CN115329415A - Wind vibration coefficient determination method and system for large-span power transmission tower - Google Patents

Wind vibration coefficient determination method and system for large-span power transmission tower Download PDF

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CN115329415A
CN115329415A CN202110510978.2A CN202110510978A CN115329415A CN 115329415 A CN115329415 A CN 115329415A CN 202110510978 A CN202110510978 A CN 202110510978A CN 115329415 A CN115329415 A CN 115329415A
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order
coefficient
section
transmission tower
segment
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徐鑫乾
邵帅
陈兵
许志勇
杨风利
陈勇
王章轩
许奇
朱姣
沈文韬
张宏杰
黄国
王飞
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State Grid Jiangsu Electric Power Co ltd Construction Branch
China Electric Power Research Institute Co Ltd CEPRI
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State Grid Jiangsu Electric Power Co ltd Construction Branch
China Electric Power Research Institute Co Ltd CEPRI
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract

A method and a system for determining a wind vibration coefficient of a large-span power transmission tower comprise the following steps: substituting the overall structural parameters of the large-span power transmission tower into a first-order natural vibration frequency and first-order natural circle frequency calculation formula of the variable cross-section cantilever beam model to obtain a first-order natural vibration frequency and a first-order natural circle frequency; dividing the power transmission tower into a set number of sections, and substituting technical parameters of each section into a first-order mode shape coefficient formula to calculate to obtain a first-order mode shape coefficient of each section; based on the overall structure parameters and technical parameters, the first-order mode-of-oscillation coefficient and the first-order natural circle frequency, the downwind first-order generalized displacement root-mean-square of each segment is obtained by combining the corresponding wind speed spectrum of each segment under the first-order condition with the downwind first-order generalized displacement root-mean-square calculation formula; and obtaining a first-order wind vibration coefficient of each section by using a first-order wind vibration coefficient calculation formula based on the first-order mode coefficient, the downwind first-order generalized displacement root mean square and the technical parameters. The invention improves the calculation precision and speed of the wind vibration coefficient of the large-span power transmission tower.

Description

Wind vibration coefficient determination method and system for large-span power transmission tower
Technical Field
The invention relates to the field of design of power transmission and transformation project tower structures, in particular to a method and a system for determining a wind vibration coefficient of a long-span power transmission tower.
Background
With the rapid development of social construction and the electric power industry, the construction scale of a large-span power transmission tower is gradually expanding as an important component of power grid infrastructure. There are currently many larger transmission towers with heights above 300m, with wind loads becoming the most important control load for large spanning towers. According to the load specification of a newly-compiled overhead transmission line, tower wind load adopts a cluster mass method to calculate wind vibration coefficients of each wind pressure segmented tower, a Davenport wind speed spectrum is adopted to represent the characteristic of the pulsating wind speed in the calculation process, but the value of the pulsating wind speed spectrum is unchanged along the height, the calculation is carried out based on actual measurement records of strong wind at different places and different heights, the maximum test height considered by the relevant actual measurement records is 244m, most test heights are less than 100m, the application range of the wind speed spectrum is exceeded for a large-span power transmission tower with the height of more than 300m, and the safety and the economy of the final wind vibration coefficient result can be influenced by uniformly applying the same pulsating wind speed spectrum along the height. The tower wind vibration coefficient is an important parameter influencing the maximum wind response calculation of the large-span power transmission tower, and the fluctuation of the fluctuation wind speed spectrum value in the existing specification is not considered, so that the reasonability of the calculation result of the large-span power transmission tower wind vibration coefficient is influenced. Meanwhile, the first-order natural vibration frequency and vibration mode coefficient information of the iron tower structure are needed in the calculation process of the existing cluster mass method, theoretical calculation and finite element simulation analysis are relatively complex, and the method is inconvenient for designers to use.
Disclosure of Invention
Aiming at the problem that the accuracy of a wind vibration coefficient calculation result of a large-span power transmission tower is low in the prior art, the invention provides a method for determining the wind vibration coefficient of the large-span power transmission tower, which comprises the following steps:
acquiring integral structure parameters of the large-span power transmission tower, and inputting the integral structure parameters into a first-order natural vibration frequency and a first-order natural circle frequency calculation formula corresponding to the variable cross-section cantilever beam model for calculation to obtain a first-order natural vibration frequency and a first-order natural circle frequency;
dividing the large-span power transmission tower into a set number of sections by using a group-level mass method, calculating to obtain technical parameters of each section, and calculating to obtain a first-order mode shape coefficient of each section by using a first-order mode shape coefficient formula based on the technical parameters of each section and the overall structure parameters;
based on the overall structure parameters and the technical parameters of each segment, the first-order mode shape coefficient and the first-order natural circle frequency of each segment, the downwind first-order generalized displacement root-mean-square of each segment is obtained by combining the corresponding wind speed spectrum of each segment under the first-order condition with the downwind first-order generalized displacement root-mean-square calculation formula;
calculating to obtain a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root-mean-square of each section and the technical parameters of each section;
wherein, the technical parameters comprise: mass, windward area, turbulence intensity, body type coefficient and wind pressure height variation coefficient;
the overall structure parameters comprise: tower material specification, material, size;
the variable cross-section cantilever beam model is formed by considering the power transmission tower as a high-rise structure and neglecting concentrated mass abstraction at the tower head and the cross arm.
Preferably, the obtaining the downwind first-order generalized displacement root-mean-square of each segment by using the corresponding wind speed spectrum of each segment in the first-order condition in combination with the downwind first-order generalized displacement root-mean-square calculation formula based on the overall structure parameters and the technical parameters of each segment, the first-order mode shape coefficient of each segment, and the first-order natural circular frequency includes:
calculating a wind speed spectrum corresponding to each segment in the first order condition based on the dimensionless frequency and the first order natural vibration frequency of each segment in the first order condition;
calculating a downwind first-order frequency response function by adopting a downwind first-order frequency response function calculation formula based on the first-order natural vibration frequency, the first-order natural circular frequency and the structure first-order damping ratio;
and substituting the wind speed spectrum corresponding to each section under the first-order condition, the integral structure parameters, the technical parameters of each section, the downwind first-order frequency response function and the first-order vibration mode coefficient of each section into the downwind first-order generalized displacement root-mean-square calculation formula to obtain the downwind first-order generalized displacement root-mean-square of each section.
Preferably, the wind speed spectrum corresponding to each segment in the first order is determined according to the following formula:
Figure BDA0003060371650000021
in the formula, S i (f, z) is the wind velocity spectrum of the ith segment in the first order case, x 1i For dimensionless frequencies of the ith segment in the first order, f 1 The first order natural frequency of the transmission tower.
Preferably, the dimensionless frequency x of the ith segment in the first order case 1i Calculated as follows:
Figure BDA0003060371650000022
in the formula, z i Is the centroid height of the ith segment,
Figure BDA0003060371650000023
is the average wind speed at the centroid height of the ith segment.
Preferably, the downwind first order frequency response function is calculated as follows:
Figure BDA0003060371650000031
in the formula, H 1 (if) is the downwind first order frequency response function, f is the frequency, ω 1 Is a first order natural circular frequency, ζ 1 The first-order damping ratio is the structure.
