CN108416083B - Two-dimensional dynamic model analysis method and system for towering television tower structure - Google Patents
Two-dimensional dynamic model analysis method and system for towering television tower structure Download PDFInfo
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Abstract
The invention discloses a two-dimensional dynamic model analysis method and a system for a towering television tower structure, wherein the method comprises the following steps: the method first concentrates the quality of all structural and non-structural members of the high-rise television tower on the selected limited node level, and determines the set positions and the set number of the node levels. And determining equivalent stiffness of the finite element sub-model based on the finite element sub-model corresponding to each node layer, and establishing a stiffness matrix and a quality matrix of the two-dimensional dynamic model. And establishing an objective function of the stiffness parameter based on the dynamic characteristics of the three-dimensional finite element model and the two-dimensional dynamic model, and correcting the stiffness parameter of the two-dimensional dynamic model. And establishing a two-dimensional dynamic model based on the corrected stiffness parameters, and rapidly solving the dynamic characteristics and dynamic response of the towering structure based on a structural characteristic equation and a motion equation. The method has the advantages of clear physical concept, strong operability, quick and accurate analysis and calculation, wide application range and the like.
Description
Technical Field
The invention relates to a performance evaluation technology of a towering television tower structure, in particular to a towering television tower structure two-dimensional dynamic model analysis method and system.
Background
In recent years, with the rapid development of social economy, the construction of a towering television tower structure in China enters a new period, and a plurality of large towering television tower structures are built in succession. The application of new technology and new materials leads the structure of the high-rise television tower to tend to be higher and softer, the structure has strong dynamic response under the action of wind load and earthquake, and the requirements of safety and comfort are difficult to meet. Therefore, how to ensure the safety of the high-rise television tower structure under the action of an external load is a practical problem which is put in front of a great number of engineering technicians and scientific researchers. Therefore, the analysis and evaluation work for the dynamic performance of the towering television tower structure has important scientific significance and practical engineering value.
The high-rise television tower has a complex structural form and numerous rod pieces. Strictly speaking, only the spatial three-dimensional finite element model can accurately reflect the multi-dimensional load and multi-dimensional dynamic response of the towering television tower structure. The method for reasonably evaluating the structural safety and the dynamic performance is an effective method for establishing a towering television tower structure analysis model by a finite element numerical simulation technology. However, in practical application, the three-dimensional dynamic model has the defects of large calculation amount and difficult parameter analysis for structural vibration research, and wind load, earthquake action and other dynamic load samples of the three-dimensional dynamic model are almost impossible to obtain accurately. Therefore, a two-dimensional series multiple degree of freedom model is generally adopted for the high-rise television tower structure to meet the requirements of power calculation and vibration analysis.
The two-dimensional series connection multi-degree-of-freedom model analysis method which is generally adopted at present has many defects: 1) the two-dimensional series multi-degree-of-freedom model analysis method is obtained based on inversion of a flexibility matrix of a three-dimensional finite element model, and due to numerical calculation errors, the flexibility matrix and the rigidity matrix of the structure are not strictly symmetrical matrixes and do not meet the requirement of symmetry of the rigidity matrix of the structure; 2) the stiffness matrix obtained by inverting the compliance matrix is a full matrix, and the calculation and analysis workload is larger and the analysis precision is limited compared with a sparse matrix in the process of dynamic analysis; 3) the model parameters of the two-dimensional series multi-degree-of-freedom model cannot be corrected based on the real structural dynamic characteristic parameters, and the precision of the model parameters completely depends on the precision of the original three-dimensional finite element model. Once the original drawing model and the actually measured structure have great difference, the precision of the two-dimensional serial multi-degree-of-freedom model can not be ensured completely.
At present, the research on a two-dimensional dynamic model of a towering television tower structure is still relatively deficient, and a long road is needed to be taken. The two-dimensional dynamic analysis model which is simple in structure, rapid in analysis and high in precision is still very deficient and needs further exploration and innovation. The structural form of the towering television tower is complex, the number of components is large, and how to reduce the order of the model with the complex structure and obtain the two-dimensional dynamic model meeting the structural dynamic analysis precision requirement is a troublesome problem. The invention provides a two-dimensional dynamic model analysis method for a towering television tower structure, aiming at the problem of model simplification of the towering television tower structure at present. The method first concentrates the quality of all structural and non-structural members of the high-rise television tower on the selected limited node level, and determines the set positions and the set number of the node levels. And determining equivalent stiffness of the finite element sub-model based on the finite element sub-model corresponding to each node layer, and establishing a stiffness matrix and a quality matrix of the two-dimensional dynamic model. And establishing a rigidity parameter objective function based on the dynamic characteristics of the three-dimensional finite element model and the two-dimensional dynamic model, and correcting the rigidity parameter of the two-dimensional dynamic analysis model. And establishing a two-dimensional dynamic analysis model based on the corrected stiffness parameters, and rapidly solving the dynamic characteristics and dynamic response of the towering structure based on a structural characteristic equation and a motion equation. The method has the advantages of clear physical concept, strong operability and quick and accurate analysis and calculation, can effectively improve the performance evaluation level of the towering television tower structure, and improves the accuracy and reliability of dynamic analysis.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method and a system for analyzing a two-dimensional power model of a towering television tower structure aiming at the defects in the prior art, which can realize the accurate and effective analysis and calculation of the two-dimensional power model of the towering television tower structure and provide an effective means for the performance evaluation and vibration analysis of the actual towering television tower structure.
