A vibration correction method for wind-induced vibration response of aeroelastic model of transmission tower

Abstract

The present invention discloses a vibration type correction method for the wind vibration response of an aeroelastic model of a transmission tower. The method includes establishing a finite element model, obtaining the vibration type matrix of the finite element model; calculating the theoretical mass distribution of the aeroelastic model, making the aeroelastic model and conducting a wind tunnel test, obtaining the actual mass distribution of the aeroelastic model and the wind vibration response time history; obtaining the vibration type matrix of the aeroelastic model and the modal response of each order of the aeroelastic model according to the wind vibration response of the aeroelastic model; obtaining the correction coefficient of the modal response of the aeroelastic model based on the quasi-steady theory; correcting the modal response according to the correction coefficient, and superimposing the corrected modal response to obtain the wind vibration response of the aeroelastic model, thereby completing the vibration type correction of the wind vibration response of the aeroelastic model. The present invention can obtain the vibration type correction coefficients of each order of modal displacement and acceleration standard deviation, and obtain the wind vibration response of the aeroelastic model after vibration type correction, thereby improving the accuracy of the test results of the aeroelastic model of the transmission tower.

Description

Technical Field

[0001] The invention belongs to the field of wind tunnel test of aeroelastic model of transmission tower, and in particular relates to a vibration mode correction method of wind vibration response of aeroelastic model of transmission tower. Background Art

[0002] Among the various loads on the transmission line, wind load is the main control load of the transmission line. The aeroelastic model test of the transmission tower is the most direct and simplest method to obtain the wind-induced vibration response of the transmission tower. The aeroelastic model and the actual structure must meet geometric similarity, mass similarity, and frequency similarity. In fact, due to the unsatisfactory material stiffness and density, manufacturing errors and other reasons, it is difficult to accurately meet the requirements of mass similarity and frequency similarity under the condition of meeting geometric similarity. The counterweight method is usually used to make the structure meet the frequency similarity ratio condition, but the mass distribution similarity of the aeroelastic model is often difficult to accurately meet the requirements, resulting in the aeroelastic model and the actual structure The vibration mode is different, which in turn causes the structural response obtained in the wind tunnel test to be different from the actual response. In view of the test errors caused by the difference in vibration mode and mass distribution, it is necessary to establish a correction method for the wind-induced vibration response of the aeroelastic model of the transmission tower to improve the accuracy of the aeroelastic model wind tunnel test, which is of great significance to the study of wind loads on transmission towers. Summary of the invention

[0003] In order to solve the problems existing in the background technology, the object of the present invention is to provide a vibration mode correction method for the wind vibration response of an aeroelastic model of a transmission tower.

[0004] The technical solution adopted by the present invention is as follows, comprising the following steps:

[0005] Step S1: First, establish a finite element model of the prototype transmission tower and obtain the first K-order vibration mode matrix Φ of the finite element model. p , and the theoretical mass of each segment of the aeroelastic model is obtained according to the mass of the finite element model;

[0006] Step S2, making an aeroelastic model and conducting a wind tunnel test to obtain the actual mass of each segment of the aeroelastic model and the wind vibration response time history;

[0007] Step S3: According to the wind vibration response of the aeroelastic model, obtain the vibration mode matrix Φ of the first K orders of the aeroelastic model m :

[0008] Step S4, obtaining modal responses of each order of the aeroelastic model according to the wind vibration response of the aeroelastic model; the modal response includes a modal displacement standard deviation and a modal acceleration standard deviation;

[0009] Step S5, based on the quasi-steady theory, according to the vibration modes of the aeroelastic model and the finite element model, and the theoretical mass and actual mass of each segment of the aeroelastic model, obtain the correction coefficient of the first K-order modal response of the aeroelastic model;

[0010] Step S6, correcting the modal response in step S4 according to the correction coefficient of the modal response to obtain a corrected target modal response, and superimposing the target modal response to obtain the wind-induced vibration response of the aeroelastic model, thereby completing the vibration mode correction of the wind-induced vibration response of the aeroelastic model.