Preferably, the downwind first-order generalized displacement root mean square of each segment is calculated according to the following formula:
Figure BDA0003060371650000032
in the formula, σ q1i Downwind first order generalized displacement root mean square, w for the ith segment 0 Is the basic wind pressure, I 10 Turbulence at a height of 10mDegree, n is the number of iron tower sections,
Figure BDA0003060371650000033
is jth 1 The body type coefficient of the segment is determined,
Figure BDA0003060371650000034
is the jth 1 The height change coefficient of the segmented wind pressure,
Figure BDA0003060371650000035
is the jth 1 The first-order mode-shape coefficient of the segment,
Figure BDA0003060371650000036
is jth 1 The degree of turbulence of the segments is such that,
Figure BDA0003060371650000037
is jth 1 The area of the segments is such that,
Figure BDA0003060371650000038
is jth 2 The body type coefficient of the segment is determined,
Figure BDA0003060371650000039
is the jth 2 The height change coefficient of the segmented wind pressure,
Figure BDA00030603716500000310
is jth 2 The first-order mode-shape coefficient of the segment,
Figure BDA00030603716500000311
is jth 2 The degree of turbulence of the segments is such that,
Figure BDA00030603716500000312
is jth 2 The area of the segments is such that,
Figure BDA00030603716500000313
is the jth 1 And j (h) th 2 Vertical coherence function between segments.
Preferably, the first-order wind vibration coefficient of each segment is calculated according to the following formula:
Figure BDA00030603716500000314
in the formula, beta zi Is the wind vibration coefficient of the ith segment, g is the peak factor, m i 、A i 、μ si 、μ zi 、
Figure BDA00030603716500000315
The mass, the area, the body form coefficient, the wind pressure height change coefficient and the first-order vibration form coefficient of the ith section are respectively.
Preferably, the first-order mode shape coefficient of each segment is calculated as follows:
Figure BDA00030603716500000316
in the formula (I), the compound is shown in the specification,
Figure BDA00030603716500000317
is the first-order mode shape coefficient of the ith section, H is the overall height of the transmission tower, and z i Is the centroid height of the ith segment.
Preferably, the first order natural circle frequency is calculated as follows:
Figure BDA0003060371650000041
in the formula, omega 1 Is the first-order natural circular frequency, H is the overall height of the transmission tower, E is the modulus of the transmission tower, ρ is the structural density of the transmission tower,
Figure BDA0003060371650000042
the average value of the moment of inertia of each main material of the power transmission tower,
Figure BDA0003060371650000043
for each main material of power transmission towerThe average value of the areas is calculated,
Figure BDA0003060371650000044
the average value of the cross section width of the power transmission tower is obtained;
wherein the cross-sectional width average of the transmission tower
Figure BDA0003060371650000045
Determined as follows:
Figure BDA0003060371650000046
in the formula, B is the root opening of the power transmission tower, and B is the head width of the power transmission tower.
Preferably, the first-order natural frequency calculation formula is as follows:
Figure BDA0003060371650000047
in the formula (f) 1 Is the first order natural frequency.
Based on the same inventive concept, the invention also provides a system for determining the wind vibration coefficient of the large-span power transmission tower, which comprises the following steps:
the first-order frequency calculation module is used for acquiring overall structure parameters of the large-span power transmission tower, inputting the overall structure parameters into a first-order natural vibration frequency and a first-order natural vibration circle frequency calculation formula corresponding to the variable cross-section cantilever beam model for calculation, and obtaining the first-order natural vibration frequency and the first-order natural vibration circle frequency;
the segmental parameter calculation module is used for dividing the large-span power transmission tower into a set number of segments by using a group-level mass method, calculating to obtain the technical parameters of each segment, and calculating to obtain a first-order mode shape coefficient of each segment by using a first-order mode shape coefficient formula based on the technical parameters of each segment and the overall structure parameters;
the downwind first-order generalized displacement root-mean-square calculation module is used for obtaining the downwind first-order generalized displacement root-mean-square of each section by combining a corresponding wind speed spectrum of each section under the first-order condition with a downwind first-order generalized displacement root-mean-square calculation formula based on the overall structure parameters and the technical parameters of each section, the first-order mode coefficient of each section and the first-order natural circle frequency;
the first-order wind vibration coefficient calculation module is used for calculating a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root mean square of each section and the technical parameters of each section;
wherein, the technical parameters comprise: mass, windward area, turbulence intensity, body type coefficient and wind pressure height variation coefficient;
the overall structure parameters comprise: tower material specification, material and size;
the variable cross-section cantilever beam model is formed by considering the power transmission tower as a high-rise structure and neglecting concentrated mass abstraction at the tower head and the cross arm.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a method and a system for determining a wind vibration coefficient of a large-span power transmission tower, wherein the method comprises the following steps: acquiring integral structure parameters of the large-span power transmission tower, and inputting the integral structure parameters into a first-order natural vibration frequency and first-order natural circle frequency calculation formula corresponding to the variable cross-section cantilever beam model for calculation to obtain the first-order natural vibration frequency and the first-order natural circle frequency; dividing the large-span power transmission tower into a set number of subsections by using a group-level mass method, calculating to obtain technical parameters of each subsection, and calculating to obtain a first-order mode shape coefficient of each subsection by using a first-order mode shape coefficient formula based on the technical parameters of each subsection and the overall structure parameters; based on the overall structure parameters and the technical parameters of each segment, the first-order mode shape coefficient and the first-order natural circle frequency of each segment, the downwind first-order generalized displacement root-mean-square of each segment is obtained by combining the corresponding wind speed spectrum of each segment under the first-order condition with the downwind first-order generalized displacement root-mean-square calculation formula; calculating to obtain a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root mean square of each section and the technical parameters of each section; wherein, the technical parameters comprise: mass, windward area, turbulence intensity, body type coefficient and wind pressure height variation coefficient; the overall structure parameters comprise: tower material specification, material, size; the variable cross-section cantilever beam model is formed by considering the power transmission tower as a high-rise structure and neglecting concentrated mass abstraction at the tower head and the cross arm. According to the invention, the wind speed spectrum corresponding to each segment in the first order is introduced, the structure of the large-span power transmission tower is simplified by using the variable cross-section cantilever beam model, and the calculation precision and the calculation speed of the wind vibration coefficient of the large-span power transmission tower are improved.
Drawings
FIG. 1 is a flow chart of a method for determining a wind vibration coefficient of a large-span power transmission tower according to the present invention;
FIG. 2 is a schematic sectional view of wind pressure of a large span power transmission tower according to an embodiment of the invention;
FIG. 3 is a schematic diagram of a system for determining a wind vibration coefficient of a large span power transmission tower according to the present invention;
fig. 4 is a schematic sectional view of wind pressure of a 500kV large-span power transmission tower in the embodiment of the invention.
Detailed Description
Aiming at the problems in the prior art, the invention provides the method and the system for determining the wind vibration coefficient by considering the influence of the height change by introducing the fluctuating wind speed spectrum along the height change and according to the downwind response calculation theory of the towering structure, and can effectively improve the wind vibration coefficient calculation applicability of the long-span power transmission tower.
Example 1
The invention provides a method for determining a wind vibration coefficient of a large-span power transmission tower, which comprises the following steps of:
step 1, obtaining integral structure parameters of a large-span power transmission tower, and inputting the integral structure parameters into a first-order natural vibration frequency and a first-order natural vibration circle frequency calculation formula corresponding to a variable cross-section cantilever beam model for calculation to obtain a first-order natural vibration frequency and a first-order natural vibration circle frequency;
step 2, dividing the large-span power transmission tower into a set number of segments by using a group-level mass method, calculating to obtain a technical parameter of each segment, and calculating to obtain a first-order mode shape coefficient of each segment by using a first-order mode shape coefficient formula based on the technical parameter of each segment and the overall structure parameter;
step 3, based on the overall structure parameters and the technical parameters of each segment, the first-order mode shape coefficient of each segment and the first-order natural circle frequency, combining the corresponding wind speed spectrum of each segment under the first-order condition with a downwind first-order generalized displacement root-mean-square calculation formula to obtain the downwind first-order generalized displacement root-mean-square of each segment;
step 4, calculating to obtain a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root mean square of each section and the technical parameters of each section;
wherein, the technical parameters comprise: mass, windward area, turbulence intensity, body type coefficient and wind pressure height variation coefficient;
the overall structure parameters comprise: tower material specification, material, size;
the variable cross-section cantilever beam model is formed by considering the power transmission tower as a high-rise structure and neglecting concentrated mass abstraction at the tower head and the cross arm.
