of plates, namely a top plate, a bottom plate, a left wing plate, a right wing plate, a left web plate and a right web plate; according to the bending mode number of the local vibration of each plate on the box-shaped beam, establishing a local vibration simulation model of the box-shaped beam under the action of vertical force of a wheel rail in a frequency division manner;
determining the type of a subsystem adopted by each corresponding plate according to the bending mode number of local vibration of each plate on the box-shaped beam under different frequency bands, wherein the subsystem can be a deterministic FE subsystem or a stochastic SEA subsystem; coupling between the subsystems is realized by calculating coupling loss factors and damping loss factor parameters, so that the local vibration simulation model is formed by coupling one or two of the deterministic FE subsystem or the stochastic SEA subsystem;
the method for determining the subsystem type adopted by each plate comprises the following steps: if the bending mode number of the local vibration of the plate is less than or equal to 5, the plate adopts FEM modeling to form the deterministic FE subsystem; if the bending mode number of the local vibration of the plate is more than 5, the plate adopts SEA modeling to form the random SEA subsystem;
the box-shaped beam vibration and sound radiation analysis frequency is 2.5Hz-500Hz, and the box-shaped beam vibration and sound radiation analysis frequency is divided into a low-frequency region, a medium-frequency region and a high-frequency region, wherein the frequency domain of the low-frequency region is 2.5 Hz-160 Hz, the frequency domain of the medium-frequency region is 160 Hz-315 Hz, and the frequency domain of the high-frequency region is 315-500 Hz;
in the low-frequency region, the bending mode number of each plate of the box beam is less than 5, and each plate adopts the deterministic FE subsystem; in the intermediate frequency region, the bending mode number of a top plate, a bottom plate, a left web plate and a right web plate on the box girder is more than 5, and the stochastic SEA subsystem is adopted; the bending mode number of a left wing plate and a right wing plate on the box beam is less than 5, and the deterministic FE subsystem is adopted; the top plate on the box beam is in mixed connection with the left wing plate and the right wing plate on the two sides; in the high-frequency region, the bending mode number of each plate of the box-shaped beam is more than 5, and each plate adopts the stochastic SEA subsystem;
obtaining the energy of the stochastic SEA subsystem through the energy response of the stochastic SEA subsystem, obtaining the displacement response of the deterministic FE subsystem through the displacement spectrum matrix expression of the deterministic FE subsystem, and further obtaining the speed and acceleration physical quantity of each subsystem; on the basis, the propagation sound pressure of any field point is obtained by the sound radiation theory, and the prediction of the local vibration and the structural noise of the box-shaped beam is realized.
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| CN111859726A (en) * | 2020-05-29 | 2020-10-30 | 西安交通大学 | Large-size shell structure intermediate frequency sound radiation forecasting method based on local optimization |
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| 基于FE-SEA混合法的车内结构噪声预测分析;罗文俊;《铁道学报》;20171215;137-145 * |
| 混合FE-SEA模型预测箱梁低频噪声及试验验证;张迅;《振动工程学报》;20160415;237-245 * |
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