[0011] The step S1 is specifically as follows:

[0012] Step S1.1: First, establish the finite element model of the prototype transmission tower, and then obtain the vibration mode matrix Φ of the first K orders of the finite element model according to the modal calculation. p :

[0013]

[0014]

[0015] in, represents the normalized vibration shape vector of the kth order of the finite element model, represents the normalized vibration mode of the k-th order and n-th segment of the finite element model, and N represents the total number of segments of the finite element model;

[0016] Step S1.2: Next, according to the finite element model of the prototype transmission tower, the mass of each segment of the finite element model is obtained, and the theoretical mass of each segment of the aeroelastic model is obtained according to the following formula:

[0017] m p (z n )=m c (z n )C m

[0018] Among them, m c (z n ) represents the mass of the nth segment of the finite element model, m p (z n ) represents the theoretical mass of the nth segment of the aeroelastic model, C m Represents the mass similarity ratio between the aeroelastic model and the finite element model.

[0019] The step S2 is specifically as follows:

[0020] Step S2.1, making an aeroelastic model: first, according to the actual size, stiffness and mass of the prototype transmission tower, the prototype transmission tower is scaled according to the similarity criterion to obtain a scaled aeroelastic model, and the actual mass m of each segment of the aeroelastic model is measured with a balance during the production process. m (z n );

[0021] Step S2.2: Next, a wind tunnel test is conducted on the aeroelastic model to obtain the displacement response time history q(z n ,t) and acceleration response time history a(z n ,t).

[0022] The step S3 is specifically as follows:

[0023] According to the wind vibration response of the aeroelastic model during the wind tunnel test, the random subspace method is used to obtain the vibration matrix Φ of the first K orders of the aeroelastic model. m :

[0024]

[0025]

[0026] in, represents the normalized vibration mode vector of the kth order of the aeroelastic model, represents the normalized vibration mode of the k-th order and n-th segment of the aeroelastic model, and N represents the total number of segments of the aeroelastic model.

[0027] The step S4 is specifically as follows:

[0028] Step S4.1: Based on the wind-induced vibration response and normalized vibration mode vector of the aeroelastic model Construct the displacement response matrix Q and acceleration response matrix A of the aeroelastic model;

[0029]

[0030]

[0031] Among them, q(z n ,t) represents the displacement response time history of the aeroelastic model in the nth segment, a(z n ,t) represents the acceleration response time history of the aeroelastic model in the nth segment; α k (t) represents the k-th order modal displacement time history of the aeroelastic model, β k (t) represents the k-th order modal acceleration time history of the aeroelastic model;

[0032] Step S4.2: According to the displacement response matrix Q and acceleration response matrix A of the aeroelastic model, the modal displacement time history α of the first K orders of the aeroelastic model is solved respectively. k (t) and modal acceleration time history β k (t), then, the modal displacement time history α of each order of the aeroelastic model is k The standard deviation of (t) in time is taken as the standard deviation of the modal displacement of this order. The modal acceleration time history β of each order of the aeroelastic model kThe standard deviation of (t) in time is taken as the standard deviation of the modal acceleration of this order.

[0033] The step S5 is specifically as follows:

[0034] Step S5.1: First, the generalized load spectrum of the first K-order mode of the aeroelastic model is obtained according to the following formula:

[0035]

[0036]

[0037] in, represents the kth mode generalized load spectrum of the aeroelastic model, S′ F (f) represents the dimensionless self-power spectrum of the fluctuating wind load, Λ represents the adjustment matrix of N*N order, represents the normalized vibration mode vector of the kth order of the aeroelastic model, E i represents the average wind load coefficient of the aeroelastic model in the i-th segment, σ u′i represents the standard deviation of the fluctuating wind speed of the aeroelastic model in the i-th segment, i and j are the row number and column number of the adjustment matrix Λ respectively, and coh(i,j) represents the fluctuating wind speed coherence function between the i-th segment and the j-th segment of the aeroelastic model;

[0038] Where, the average wind load coefficient E of the aeroelastic model in the nth segment is n According to the following formula:

[0039]

[0040] Where ρ represents the air density, represents the average wind speed at the top of the aeroelastic model, H represents the total height of the aeroelastic model, z n represents the height of the nth segment of the aeroelastic model, C d (z n ) represents the wind load shape coefficient of the nth segment of the aeroelastic model, A(z n ) represents the projected area of ​​the nth segment of the aeroelastic model facing the wind;

[0041] Step S5.2, then, the modal generalized load spectrum based on the first K-order vibration modes of the finite element model is obtained according to the following formula:

[0042]

[0043]

[0044] in, represents the modal generalized load spectrum based on the k-th vibration mode of the finite element model, represents the normalized vibration mode vector of the kth order of the finite element model, η F (k) represents the mode correction coefficient of the k-th mode generalized load spectrum of the aeroelastic model;