In the step 1, obtaining the overall structural parameters of the large-span power transmission tower and the specification, material and size of the large-span power transmission tower, regarding the power transmission tower as a high-rise structure, regarding the whole tower body as a trapezoid, regarding the root opening B of the power transmission tower as the lower bottom of the trapezoid, regarding the head width B of the power transmission tower as the upper bottom of the trapezoid, regarding the height H of the power transmission tower as the height of the trapezoid, abstracting the large-span power transmission tower into a variable cross-section cantilever beam model after neglecting the concentrated mass at the tower head and the cross arm, and then simply calculating the first-order natural vibration frequency and the first-order natural vibration circle frequency of the large-span power transmission tower by using a calculation formula of the first-order natural vibration frequency and the first-order natural vibration circle frequency corresponding to the variable cross-section cantilever beam model;
the detailed process for simplifying the calculation of the first-order natural vibration frequency of the transmission tower comprises the following steps:
by abstracting the power transmission tower into a variable cross-section flexible cantilever beam model, the transverse or longitudinal natural vibration of the power transmission tower can be determined according to the following formula:
Figure BDA0003060371650000071
wherein w (z) represents a vibration displacement of the power transmission tower, EI (z) represents a cross-sectional bending stiffness of the power transmission tower, ρ a (z) represents a unit mass of the power transmission tower, and a (z) is a cross-sectional area of the power transmission tower;
wherein the boundary conditions are as follows:
Figure BDA0003060371650000072
calculating the first-order natural circular frequency of the power transmission tower by using a first-order natural circular frequency calculation formula of a variable cross-section cantilever beam model according to a vibration theory;
the first-order natural frequency calculation formula of the variable cross-section cantilever beam model is shown as the following formula:
Figure BDA0003060371650000073
in the formula, ω 1 Is the first order natural circular frequency, E is the modulus, ρ is the density, I is the section moment of inertia, A is the cross-sectional area;
considering the structural characteristics and the section characteristics of the power transmission tower, the formula (3) can be further rewritten according to the structural parameters of the power transmission tower;
the cross sectional area of the main material of each tower leg of the power transmission tower is A 0 (z) the moment of inertia of the main material of each tower leg to the own symmetry axis is I 0 (z), the overall cross-sectional area of the transmission tower can be calculated as follows:
A(z)＝4A 0 (z) (4)
wherein A (z) is the total cross-sectional area of the power transmission tower，A 0 (z) is the cross sectional area of the main material of each tower leg of the power transmission tower;
the integral section inertia moment of the power transmission tower is calculated according to the following formula:
Figure BDA0003060371650000074
wherein I (z) is the overall section moment of inertia of the transmission tower, I 0 (z) is the moment of inertia of the main material of each tower leg to the own symmetry axis, and B (z) is the width of the power transmission tower;
wherein the width B (z) of the transmission tower is calculated according to the following formula:
Figure BDA0003060371650000081
in the formula, B is the root opening of the power transmission tower, and B is the head width of the power transmission tower.
Substituting the formula (4) and the formula (5) into the formula (3) to calculate, so as to obtain a first-order natural circular frequency calculation formula of the power transmission tower, as shown in the following formula:
Figure BDA0003060371650000082
respectively calculating the average values of the moment of inertia, the cross sectional area and the cross sectional width of the power transmission tower of the main material of the tower leg of the power transmission tower, respectively replacing the moment of inertia, the cross sectional area and the cross sectional width of the iron tower by the average values, and substituting the average values into an equation (7) to obtain a first-order natural circular frequency calculation equation of the power transmission tower, wherein the equation is shown as the following equation:
Figure BDA0003060371650000083
in the formula (I), the compound is shown in the specification,
Figure BDA0003060371650000084
the average value of the inertia moment of each main material of the power transmission tower,
Figure BDA0003060371650000085
is the average of each main material area of the transmission tower,
Figure BDA0003060371650000086
is the average value of the cross-sectional width of the transmission tower;
wherein the cross-sectional width average of the transmission tower
Figure BDA0003060371650000087
Determined as follows:
Figure BDA0003060371650000088
based on the first-order natural vibration frequency calculation formula of the variable cross-section cantilever beam model, the first-order natural circular frequency omega of the power transmission tower obtained by calculating the formula (8) 1 Substituting the calculation formula into a first-order natural vibration frequency calculation formula of the variable cross-section cantilever beam model to obtain a first-order natural vibration frequency calculation formula of the power transmission tower;
the first-order natural vibration frequency calculation formula of the variable cross-section cantilever beam model is as follows:
Figure BDA0003060371650000089
in the formula, f 1 Is a first order natural frequency;
substituting the equation (8) into the equation (10) to obtain a first-order natural frequency calculation equation of the transmission tower as follows:
Figure BDA0003060371650000091
wherein when
Figure BDA0003060371650000092
And with
Figure BDA0003060371650000093
Compared with the condition that the frequency is negligible, the formula (11) can be further simplified, and the calculation formula of the first-order natural frequency of the transmission tower obtained after the simplification is shown as the following formula:
Figure BDA0003060371650000094
in this embodiment, the value of E may be 2.06 × 10 according to the Young's modulus of the steel material 11 N/m 2 The density rho is set to be 7.85 multiplied by 10 3 kg/m 3 And substituting the values of E and rho into an equation (12) for calculation, as shown in the following equation:
Figure BDA0003060371650000095
in step 2, the large-span transmission tower is divided into n clique quality segments by using the clique quality method, as shown in fig. 2, thereby obtaining the quality m of each segment i Windward area A i Turbulence intensity I zi Figure of body type mu si And the height variation coefficient mu of wind pressure zi Calculating to obtain a first-order mode shape coefficient of each section by using a first-order mode shape coefficient formula based on the centroid height of each section and the overall height of the power transmission tower; wherein m is i 、A i Calculating according to the tower material specification, material and size information of the power transmission tower;
intensity of turbulence I zi Calculated as follows:
I zi ＝(z i /10) -α (14)
in the formula I zi Turbulence intensity for the i-th segment, z i The centroid height of the ith segment is defined, and alpha is a landform type index of the position of the power transmission tower;
the wind pressure height variation coefficient mu zi Calculated as follows:
μ zi ＝(z i /10) 2α (15)
the figure factor mu si Calculated as follows:
μ si ＝1.3×(1+η) (16)
in the formula, eta is a reduction coefficient of a leeward side of the iron tower;
the iron tower leeward side reduction coefficient eta is determined according to a table given in overhead transmission line load specification DL/T5551-2018 and according to the ratio of each wind pressure subsection windward area of the power transmission tower to the tower profile area and the depth-to-width ratio b/a combined linear interpolation (b is the distance between the windward side and the leeward side of the tower, and a is the tower windward side width).
Calculating to obtain a first-order mode shape coefficient of each segment by using a first-order mode shape coefficient approximation formula given in building structure load specification GB50009-2012 based on the overall height of the power transmission tower obtained in the step 1 and the centroid height of each segment calculated in the step 2;
the first-order mode coefficient is calculated as follows:
Figure BDA0003060371650000101
in the formula (I), the compound is shown in the specification,
Figure BDA0003060371650000102
and H is the integral height of the transmission tower.