[0045] Step S5.3: Next, according to the actual / theoretical mass of the aeroelastic model, the actual modal mass of the first K orders of the aeroelastic model is obtained by the following formula: and theoretical modal mass

[0046]

[0047]

[0048] in, represents the actual modal mass of the kth order of the aeroelastic model; represents the theoretical modal mass of the kth order of the aeroelastic model; m m (z n ) represents the actual mass of the nth segment of the aeroelastic model, m p (z n ) represents the theoretical mass of the nth segment of the aeroelastic model; represents the normalized vibration shape of the kth order and nth segment of the aeroelastic model, represents the normalized vibration shape of the k-th order and n-th segment of the finite element model;

[0049] Step S5.3: Finally, according to the actual / theoretical modal mass of the aeroelastic model, the correction coefficient η of the first K-order modal response of the aeroelastic model is obtained. k :

[0050]

[0051] Among them, η k It represents the vibration correction coefficient of the kth-order mode wind-induced vibration response of the aeroelastic model.

[0052] The step S6 is specifically as follows:

[0053] Step S6.1: Correct the modal responses of each order of the aeroelastic model according to the correction coefficient to obtain the corrected target modal displacement standard deviation. and target modal acceleration standard deviation

[0054]

[0055]

[0056] in, represents the standard deviation of the k-th order target modal displacement of the modified aeroelastic model, represents the standard deviation of the k-th order target modal acceleration of the modified aeroelastic model, represents the standard deviation of the k-th modal displacement of the aeroelastic model before correction, represents the standard deviation of the kth modal acceleration of the aeroelastic model before correction;

[0057] Step S6.2: Superimpose the target modal displacement standard deviation and the target modal acceleration standard deviation respectively, and obtain the displacement response of each segment of the aeroelastic model according to the following formula: and acceleration response

[0058]

[0059]

[0060] in, represents the displacement response of the nth segment of the modified aeroelastic model, represents the acceleration response of the nth segment of the modified aeroelastic model.

[0061] The total number of segments N of the aeroelastic model is greater than the number of vibration modes K during the wind tunnel test.

[0062] The present invention uses a wind tunnel vibration test to obtain the displacement, acceleration response and mass of each segment of the aeroelastic model of the transmission tower, and adopts the SSI method to obtain the multi-order vibration modes of the aeroelastic model; uses finite element modal analysis to obtain the true mass and vibration mode of each segment of the transmission tower, and decomposes the displacement response and acceleration response into the superposition of multiple modal responses; combines the quasi-steady theory and the structural frequency domain motion equation to derive the wind vibration response modal correction coefficient, and corrects the standard deviation of each modal displacement and acceleration; superimposes the corrected modal responses of each order to obtain the corrected wind vibration response of each segment of the transmission tower. The present invention can obtain the vibration mode correction coefficient of each order of modal displacement and acceleration standard deviation, and obtain the wind vibration response of the aeroelastic model after vibration mode correction, which effectively improves the accuracy of the wind tunnel test results of the aeroelastic model of the transmission tower.

[0063] The beneficial effects of the present invention are:

[0064] 1. Based on the quasi-steady theory, the present invention derives the vibration correction coefficients of each order of modal wind loads of the aeroelastic model of the transmission tower. The coefficients take into account the structural characteristics of the transmission tower and the influence of the wind field at the same time, and can more accurately predict the modal wind loads of the transmission tower.

[0065] 2. The present invention proposes a method for deriving each order of modal response based on the wind-induced vibration response of the transmission tower aeroelastic model, which can be used to analyze the distribution of each order of modal response of the transmission tower wind-induced vibration.

[0066] 3. Based on the quasi-steady theory, the present invention derives the vibration type correction coefficients of each order modal wind-induced vibration response of the transmission tower aeroelastic model, and superimposes the corrected modal responses of each order to obtain the corrected wind-induced vibration response of each segment, thereby improving the accuracy of the aeroelastic model wind tunnel test. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a specific flow chart of the method of the present invention. DETAILED DESCRIPTION

[0068] The present invention is described in detail below in conjunction with specific implementation cases. The following implementation cases will help those skilled in the art to further understand the present invention, but will not limit the present invention in any form.