In the step 3, based on the overall structure parameters and the technical parameters of each segment, the first-order mode shape coefficient and the first-order natural circle frequency of each segment, the downwind first-order generalized displacement root-mean-square calculation formula is combined with the downwind first-order generalized displacement root-mean-square calculation formula by using the corresponding wind speed spectrum of each segment under the first-order condition, so that the downwind first-order generalized displacement root-mean-square of each segment is calculated;
the calculation formula of the downwind first-order generalized displacement root mean square is as follows:
Figure BDA0003060371650000103
in the formula, σ q1 Is downwind first order generalized displacement root mean square, w 0 Is the basic wind pressure, I 10 The turbulence degree at the height of 10m, n is the number of iron tower segments,
Figure BDA0003060371650000104
and
Figure BDA0003060371650000105
Figure BDA0003060371650000106
are respectively j (th) 1 And j 2 The sectional mass, area, shape coefficient, wind pressure height variation coefficient, first-order vibration mode coefficient and turbulence degree,
Figure BDA0003060371650000107
is jth 1 And j 2 Segmented vertical coherence function, H 1 (if) is the downwind first order frequency response function, S v (f, z) is a pulsating wind velocity spectrum;
wherein the downwind first order frequency response function H 1 (if), calculated as:
Figure BDA0003060371650000108
wherein f is the frequency, ζ 1 The first-order damping ratio is the structure of the power transmission tower;
further, formula (19) can also be rewritten as:
Figure BDA0003060371650000111
according to the structure dynamics theory, the integral term related to frequency in equation (18) can be approximated as shown in the following equation:
Figure BDA0003060371650000112
according to an integral term related to frequency in the downwind first-order displacement root mean square after the approximate calculation of the formula (21), introducing a Kaimal wind speed spectrum considering the influence of height change of each section of the power transmission tower;
the corresponding Kaimal wind speed spectrum of each segment is shown as follows:
Figure BDA0003060371650000113
in the formula, S i (f, z) is the Kaimal wind velocity spectrum corresponding to the ith segment, x 1i Dimensionless frequency in the first order case for the ith segment;
wherein the dimensionless frequency x of the ith segment in the first order case 1i Calculated as follows:
Figure BDA0003060371650000114
in the formula, z i Is the centroid height of the ith segment,
Figure BDA0003060371650000115
the average wind speed at the centroid height corresponding to the ith segment;
average wind speed at centroid height corresponding to the ith segment
Figure BDA0003060371650000118
The calculation can be made from the wind speed at 10m height as shown in the following equation:
Figure BDA0003060371650000116
in the formula, v 10 Is the wind speed at a height of 10 m.
The calculation is carried out by substituting the formula (22) into the formula (21), as shown in the following formula:
Figure BDA0003060371650000117
in the formula, R i Resonance factor in the first order for the ith segment;
substituting the centroid height of each section calculated by the kaimal wind speed spectrum in the first order situation into the corresponding wind speed spectrum and the technical parameters of each section calculated in the step 2 in the formula (18) for rewriting, and obtaining the downwind first-order generalized displacement root mean square of each section, wherein the centroid height is shown in the following formula:
Figure BDA0003060371650000121
in the formula, σ q1i The downwind first-order generalized displacement root mean square of the ith segment.
In the step 4, based on the first-order mode shape coefficient, the downwind first-order generalized displacement root mean square of each segment and the technical parameters of each segment, calculating by using a wind vibration coefficient calculation formula corresponding to the first-order mode shape to obtain a first-order wind vibration coefficient of each segment;
according to the theory of the first-order vibration along the structure wind direction, a calculation formula of a wind vibration coefficient corresponding to the first-order vibration mode is shown as the following formula:
Figure BDA0003060371650000122
in the formula, beta zi For the first order wind vibration coefficient of the ith section of the transmission tower,
Figure BDA0003060371650000123
and
Figure BDA0003060371650000124
respectively obtaining the peak value of the average wind power and the first-order wind vibration inertia force at the ith segmental centroid height along the wind direction;
wherein the average wind power at the ith segmental centroid height in the downwind direction
Figure BDA0003060371650000125
The calculation formula of (a) is as follows:
Figure BDA0003060371650000126
in the formula, B i The width of the windward side at the height of the ith segmental centroid;
the first-order wind vibration inertia force peak value at the ith subsection centroid height in the downwind direction
Figure BDA0003060371650000127
The calculation formula of (a) is as follows:
Figure BDA0003060371650000128
wherein g is the crest factor, ω 1 Is the first-order natural vibration circular frequency, sigma, of downwind direction of the power transmission tower q1 Is the downwind first-order generalized displacement root-mean-square.
Substituting the formula (28) and the formula (29) into the formula (27) for simplification, and determining a first-order wind vibration coefficient calculation formula for each segment as shown in the following formula:
Figure BDA0003060371650000131
substituting the technical parameters of each segment calculated in the step 2 and the downwind first-order generalized displacement root-mean-square corresponding to each segment calculated in the step 3 into a formula (30) to calculate a first-order wind vibration coefficient of each segment, which is shown as the following formula;
Figure BDA0003060371650000132
Figure BDA0003060371650000133
Figure BDA0003060371650000134
the invention provides a wind vibration coefficient determining method aiming at a large-span power transmission tower on the basis of considering the influence of the height change of a pulsating wind spectrum, the wind vibration coefficient determining method can simplify the flow of acquiring the structural vibration characteristic information of the iron tower, and improve the accuracy and convenience of the wind-resistant design of the large-span power transmission tower.
Example 2
Based on the unified inventive concept, the present invention further provides a system for determining a wind vibration coefficient of a large-span power transmission tower, as shown in fig. 3, including:
the first-order frequency calculation module is used for acquiring overall structure parameters of the large-span power transmission tower, inputting the overall structure parameters into a first-order natural vibration frequency and a first-order natural vibration circle frequency calculation formula corresponding to the variable cross-section cantilever beam model for calculation, and obtaining the first-order natural vibration frequency and the first-order natural vibration circle frequency;
the segmental parameter calculation module is used for dividing the large-span power transmission tower into a set number of segments by using a group-level mass method, calculating to obtain the technical parameters of each segment, and calculating to obtain a first-order mode shape coefficient of each segment by using a first-order mode shape coefficient formula based on the technical parameters of each segment and the overall structure parameters;
the downwind first-order generalized displacement root-mean-square calculation module is used for obtaining the downwind first-order generalized displacement root-mean-square of each section by combining a corresponding wind speed spectrum of each section under the first-order condition with a downwind first-order generalized displacement root-mean-square calculation formula based on the overall structure parameters and the technical parameters of each section, the first-order mode coefficient of each section and the first-order natural circle frequency;
the first-order wind vibration coefficient calculation module is used for calculating a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root mean square of each section and the technical parameters of each section;
wherein, the technical parameters comprise: mass, windward area, turbulence intensity, body type coefficient and wind pressure height variation coefficient;
the overall structure parameters comprise: tower material specification, material, size;
the variable cross-section cantilever beam model is formed by considering the power transmission tower as a high-rise structure and neglecting concentrated mass abstraction at the tower head and the cross arm.