[0069] The method of the present invention comprises the following steps:

[0070] Step S1: First, establish a finite element model of the prototype transmission tower and obtain the first K-order vibration mode matrix Φ of the finite element model. p , and the theoretical mass of each segment of the aeroelastic model is obtained according to the mass and mass similarity ratio of each segment of the finite element model;

[0071] Step S2, making an aeroelastic model and conducting a wind tunnel test to obtain the actual mass of each section of the aeroelastic model and the wind vibration response time history;

[0072] The wind-induced vibration response time history includes the displacement response time history and the acceleration response time history, and the wind-induced vibration response includes the displacement response and the acceleration response;

[0073] Step S3: According to the wind vibration response of the aeroelastic model, obtain the vibration mode matrix Φ of the first K order along the line of the aeroelastic model m :

[0074] Step S4, obtaining modal responses of each order of the aeroelastic model according to the wind vibration response of the aeroelastic model; the modal response includes a modal displacement standard deviation and a modal acceleration standard deviation;

[0075] Step S5, based on the quasi-steady theory, according to the vibration modes of the aeroelastic model and the finite element model, and the theoretical mass and actual mass of each segment of the aeroelastic model, obtain the correction coefficient of the first K-order modal response of the aeroelastic model;

[0076] Step S6, correcting the modal response in step S4 according to the correction coefficient of the modal response to obtain a corrected target modal response, and superimposing the target modal response to obtain the wind vibration response after the aeroelastic model correction, thereby completing the vibration mode correction of the aeroelastic model test results.

[0077] Step S1 is specifically as follows:

[0078] Step S1.1: First, establish the finite element model of the prototype transmission tower, and then obtain the vibration mode matrix Φ of the first K orders of the finite element model according to the modal calculation. p :

[0079]

[0080]

[0081] in, represents the normalized vibration shape vector of the kth order of the finite element model, represents the normalized vibration mode of the k-th order and n-th segment of the finite element model, and N represents the total number of segments of the finite element model;

[0082] Among them, the normalized vibration modes are all taken from the same direction, which can be the direction along the transmission tower or the direction across the transmission tower. In this embodiment, the along-line direction of the transmission tower is taken as an example for analysis. p In addition, the transmission tower response can be measured on site, and then the random subspace method (SSI) can be used to obtain the vibration matrix Φ of the first K order of the transmission tower. p .

[0083] Step S1.2: Next, according to the finite element model of the prototype transmission tower, the mass of each segment of the finite element model is obtained, and the theoretical mass of each segment of the aeroelastic model is obtained according to the following formula:

[0084] m p (z n )=m c (z n )C m

[0085] Among them, m c (z n ) represents the mass of the nth segment of the finite element model, m p (z n ) represents the theoretical mass of the nth segment of the aeroelastic model, C m Represents the mass similarity ratio between the aeroelastic model and the finite element model.

[0086] The specific steps of step S2 are:

[0087] Step S2.1, making an aeroelastic model: first, according to the actual size, stiffness and mass of the prototype transmission tower, the prototype transmission tower is scaled according to the similarity criterion to obtain a scaled aeroelastic model, and the actual mass m of each segment of the aeroelastic model is measured with a balance during the production process. m (z n );

[0088] Step S2.2: Next, a wind tunnel test is conducted on the aeroelastic model to obtain the linear displacement response time history q(z n ,t) and acceleration response time history a(z n ,t).

[0089] Step S3 is specifically as follows:

[0090] According to the wind vibration response of the aeroelastic model during the wind tunnel test, the random subspace method SSI method is used to obtain the K-order vibration matrix Φ of the aeroelastic model along the line. m :

[0091]

[0092]

[0093] in, represents the normalized vibration mode vector of the kth order of the aeroelastic model, represents the normalized vibration mode of the kth order and nth segment of the aeroelastic model, and N represents the total number of segments of the aeroelastic model. The total number of segments of the aeroelastic model is equal to that of the finite element model.

[0094] Step S4 is specifically as follows:

[0095] Step S4.1: Based on the wind-induced vibration response and normalized vibration mode vector of the aeroelastic model Construct the displacement response matrix Q and acceleration response matrix A of the aeroelastic model;

[0096]

[0097]

[0098] Among them, q(z n ,t) represents the time history of the displacement response of the aeroelastic model in the nth segment, a(z n ,t) represents the acceleration response time history of the aeroelastic model in the nth segment, N represents the total number of segments of the aeroelastic model, and to ensure the existence of a solution to the above formula, N ≥ K must be satisfied; α k (t) represents the k-th order linear modal displacement time history of the aeroelastic model, β k (t) represents the time history of the k-th order linear modal acceleration of the aeroelastic model;

[0099] Step S4.2: According to the displacement response matrix Q and acceleration response matrix A of the aeroelastic model, the modal displacement time history α of the first K orders of the aeroelastic model is solved respectively. k (t) and modal acceleration time history β k (t), then, the modal displacement time history α of each order of the aeroelastic model is kThe standard deviation of (t) in time is taken as the standard deviation of the modal displacement of this order. The modal acceleration time history β of each order of the aeroelastic model k The standard deviation of (t) in time is taken as the standard deviation of the modal acceleration of this order.

[0100] Step S5 is specifically as follows:

[0101] Step S5.1: First, based on the quasi-steady theory, the generalized load spectrum of the first K-order mode of the aeroelastic model is obtained according to the following formula:

[0102]

[0103]

[0104] in, represents the kth mode generalized load spectrum of the aeroelastic model, S′ F (f) represents the dimensionless self-power spectrum of the fluctuating wind load, Λ represents the adjustment matrix of N*N order, represents the normalized vibration mode vector of the kth order of the aeroelastic model, E i represents the average wind load coefficient of the aeroelastic model in the i-th segment, σ u′i represents the standard deviation of the fluctuating wind speed of the aeroelastic model in the i-th segment, i and j are the row number and column number of the adjustment matrix Λ respectively, and coh(i,j) represents the fluctuating wind speed coherence function between the i-th segment and the j-th segment of the aeroelastic model;

[0105] Where, the average wind load factor E of the aeroelastic model / prototype transmission tower in the nth segment is n According to the following formula:

[0106]

[0107] Where ρ represents the air density, represents the average wind speed at the top of the aeroelastic model / prototype transmission tower, H represents the total height of the aeroelastic model / prototype transmission tower, z n represents the height of the nth section of the aeroelastic model / prototype transmission tower, C d (z n ) represents the wind load shape coefficient of the nth section of the aeroelastic model / prototype transmission tower, A(z n ) represents the projected area of ​​the nth section of the aeroelastic model / prototype transmission tower facing the wind. This formula is applicable to both the aeroelastic model and the prototype transmission tower;

[0108] Step S5.2, then, the modal generalized load spectrum based on the first K orders of the finite element model is obtained according to the following formula:

[0109]

[0110]

[0111] in, represents the modal generalized load spectrum based on the k-th vibration mode of the finite element model, represents the normalized vibration mode vector of the kth order of the finite element model, η F (k) represents the vibration mode correction coefficient of the kth order mode generalized load spectrum of the aeroelastic model,

[0112] Step S5.3: Next, according to the actual / theoretical mass of the aeroelastic model, the actual modal mass of the first K orders of the aeroelastic model is obtained by the following formula: and theoretical modal mass

[0113]

[0114]

[0115] in, represents the actual modal mass of the kth order of the aeroelastic model; represents the theoretical modal mass of the kth order of the aeroelastic model; m m (z n ) represents the actual mass m of the nth segment of the aeroelastic model m (z n ), m p (z n ) represents the theoretical mass of the nth segment of the aeroelastic model; represents the normalized vibration shape of the kth order and nth segment of the aeroelastic model, represents the normalized vibration shape of the k-th order and n-th segment of the finite element model;

[0116] Step S5.3: Finally, according to the actual / theoretical modal mass of the aeroelastic model, the correction coefficient η of the first K-order modal response of the aeroelastic model is obtained. k :

[0117]

[0118] Among them, η k It represents the vibration correction coefficient of the kth-order mode wind-induced vibration response of the aeroelastic model.

[0119] Step S6 is specifically as follows:

[0120] Step S6.1: Correct the modal responses of each order of the aeroelastic model according to the correction coefficient to obtain the corrected target modal displacement standard deviation. and target modal acceleration standard deviation

[0121]

[0122]

[0123] in, represents the standard deviation of the k-th order target modal displacement of the modified aeroelastic model, represents the standard deviation of the k-th order target modal acceleration of the modified aeroelastic model, represents the standard deviation of the k-th modal displacement of the aeroelastic model before correction, represents the standard deviation of the kth modal acceleration of the aeroelastic model before correction;

[0124] Step S6.2, respectively superimpose the corrected target modal displacement standard deviation and target modal acceleration standard deviation, and process them according to the following formula to obtain the displacement response of each segment of the aeroelastic model: and acceleration response

[0125]

[0126]

[0127] in, represents the displacement response of the nth segment of the modified aeroelastic model, represents the acceleration response of the nth segment of the modified aeroelastic model.