The first-order frequency calculation module is used for obtaining the overall structural parameters of the large-span power transmission tower and the specification, material and size of the large-span power transmission tower, then regarding the power transmission tower as a high-rise structure, regarding the whole tower body as a trapezoid, regarding the root B of the power transmission tower as the lower bottom of the trapezoid, regarding the head width B of the power transmission tower as the upper bottom of the trapezoid, regarding the height H of the power transmission tower as the height of the trapezoid, abstracting the large-span power transmission tower into a variable-section cantilever beam model after neglecting the mass concentration at the tower head and the cross arm, and then simply calculating the first-order natural vibration frequency and the first-order natural vibration circle frequency of the large-span power transmission tower by using the calculation formula of the first-order natural vibration frequency and the first-order natural vibration circle frequency corresponding to the variable-section cantilever beam model;
by abstracting the power transmission tower into a variable cross-section flexible cantilever beam model, the transverse or longitudinal natural vibration of the power transmission tower can be determined according to the following formula:
Figure BDA0003060371650000141
wherein w (z) represents a vibration displacement of the power transmission tower, EI (z) represents a section flexural rigidity of the power transmission tower, ρ a (z) represents a unit mass of the power transmission tower, and a (z) is a cross-sectional area of the power transmission tower;
wherein the boundary conditions are as follows:
Figure BDA0003060371650000142
calculating the first-order natural circular frequency of the power transmission tower by using a first-order natural circular frequency calculation formula of a variable cross-section cantilever beam model according to a vibration theory;
the first-order natural frequency calculation formula of the variable cross-section cantilever beam model is shown as the following formula:
Figure BDA0003060371650000151
in the formula, ω 1 Is the first order natural circular frequency, E is the modulus, ρ is the density, I is the section moment of inertia, A is the cross-sectional area;
considering the structural characteristics and the section characteristics of the power transmission tower, the formula (3) can be further rewritten according to the structural parameters of the power transmission tower;
the cross sectional area of a main material of each tower leg of the power transmission tower is set as A 0 (z) the moment of inertia of each tower leg main material to the self symmetry axis is I 0 (z), the overall cross-sectional area of the transmission tower can be calculated as follows:
A(z)＝4A 0 (z) (4)
wherein A (z) is the total cross-sectional area of the power transmission tower, A 0 (z) is the cross sectional area of the main material of each tower leg of the power transmission tower;
the integral section inertia moment of the power transmission tower is calculated according to the following formula:
Figure BDA0003060371650000152
wherein I (z) is the overall section moment of inertia of the transmission tower, I 0 (z) is the moment of inertia of the main material of each tower leg to the own symmetry axis, and B (z) is the width of the power transmission tower;
wherein the width B (z) of the transmission tower is calculated as follows:
Figure BDA0003060371650000153
in the formula, B is the root opening of the power transmission tower, and B is the head width of the power transmission tower.
Substituting the formula (4) and the formula (5) into the formula (3) to calculate, so as to obtain a first-order natural circular frequency calculation formula of the power transmission tower, as shown in the following formula:
Figure BDA0003060371650000154
respectively calculating the average values of the moment of inertia, the cross sectional area and the cross sectional width of the power transmission tower of the main material of the tower leg of the power transmission tower, respectively replacing the moment of inertia, the cross sectional area and the cross sectional width of the iron tower by the average values, and substituting the average values into an equation (7) to obtain a first-order natural circular frequency calculation equation of the power transmission tower, wherein the equation is shown as the following equation:
Figure BDA0003060371650000155
in the formula (I), the compound is shown in the specification,
Figure BDA0003060371650000161
the average value of the inertia moment of each main material of the transmission tower,
Figure BDA0003060371650000162
the average value of the area of each main material of the transmission tower,
Figure BDA0003060371650000163
the average value of the cross section width of the power transmission tower is obtained;
wherein the cross-sectional width average of the transmission tower
Figure BDA0003060371650000164
Determined as follows:
Figure BDA0003060371650000165
based on the variable cross sectionThe first-order natural vibration frequency calculation formula of the cantilever beam model can be used for calculating the first-order natural circular frequency omega of the power transmission tower obtained by the calculation of the formula (8) 1 Substituting the calculation formula into a first-order natural vibration frequency calculation formula of the variable cross-section cantilever beam model to obtain a first-order natural vibration frequency calculation formula of the power transmission tower;
the first-order natural vibration frequency calculation formula of the variable cross-section cantilever beam model is as follows:
Figure BDA0003060371650000166
in the formula (f) 1 Is a first order natural frequency;
substituting the equation (8) into equation (10) to obtain a calculation equation of the first-order natural frequency of the transmission tower as follows:
Figure BDA0003060371650000167
wherein when
Figure BDA0003060371650000168
And with
Figure BDA0003060371650000169
Compared with the condition that the frequency is negligible, the formula (11) can be further simplified, and the calculation formula of the first-order natural frequency of the transmission tower obtained after the simplification is shown as the following formula:
Figure BDA00030603716500001610
in this embodiment, E can be set to 2.06 × 10 according to the Young's modulus of steel 11 N/m 2 The density rho is set to be 7.85 multiplied by 10 3 kg/m 3 Substituting the values of E and rho into the formula (12) for calculation, as shown in the following formula:
Figure BDA00030603716500001611
the segmentation parameter calculation module comprises: a subsection technical parameter calculation submodule and a first-order vibration mode coefficient calculation submodule;
the segmentation technical parameter calculation submodule is used for dividing the large-span power transmission tower into n cluster quality segments by using a cluster-level quality method, as shown in FIG. 2, so as to obtain the quality m of each segment i Windward area A i Turbulence intensity I zi Figure of body type mu si And the height variation coefficient mu of wind pressure zi (ii) a Wherein m is i 、A i Calculating according to the tower material specification, material and size information of the power transmission tower;
intensity of turbulence I zi Calculated as follows:
I zi ＝(z i /10) -α (14)
in the formula I zi Turbulence intensity for the i-th segment, z i The centroid height of the ith segment is defined, and alpha is a landform type index of the position of the power transmission tower;
the wind pressure height variation coefficient mu zi Calculated as follows:
μ zi ＝(z i /10) 2α (15)
the body type coefficient mu si Calculated as follows:
μ si ＝1.3×(1+η) (16)
in the formula, eta is a reduction coefficient of a leeward side of the iron tower;
the iron tower leeward side reduction coefficient eta is determined according to a table given in overhead transmission line load specification DL/T5551-2018 and according to the ratio of each wind pressure subsection windward area of the power transmission tower to the tower profile area and the depth-to-width ratio b/a combined linear interpolation (b is the distance between the windward side and the leeward side of the tower, and a is the tower windward side width).
The first-order mode-shape coefficient calculation submodule is used for calculating and obtaining a first-order mode-shape coefficient of each section by using a first-order mode-shape coefficient formula based on the centroid height of each section and the overall height of the power transmission tower;
based on the overall height of the power transmission tower and the centroid height of each section, calculating by using a first-order mode-shape coefficient approximation formula given in building structure load specification GB50009-2012 to obtain a first-order mode-shape coefficient of each section;
the first-order mode coefficient calculation formula is as follows:
Figure BDA0003060371650000171
in the formula (I), the compound is shown in the specification,
Figure BDA0003060371650000172
and H is the integral height of the power transmission tower.
The downwind first-order generalized displacement root-mean-square calculation module is used for obtaining the downwind first-order generalized displacement root-mean-square of each section by combining a downwind first-order generalized displacement root-mean-square calculation formula with a corresponding wind speed spectrum of each section under the first-order condition based on the overall structure parameters and the technical parameters of each section, the first-order mode shape coefficient of each section and the first-order natural circle frequency;
the calculation formula of the downwind first-order generalized displacement root mean square is as follows:
Figure BDA0003060371650000181
in the formula, σ q1 Is downwind first-order generalized displacement root mean square, w 0 Basic wind pressure, I 10 The turbulence degree at the height of 10m, n is the number of iron tower segments,
Figure BDA0003060371650000182
and
Figure BDA0003060371650000183
Figure BDA0003060371650000184
are respectively j (th) 1 And j 2 The sectional mass, area, shape coefficient, wind pressure height variation coefficient, first-order vibration mode coefficient and turbulence degree,
Figure BDA0003060371650000185
is jth 1 And j 2 Segmented vertical coherence function, H 1 (if) is the downwind first order frequency response function, S v (f, z) is a fluctuating wind velocity spectrum;
wherein the downwind first order frequency response function H 1 (if), calculated as:
Figure BDA0003060371650000186
wherein f is frequency, ζ 1 The first-order damping ratio is the structure of the power transmission tower;
further, formula (19) can also be rewritten as:
Figure BDA0003060371650000187
according to the structure dynamics theory, the integral term with respect to frequency in equation (18) can be approximated as shown in the following equation:
Figure BDA0003060371650000188
according to an integral term related to frequency in the downwind first-order displacement root mean square after approximate calculation of the formula (21), introducing a Kaimal wind speed spectrum considering the influence of height change of each section of the power transmission tower;
the centroid height of each segment corresponds to the Kaimal wind speed spectrum at first order as shown in the following equation:
Figure BDA0003060371650000189
in the formula, S i (f, z) corresponds to the ith segmentKaimal wind velocity spectrum of (x) 1i Dimensionless frequency in the first order case for the ith segment;
wherein the dimensionless frequency x of the ith segment in the first order case 1i Calculated as follows:
Figure BDA0003060371650000191
in the formula, z i Is the centroid height of the ith segment,
Figure BDA0003060371650000192
the average wind speed at the centroid height corresponding to the ith segment;
average wind speed at centroid height corresponding to the ith segment
Figure BDA0003060371650000193
The calculation can be made from the wind speed at 10m height as shown in the following equation:
Figure BDA0003060371650000194
in the formula, v 10 Is the wind speed at a height of 10 m.