[0128] The total number of segments N of the aeroelastic model should be greater than the number of vibration modes K taken during the wind tunnel test.

[0129] In specific implementation, the derivation process of step S5 is as follows:

[0130] Firstly, the fluctuating wind pressure p(z n ,t):

[0131]

[0132] In the formula, ρ represents the air density, is the average wind speed of the aeroelastic model at the nth segment, represents the fluctuating wind speed of the aeroelastic model at the nth segment, represents the average wind speed at the top of the aeroelastic model, H represents the total height of the tower model, z n represents the height of the aeroelastic model in the nth segment, and α is the ground roughness index;

[0133] The fluctuating wind load F(z n ,t) can be expressed as:

[0134]

[0135] In the formula, C d (z n ) is the wind load shape coefficient of the aeroelastic model in the nth segment, A(z n ) is the projected area of ​​the aeroelastic model in the nth segment facing the wind, E n is the average wind load coefficient of the aeroelastic model in the nth segment;

[0136] Therefore, combining formula (1) and formula (2), E n It can be expressed as:

[0137]

[0138] The standard deviation of wind load of the aeroelastic model in the nth segment is σ F (z n ) can be expressed as:

[0139] σ F (z n )=E n σ u′n (4)

[0140] In the formula, σ u′n represents the standard deviation of the fluctuating wind speed of the aeroelastic model in the nth segment;

[0141] Assume that the dimensionless auto-power spectrum S′ of the fluctuating wind load F (f) It remains constant along the height of the building, that is:

[0142]

[0143] In the formula, S F (z i ; f), S F (z j ; f) represent the power spectrum of the pulsating wind load of the aeroelastic model in the i-th and j-th segments, respectively. represent the standard deviation of wind load of the aeroelastic model in the i-th and j-th segments respectively;

[0144] The mutual power spectrum of wind loads in different segments of the aeroelastic model can be written as:

[0145]

[0146] In the formula, S F (z i ,z j ; f) represents the wind load mutual power spectrum between the i-th segment and the j-th segment of the tower model, coh F (z i,z j ) represents the coherence function of the fluctuating wind load between the ith and jth segments of the tower model;

[0147] The coherence function of the fluctuating wind load based on the quasi-steady theory is replaced by the coherence function of the fluctuating wind speed, that is:

[0148] coh F (z i ,z j )=coh(z i ,z j ) (7)

[0149] In the formula, coh(z i ,z j ) is the coherence function of the fluctuating wind speed between the i-th segment position and the j-th segment position of the aeroelastic model;

[0150] According to the "Overhead Transmission Line Load Code" (DL / T5551-2018), the fluctuating wind speed coherence function can be expressed as follows:

[0151]

[0152] Among them, z i 、z j Respectively represent the height of the tower model in the i-th and j-th sections;

[0153] In a specific implementation, formula (1) to formula (8) are applicable to both the experimental (mass, vibration mode) values ​​and the theoretical (mass, vibration mode) values ​​of the aeroelastic model.

[0154] Ignoring the modal cross terms, according to the Wiener-Schinchin relationship, for the aeroelastic model, the k-th modal generalized load spectrum is It can be expressed as:

[0155]

[0156] in, represents the normalized vibration shape of the kth order and ith segment of the aeroelastic model, represents the normalized vibration mode of the kth order and jth segment of the aeroelastic model;

[0157] Substituting formula (6) into the above formula, we can obtain:

[0158]

[0159]

[0160] Using the vibration mode of the prototype transmission tower (i.e., finite element model), the k-th order modal generalized load spectrum It is expressed as:

[0161]

[0162]

[0163] in, represents the modal generalized load spectrum based on the k-th vibration mode of the finite element model, represents the normalized vibration mode vector of the kth order of the finite element model, η F (k) represents the vibration mode correction coefficient of the kth mode generalized load spectrum of the aeroelastic model.

[0164] According to the principle of random vibration, the frequency domain motion equation of each mode is:

[0165]

[0166]

[0167]

[0168] Among them, S q (k,f) is the k-th order generalized displacement response; S a (k,f) is the k-th order generalized acceleration response; f k is the kth modal frequency, is the k-th mode generalized mass; Can be It can also be f is the frequency; ζ k is the kth order modal damping; H k (f) represents the k-th order modal mechanical admittance; this formula is applicable to both the aeroelastic test model and the theoretical model calculated according to the similarity criterion.