The calculation is carried out by substituting the formula (22) into the formula (21), as shown in the following formula:
Figure BDA0003060371650000195
in the formula, R i Resonance factor in the first order for the ith segment;
and (3) rewriting the formula (25) and the technical parameters of each segment, which are obtained by calculating the centroid height of each segment by using the kaimal wind speed spectrum in the first order, in the corresponding wind speed spectrum and segment parameter calculation module, in place of the formula (18), so as to obtain the downwind first-order generalized displacement root-mean-square of each segment, which is shown as the following formula:
Figure BDA0003060371650000196
in the formula, σ q1i The downwind first-order generalized displacement root mean square of the ith segment.
The first-order wind vibration coefficient calculation module is used for calculating a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root mean square of each section and the technical parameters of each section;
according to the theory of the structure downwind direction first-order vibration, a calculation formula of a wind vibration coefficient corresponding to the first-order vibration mode is shown as the following formula:
Figure BDA0003060371650000201
in the formula, beta zi For the first order wind vibration coefficient of the ith section of the transmission tower,
Figure BDA0003060371650000202
and
Figure BDA0003060371650000203
respectively obtaining the peak value of the average wind power and the first-order wind vibration inertia force at the ith segmental centroid height along the wind direction;
wherein the average wind power at the ith segmental centroid height in the downwind direction
Figure BDA0003060371650000204
The calculation formula of (a) is as follows:
Figure BDA0003060371650000205
in the formula, B i The width of the windward side at the height of the ith segmental centroid;
the first-order wind vibration inertia force peak value at the ith subsection centroid height in the downwind direction
Figure BDA0003060371650000206
The calculation formula of (c) is as follows:
Figure BDA0003060371650000207
wherein g is the crest factor, ω 1 Is the first-order natural vibration circular frequency, sigma, of the downwind direction of the power transmission tower q1 Is the downwind first-order generalized displacement root mean square.
Substituting the formula (28) and the formula (29) into the formula (27) for simplification, and determining a first-order wind vibration coefficient calculation formula for each segment as shown in the following formula:
Figure BDA0003060371650000208
substituting the technical parameters of each segment calculated by the segment parameter calculation module and the downwind first-order generalized displacement root-mean-square corresponding to each segment calculated by the downwind first-order generalized displacement root-mean-square calculation module into a formula (30) to calculate a first-order wind vibration coefficient of each segment, as shown in the following formula:
Figure BDA0003060371650000209
Figure BDA00030603716500002010
Figure BDA00030603716500002011
the wind vibration coefficient is an important parameter influencing the maximum wind response calculation of the large-span power transmission tower, and the fluctuation of the fluctuation wind speed spectrum value in the existing specification is not considered along the height, so that the reasonability of the calculation result of the wind vibration coefficient of the large-span power transmission tower is influenced. The present invention therefore provides a system for determining the wind vibration coefficient of a large span transmission tower, which addresses the above problems. A calculation method is simplified by introducing a fluctuating wind speed spectrum along height change and the natural vibration characteristic of the iron tower structure, and a wind vibration coefficient determination system considering the influence of height change is provided according to the downwind response calculation theory of the towering structure, so that the calculation precision and the calculation applicability of the heating wind vibration coefficient of the long-span power transmission tower can be effectively improved.
Example 3
According to the method for determining the wind vibration coefficient of the large-span power transmission tower provided by the invention, taking a certain 500kV power transmission line large-span power transmission tower as an example, the method for determining the wind vibration coefficient of each section of the 500kV power transmission line large-span power transmission tower comprises the following steps:
(1) Acquiring integral structural parameters of the large-span power transmission tower and specifications, materials and dimensions of the large-span power transmission tower, regarding the power transmission tower as a high-rise structure, neglecting concentrated mass at a tower head and a cross arm, and abstracting the power transmission tower into a variable cross-section cantilever beam model; therefore, the whole tower body can be regarded as a trapezoid, the root opening B of the power transmission tower can be equivalent to the lower bottom of the trapezoid, the head width B of the power transmission tower can be equivalent to the upper bottom of the trapezoid, and the height H of the power transmission tower can be equivalent to the height of the trapezoid;
in this example, the root opening B =12.7m, the head width B =1.8m, and the transmission tower height H =72.5m, are calculated by substituting the cross-sectional width average calculation formula for the transmission tower, as shown in the following equation:
Figure BDA0003060371650000211
in the formula (I), the compound is shown in the specification,
Figure BDA0003060371650000212
the average value of the width of the cross section of the power transmission tower is B, the root of the power transmission tower is opened, and B is the width of the head of the power transmission tower;
the average value of the height of the power transmission tower calculated by the formula
Figure BDA0003060371650000213
Into transmission of electricityIn the calculation formula of the first-order natural vibration frequency of the tower, the modulus is taken to be 2.06 multiplied by 10 according to the structural steel of the power transmission tower 11 N/m 2 The density is 7.85 multiplied by 10 3 kg/m 3 The calculation is carried out as shown in the following formula:
Figure BDA0003060371650000214
in the formula (f) 1 The first-order natural vibration frequency, the modulus, the density and the overall height of the power transmission tower.
(2) Dividing the large-span power transmission tower into 22 cluster quality segments by using a cluster-level quality method, as shown in FIG. 4, and calculating the quality m of each segment i Windward area A i Turbulence intensity I zi Figure of body type mu si And the height variation coefficient mu of wind pressure zi And calculating to obtain the first-order mode shape coefficient of each segment by using a first-order mode shape coefficient formula, wherein m i 、A i Counting according to the specification and material information of the power transmission tower;
intensity of turbulence I zi Calculated as follows:
I zi ＝(z i /10) -α
in the formula, z i Is the height of the centroid, alpha is the landform type index;
the wind pressure height variation coefficient mu zi Calculated as follows:
μ zi ＝(z i /10) 2α
the figure factor mu si Calculated as follows:
μ si ＝1.3×(1+η)
in the formula, eta is a reduction coefficient of a leeward side of the iron tower;
wherein eta is a tower leeward side load reduction coefficient table according to the overhead transmission line load specification DL/T5551-2018, and the windward area (A) is segmented according to each wind pressure as shown in table 1 i ) And tower profile area (A) si ) The ratio and the aspect ratio b/a are determined by linear interpolation (b is the windward side and the wind side of the tower)The distance between the leeward sides, a being the windward side width of the tower).
TABLE 1
Figure BDA0003060371650000221
In the present embodiment, the mass m of each segment obtained based on the above calculation i Windward area A i Turbulence intensity I zi Figure of body type mu si And the height variation coefficient mu of wind pressure zi Height z of centroid i The results are shown in Table 2.