[0169] Due to the differences in vibration shapes and the mass of each segment, the actual modal mass of the aeroelastic model is different from the theoretical modal mass calculated by similarity theory:

[0170]

[0171]

[0172] in, represents the actual modal mass of the kth order of the aeroelastic model; represents the k-th order theoretical modal mass of the aeroelastic model;

[0173] Combining the above formula, we can get:

[0174]

[0175]

[0176]

[0177] In the formula, is the k-th order displacement generalized spectrum based on theoretical vibration shape and theoretical mass, is the k-th order acceleration generalized spectrum based on theoretical vibration shape and theoretical mass, is the k-th order displacement generalized spectrum based on the test vibration shape and test mass, is the kth order acceleration generalized spectrum based on the test vibration shape and test mass, η k is the vibration correction coefficient of the k-th order modal wind vibration response. Among them, the theoretical vibration shape is the vibration shape of the prototype transmission tower / finite element model, the experimental vibration shape is the vibration shape of the aeroelastic model, the theoretical mass is the mass of the aeroelastic model calculated according to the mass similarity ratio, and the experimental mass is the actual mass of the aeroelastic model.

Claims

1. A vibration mode correction method for wind-induced vibration response of a transmission tower aeroelastic model, characterized in that: The following steps are involved: Step S1: First, establish a finite element model of the prototype transmission tower and obtain the first K-order vibration mode matrix Φ of the finite element model. p , and the theoretical mass of each segment of the aeroelastic model is obtained according to the mass of the finite element model; Step S2, making an aeroelastic model and conducting a wind tunnel test to obtain the actual mass of each segment of the aeroelastic model and the wind vibration response time history; Step S3: According to the wind vibration response of the aeroelastic model, obtain the vibration mode matrix Φ of the first K orders of the aeroelastic model m : Step S4, obtaining modal responses of each order of the aeroelastic model according to the wind vibration response of the aeroelastic model; the modal response includes a modal displacement standard deviation and a modal acceleration standard deviation; Step S5, based on the quasi-steady theory, according to the vibration modes of the aeroelastic model and the finite element model, and the theoretical mass and actual mass of each segment of the aeroelastic model, obtain the correction coefficient of the first K-order modal response of the aeroelastic model; Step S6, correcting the modal response in step S4 according to the correction coefficient of the modal response to obtain a corrected target modal response, and superimposing the target modal response to obtain a wind-induced vibration response corrected by the aeroelastic model, thereby completing the vibration mode correction of the wind-induced vibration response of the aeroelastic model; The step S1 is specifically as follows: Step S1.1: First, establish the finite element model of the prototype transmission tower, and then obtain the first K-order vibration mode matrix Φ of the finite element model according to the modal calculation. p : in, represents the normalized vibration shape vector of the kth order of the finite element model, represents the normalized vibration mode of the k-th order and n-th segment of the finite element model, and N represents the total number of segments of the finite element model; Step S1.2: Next, according to the finite element model of the prototype transmission tower, the mass of each segment of the finite element model is obtained, and the theoretical mass of each segment of the aeroelastic model is obtained according to the following formula: m p (z n )=m c (z n )C m Among them, m c (z n ) represents the mass of the nth segment of the finite element model, m p (z n ) represents the theoretical mass of the nth segment of the aeroelastic model, C m It represents the mass similarity ratio between the aeroelastic model and the finite element model; The step S3 is specifically as follows: According to the wind vibration response of the aeroelastic model during the wind tunnel test, the random subspace method is used to obtain the vibration matrix Φ of the first K orders of the aeroelastic model. m : in, represents the normalized vibration mode vector of the kth order of the aeroelastic model, represents the normalized vibration mode of the kth order and nth segment of the aeroelastic model, and N represents the total number of segments of the aeroelastic model; The step S4 is specifically as follows: Step S4.1: Based on the wind-induced vibration response and normalized vibration mode vector of the aeroelastic model Construct the displacement response matrix Q and acceleration response matrix A of the aeroelastic model; Among them, q(z n ,t) represents the displacement response time history of the aeroelastic model in the nth segment, a(z n ,t) represents the acceleration response time history of the aeroelastic model in the nth segment; α k (t) represents the k-th order modal displacement time history of the aeroelastic model, β k (t) represents the k-th order modal acceleration time history of the aeroelastic model; Step S4.2: Solve the first K-order modal displacement time history α of the aeroelastic model according to the displacement response matrix Q and acceleration response matrix A of the aeroelastic model. k (t) and modal acceleration time history β k (t), then, the modal displacement time