TABLE 2
Figure BDA0003060371650000222
Figure BDA0003060371650000231
In the present embodiment, the first order mode shape coefficient at the height of each segment centroid
Figure BDA0003060371650000232
The calculation is carried out according to a first-order mode shape coefficient approximate formula given in building structure load specification GB50009-2012, and is shown as the following formula:
Figure BDA0003060371650000233
in the formula (I), the compound is shown in the specification,
Figure BDA0003060371650000234
first order mode shape coefficient of i-th segment, z i Is the centroid height of the ith segment;
the calculated first-order mode shape coefficient calculation results of the respective segments are summarized as shown in table 3.
TABLE 3
Figure BDA0003060371650000235
Figure BDA0003060371650000241
(3) According to the overall structure parameters, the technical parameters of each section, the first-order mode-shape coefficient of each section and the first-order natural circle frequency, calculating the downwind first-order generalized displacement root-mean-square of each section by utilizing the corresponding wind speed spectrum of each section under the first-order condition and combining the downwind first-order generalized displacement root-mean-square calculation formula;
the centroid height of each section of the large-span power transmission tower corresponds to a Kaimal wind speed spectrum in the first order, as shown in the following formula:
Figure BDA0003060371650000242
in the formula, S i (f, z) is the Kaimal wind velocity spectrum corresponding to the ith segment, x 1i Dimensionless frequency in the first order case for the ith segment;
dimensionless frequency of the case;
wherein the dimensionless frequency x of the ith segment in the first order case 1i Calculated as follows:
Figure BDA0003060371650000243
in the formula, z i Is the centroid height of the ith segment,
Figure BDA0003060371650000244
the average wind speed at the centroid height corresponding to the ith segment;
average wind speed at the centroid height corresponding to the ith segment
Figure BDA0003060371650000245
The calculation can be made from the wind speed at 10m height as shown in the following equation:
Figure BDA0003060371650000246
in the formula, v 10 Is the wind speed at a height of 10 m.
Substituting the wind speed spectrum corresponding to the centroid height of each section of the long-span power transmission tower under the first-order condition and the technical parameters of each section into a downwind first-order generalized displacement root-mean-square calculation formula, and simplifying the downwind first-order generalized displacement root-mean-square calculation formula to obtain the downwind first-order generalized displacement root-mean-square calculation formula of each section, wherein the formula is shown as follows:
Figure BDA0003060371650000251
in the formula, σ q1i Downwind first order generalized displacement root mean square, w, for the ith segment 0 Is the basic wind pressure, I 10 The turbulence degree at the height of 10m, n is the number of iron tower segments,
Figure BDA0003060371650000252
is jth 1 The body type coefficient of the segment is determined,
Figure BDA0003060371650000253
is jth 1 The height change coefficient of the segmented wind pressure,
Figure BDA0003060371650000254
is jth 1 The first-order mode-shape coefficient of the segment,
Figure BDA0003060371650000255
is jth 1 The degree of turbulence of the segments is such that,
Figure BDA0003060371650000256
is jth 1 The area of the segments is such that,
Figure BDA0003060371650000257
is jth 2 The body type coefficient of the segment is determined,
Figure BDA0003060371650000258
is jth 2 The height change coefficient of the segmented wind pressure,
Figure BDA0003060371650000259
is the jth 2 The first-order mode-shape coefficient of the segment,
Figure BDA00030603716500002510
is jth 2 The degree of turbulence of the segments is such that,
Figure BDA00030603716500002511
is jth 2 The area of the segments is such that,
Figure BDA00030603716500002512
is jth 1 And j (h) th 2 Vertical coherence function between segments.
(4) In this embodiment, the wind vibration coefficient corresponding to the first-order mode shape of each segment of the large-span power transmission tower may be calculated according to a first-order mode shape coefficient calculation formula of each segment that varies along the height, as shown in the following equation:
Figure BDA00030603716500002513
Figure BDA00030603716500002514
Figure BDA00030603716500002515
in the formula, beta zi Is the first-order mode coefficient of the ith segment, g is the crest factor, I 10 Turbulence at a height of 10m, R i Resonance factor, m, in the first order for the ith segment i 、A i 、μ si 、μ zi 、
Figure BDA00030603716500002516
I zi Respectively the mass, area, shape coefficient, wind pressure height variation coefficient, first-order vibration shape coefficient, turbulence degree, zeta 1 The first-order damping ratio is the structure of the power transmission tower;
in this embodiment, the wind speed v at a height of 10m can be taken 10 Taking 27m/s; the power transmission tower in the embodiment corresponds to a class B landform, so that the landform coefficient alpha is 0.15 and the height z is 0.001 meter; the power transmission iron tower is of a steel structure, and the first-order damping ratio zeta of the structure 1 The value was 0.02.
All the relevant parameters are brought into a first-order mode-vibration coefficient calculation formula of each section which changes along the height, so that a first-order wind vibration coefficient corresponding to each section can be calculated, and calculation results are summarized as shown in table 4.
TABLE 4
Segmentation 1 2 3 4 5 6 7 8 9
β zi 4.24 4.19 3.88 3.87 2.68 2.31 2.40 2.39 2.03
Segmentation 10 11 12 13 14 15 16 17 18
β zi 2.12 2.35 2.30 1.92 2.08 2.08 1.95 1.97 1.69
Segmentation 19 20 21 22
β zi 1.70 1.51 1.38 1.16
In this embodiment, in the process of calculating the wind vibration coefficient of the large-span power transmission tower, under the condition that all conditions and structural coefficients are the same, the calculation is performed by using the Davenport wind velocity spectrum which is not changed along the height, and the calculated wind vibration coefficients of the segments are shown in table 5.
TABLE 5
Segmentation 1 2 3 4 5 6 7 8 9
β zi 2.98 2.94 2.68 2.60 2.02 1.79 1.84 1.83 1.60
Segmentation 10 11 12 13 14 15 16 17 18
β zi 1.65 1.77 1.73 1.51 1.59 1.58 1.50 1.49 1.34
Segmentation 19 20 21 22
β zi 1.34 1.23 1.16 1.06
Comparing the results of wind vibration coefficient calculation in tables 4 and 5, it can be found that the calculated result based on the Davenport wind speed spectrum is close to 50% smaller in cross-arm part than the calculated result obtained by the method provided by the present invention, and the tower body part is about 30% smaller, and the smaller rate is reduced to about 20% as the height of the power transmission tower section is reduced. The comparison shows that the wind vibration coefficient determination method based on the Davenport wind speed spectrum in the prior art may underestimate the wind load of the large-span power transmission tower, and further may affect the structural safety of the large-span power transmission tower.
It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The present invention is not limited to the above embodiments, and any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are included in the scope of the claims of the present invention which are filed as the application.

Claims (11)

1. A method for determining a wind vibration coefficient of a long-span power transmission tower is characterized by comprising the following steps:
acquiring integral structure parameters of the large-span power transmission tower, and inputting the integral structure parameters into a first-order natural vibration frequency and first-order natural circle frequency calculation formula corresponding to the variable cross-section cantilever beam model for calculation to obtain the first-order natural vibration frequency and the first-order natural circle frequency;
dividing the large-span power transmission tower into a set number of sections by using a group-level mass method, calculating to obtain technical parameters of each section, and calculating to obtain a first-order mode shape coefficient of each section by using a first-order mode shape coefficient formula based on the technical parameters of each section and the overall structure parameters;
based on the overall structure parameters, the technical parameters of each section, the first-order mode shape coefficient of each section and the first-order natural circle frequency, the downwind first-order generalized displacement root-mean-square of each section is obtained by combining the corresponding wind speed spectrum of each section under the first-order condition with the downwind first-order generalized displacement root-mean-square calculation formula;
calculating to obtain a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root-mean-square of each section and the technical parameters of each section;
wherein, the technical parameters comprise: mass, windward area, turbulence intensity, body type coefficient and wind pressure height variation coefficient;
the overall structure parameters comprise: tower material specification, material, size;
the variable cross-section cantilever beam model is formed by considering the power transmission tower as a high-rise structure and neglecting concentrated mass abstraction at the tower head and the cross arm.
2. The method according to claim 1, wherein the obtaining the downwind first-order generalized displacement root-mean-square of each segment by using the corresponding wind speed spectrum of each segment in the first-order case in combination with the downwind first-order generalized displacement root-mean-square calculation formula based on the overall structure parameters and the technical parameters of each segment, the first-order mode shape coefficient of each segment, and the first-order natural circular frequency comprises:
calculating a wind speed spectrum corresponding to each segment in the first order condition based on the dimensionless frequency and the first order natural vibration frequency of each segment in the first order condition;
calculating a downwind first-order frequency response function by adopting a downwind first-order frequency response function calculation formula based on the first-order natural vibration frequency, the first-order natural circular frequency and the structure first-order damping ratio;
and substituting the wind speed spectrum corresponding to each section in the first order, the integral structure parameters, the technical parameters of each section, the downwind first-order frequency response function and the first-order vibration mode coefficient of each section into the downwind first-order generalized displacement root-mean-square calculation formula to obtain the downwind first-order generalized displacement root-mean-square of each section.
3. The method of claim 2, wherein the wind speed spectrum corresponding to each segment in the first order is determined according to the following formula:
Figure FDA0003060371640000021
in the formula, S i (f, z) is the wind velocity spectrum of the ith segment in the first order case, x 1i For dimensionless frequencies of the ith segment in the first order, f 1 The first order natural frequency of the transmission tower.
4. Method according to claim 3, characterized in that the dimensionless frequency x of the ith segment in the first order case 1i Calculated as follows:
Figure FDA0003060371640000022
in the formula, z i Is the centroid height of the ith segment,
Figure FDA0003060371640000023
is the average wind speed at the centroid height of the ith segment.
5. The method of claim 3, wherein the downwind first order frequency response function is calculated as follows:
Figure FDA0003060371640000024
in the formula, H 1 (if) is the downwind first order frequency response function, f is the frequency, ω 1 Is a first order natural circular frequency, ζ 1 The first-order damping ratio is the structure.
6. The method of claim 5, wherein the downwind first order generalized displacement root mean square of each segment is calculated as follows:
Figure FDA0003060371640000025
in the formula, σ q1i Downwind first order generalized displacement root mean square, w for the ith segment 0 Is the basic wind pressure, I 10 Is the turbulence degree at the height of 10m, n is the number of the iron tower sections,
Figure FDA0003060371640000026
is jth 1 The body type coefficient of the segment is determined,
Figure FDA0003060371640000027
is jth 1 The height change coefficient of the segmented wind pressure,
Figure FDA0003060371640000031
is jth 1 The first-order mode-shape coefficient of the segment,
Figure FDA0003060371640000032
is jth 1 The degree of turbulence of the segments is such that,
Figure FDA0003060371640000033
is jth 1 Segmented facesThe volume of the mixture is accumulated,
Figure FDA0003060371640000034
is jth 2 The body type coefficient of the segment is determined,
Figure FDA0003060371640000035
is jth 2 The height change coefficient of the segmented wind pressure,
Figure FDA0003060371640000036
is the jth 2 The first-order mode-shape coefficient of the segment,
Figure FDA0003060371640000037
is jth 2 The degree of turbulence of the segments is such that,
Figure FDA0003060371640000038
is jth 2 The area of the segments is such that,
Figure FDA0003060371640000039
is jth 1 And j (h) th 2 Vertical coherence function between segments.
7. The method of claim 6, wherein the first-order wind vibration coefficient of each segment is calculated according to the following formula:
Figure FDA00030603716400000310
in the formula, beta zi Is the wind vibration coefficient of the ith segment, g is the peak factor, m i 、A i 、μ si 、μ zi 、
Figure FDA00030603716400000311
The mass, the area, the body form coefficient, the wind pressure height change coefficient and the first-order vibration form coefficient of the ith section are respectively.
8. The method of claim 1, wherein the first order mode shape coefficient of each segment is calculated as follows:
Figure FDA00030603716400000312
in the formula (I), the compound is shown in the specification,
Figure FDA00030603716400000313
the first-order mode shape coefficient of the ith section, H is the overall height of the power transmission tower, and z i Is the centroid height of the ith segment.
9. The method of claim 1, wherein the first order natural circle frequency is calculated as follows:
Figure FDA00030603716400000314
in the formula, ω 1 Is the first-order natural circular frequency, H is the overall height of the transmission tower, E is the modulus of the transmission tower, ρ is the structural density of the transmission tower,
Figure FDA00030603716400000315
the average value of the moment of inertia of each main material of the power transmission tower,
Figure FDA00030603716400000316
is the average of each main material area of the transmission tower,
Figure FDA00030603716400000317
the average value of the cross section width of the power transmission tower is obtained;
wherein the cross-sectional width average of the transmission tower
Figure FDA00030603716400000318
Is as followsDetermining:
Figure FDA00030603716400000319
in the formula, B is the root opening of the power transmission tower, and B is the head width of the power transmission tower.
10. The method of claim 8, wherein the first order natural frequency is calculated as follows:
Figure FDA0003060371640000041
in the formula (f) 1 Is the first order natural frequency.
11. A wind vibration coefficient determination system for a large span power transmission tower, comprising:
the first-order frequency calculation module is used for acquiring overall structure parameters of the large-span power transmission tower, inputting the overall structure parameters into a first-order natural vibration frequency and a first-order natural vibration circle frequency calculation formula corresponding to the variable cross-section cantilever beam model for calculation, and obtaining the first-order natural vibration frequency and the first-order natural vibration circle frequency;
the segmental parameter calculation module is used for dividing the large-span power transmission tower into a set number of segments by using a group-level mass method, calculating to obtain the technical parameters of each segment, and calculating to obtain a first-order mode shape coefficient of each segment by using a first-order mode shape coefficient formula based on the technical parameters of each segment and the overall structure parameters;
the downwind first-order generalized displacement root-mean-square calculation module is used for obtaining the downwind first-order generalized displacement root-mean-square of each section by combining a corresponding wind speed spectrum of each section under the first-order condition with a downwind first-order generalized displacement root-mean-square calculation formula based on the overall structure parameters and the technical parameters of each section, the first-order mode coefficient of each section and the first-order natural circle frequency;
the first-order wind vibration coefficient calculation module is used for calculating a first-order wind vibration coefficient of each section by using a wind vibration coefficient calculation formula corresponding to the first-order vibration mode based on the first-order vibration mode coefficient, the downwind first-order generalized displacement root mean square of each section and the technical parameters of each section;
wherein, the technical parameters comprise: mass, windward area, turbulence intensity, body type coefficient and wind pressure height variation coefficient;
the overall structure parameters comprise: tower material specification, material, size;
the variable cross-section cantilever beam model is formed by considering the power transmission tower as a high-rise structure and neglecting concentrated mass abstraction at the tower head and the cross arm.
CN202110510978.2A 2021-05-11 2021-05-11 Wind vibration coefficient determination method and system for large-span power transmission tower Pending CN115329415A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116150842A (en) * 2022-12-30 2023-05-23 重庆科技学院 Method for calculating design wind load of bent torsion column spiral Liang Jingguan tower based on IWL method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116150842A (en) * 2022-12-30 2023-05-23 重庆科技学院 Method for calculating design wind load of bent torsion column spiral Liang Jingguan tower based on IWL method
CN116150842B (en) * 2022-12-30 2023-09-22 重庆科技学院 Method for calculating design wind load of bent torsion column spiral Liang Jingguan tower based on IWL method

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