history α of each order of the aeroelastic model is k The standard deviation of (t) in time is taken as the standard deviation of the modal displacement of this order. The modal acceleration time history β of each order of the aeroelastic model k The standard deviation of (t) in time is taken as the standard deviation of the modal acceleration of this order. The step S5 is specifically as follows: Step S5.1: First, the generalized load spectrum of the first K-order mode of the aeroelastic model is obtained according to the following formula: in, represents the kth mode generalized load spectrum of the aeroelastic model, S′ F (f) represents the dimensionless self-power spectrum of the fluctuating wind load, Λ represents the adjustment matrix of N*N order, represents the normalized vibration mode vector of the kth order of the aeroelastic model, E i represents the average wind load coefficient of the aeroelastic model in the i-th segment, σ u′i represents the standard deviation of the fluctuating wind speed of the aeroelastic model in the i-th segment, i and j are the row number and column number of the adjustment matrix Λ respectively, and coh(i,j) represents the fluctuating wind speed coherence function between the i-th segment and the j-th segment of the aeroelastic model; Where, the average wind load coefficient E of the aeroelastic model in the nth segment is n According to the following formula: Where ρ represents the air density, represents the average wind speed at the top of the aeroelastic model, H represents the total height of the aeroelastic model, z n represents the height of the nth segment of the aeroelastic model, C d (z n ) represents the wind load shape coefficient of the nth segment of the aeroelastic model, A(z n ) represents the projected area of ​​the nth segment of the aeroelastic model facing the wind; Step S5.2, then, the modal generalized load spectrum based on the first K-order vibration modes of the finite element model is obtained according to the following formula: in, represents the modal generalized load spectrum based on the k-th vibration mode of the finite element model, represents the normalized vibration mode vector of the kth order of the finite element model, η F (k) represents the mode correction coefficient of the kth-order mode generalized load spectrum of the aeroelastic model; Step S5.3: Then, according to the actual / theoretical mass of the aeroelastic model, the actual modal mass of the first K orders of the aeroelastic model is obtained by the following formula: and theoretical modal mass in, represents the actual modal mass of the kth order of the aeroelastic model; represents the theoretical modal mass of the kth order of the aeroelastic model; m m (z n ) represents the actual mass of the nth segment of the aeroelastic model, m p (z n ) represents the theoretical mass of the nth segment of the aeroelastic model; represents the normalized vibration shape of the kth order and nth segment of the aeroelastic model, represents the normalized vibration shape of the k-th order and n-th segment of the finite element model; Step S5.3: Finally, according to the actual / theoretical modal mass of the aeroelastic model, the correction coefficient η of the first K-order modal response of the aeroelastic model is obtained. k : Among them, η k It represents the vibration correction coefficient of the kth-order mode wind vibration response of the aeroelastic model; The step S6 is specifically as follows: Step S6.1: Correct the modal responses of each order of the aeroelastic model according to the correction coefficient to obtain the corrected target modal displacement standard deviation. and target modal acceleration standard deviation in, represents the standard deviation of the k-th order target modal displacement of the modified aeroelastic model, represents the standard deviation of the k-th order target modal acceleration of the modified aeroelastic model, represents the standard deviation of the k-th modal displacement of the aeroelastic model before correction, represents the standard deviation of the kth modal acceleration of the aeroelastic model before correction; Step S6.2: Superimpose the target modal displacement standard deviation and the target modal acceleration standard deviation respectively, and obtain the displacement response of each segment of the aeroelastic model according to the following formula: and acceleration response in, represents the displacement response of the nth segment of the modified aeroelastic model, represents the acceleration response of the nth segment of the modified aeroelastic model.

2. The vibration mode correction method of the wind vibration response of the aeroelastic model of a transmission tower according to claim 1 is characterized by: The step S2 is specifically as follows: Step S2.1, making an aeroelastic model: first, according to the actual size, stiffness and mass of the prototype transmission tower, the prototype transmission tower is scaled according to the similarity criterion to obtain a scaled aeroelastic model, and the actual mass m of each segment of the aeroelastic model is measured with a balance during the production process. m (z n ); Step S2.2: Next, a wind tunnel test is conducted on the aeroelastic model to obtain the displacement response time history q(z n ,t) and acceleration response time history a(z n ,t).

3. The vibration mode correction method of the wind vibration response of the aeroelastic model of a transmission tower according to claim 1 is characterized by: The total number of segments N of the aeroelastic model is greater than the number of vibration modes K during the wind tunnel test.

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