The technical scheme adopted by the invention for solving the technical problems is as follows: a two-dimensional dynamic model analysis method for a towering television tower structure comprises the following steps:
1) establishing a three-dimensional finite element model of the towering structure, determining the mass concentration positions of main structural components and non-structural components of the structure based on the three-dimensional finite element model, taking the mass concentration positions as node layers, and determining a two-dimensional dynamic model and the node layer positions and number of the two-dimensional dynamic model;
2) determining the initial rigidity of each node layer: separating the finite element sub-models corresponding to the node layers from the integral three-dimensional finite element model, and enabling the finite element sub-models to be equivalent to a single-degree-of-freedom system and determining the equivalent stiffness of the single-degree-of-freedom system;
3) determining a rigidity matrix and a quality matrix of the two-dimensional dynamic model according to the initial rigidity of each node layer;
4) determining the dynamic characteristics of the three-dimensional finite element model and the two-dimensional dynamic model;
5) establishing a stiffness parameter correction objective function;
6) correcting the rigidity parameter of the two-dimensional dynamic analysis model;
7) and establishing a two-dimensional dynamic analysis model based on the corrected stiffness parameters, and solving the dynamic characteristics and dynamic response of the towering structure based on a structural characteristic equation and a motion equation.
According to the scheme, the initial rigidity of the ith node layer is determined in the step 2) through the following formula:
wherein the content of the first and second substances,
wherein, KiThe initial rigidity of the ith node layer;
is the average displacement of the ith node layer; fiApplying a total horizontal load to the upper part of the finite element sub-model of the ith node layer; n isiThe number of plane nodes on the upper part of the finite element sub model of the ith node layer is counted; x is the number ofmHorizontally displacing each node on the top of the sub-model under the action of horizontal load;
initial bending stiffness EI of i-th node layer0Comprises the following steps:
wherein: l isiIs the height of the node layer, KiIs the initial stiffness of the ith node layer.
According to the scheme, the rigidity matrix K of the two-dimensional dynamic model in the step 3)0And the quality matrix M is formulated as follows:
M＝diag[m1,m2...mi...mnt]
in the formula: m isiIs section iConcentrated mass of the dot layer, ntNumber of node layers, K, for a two-dimensional power modeliIs the initial stiffness of the ith node layer.
According to the scheme, the dynamic characteristics of the three-dimensional finite element model and the two-dimensional dynamic model in the step 4) are as follows:
in the formula: m3DAnd K3DRespectively a mass matrix and a rigidity matrix of the three-dimensional finite element model;
the mode shape of the three-dimensional model is taken as the mode shape; omega3DIs the circular frequency of the three-dimensional model; m and K0Respectively a mass matrix and an initial stiffness matrix of the two-dimensional dynamic model;
the vibration mode is a two-dimensional dynamic model; omega2DThe circular frequency of the two-dimensional dynamic model.
According to the scheme, the objective function of stiffness parameter correction in the step 5) is established as follows:
J1(δEI)＝δEITWPδEI
J2(δEI)＝(δR-SδEI)TWR(δR-SδEI)
in the formula: wPWeighting a matrix for the stiffness parameters; wRWeighting matrix for self-oscillation frequency; δ R is a self-vibration frequency error vector of the two-dimensional model and the three-dimensional model; and S is the sensitivity of the natural vibration frequency of the two-dimensional dynamic model to the rigidity parameter EI.
According to the scheme, the stiffness parameter correction quantity delta EI of the two-dimensional dynamic model in the step 6) is determined by adopting the following formula:
in the formula: wPWeighting a matrix for the stiffness parameters; wRWeighting matrix for self-oscillation frequency; δ R is a self-vibration frequency error vector of the two-dimensional model and the three-dimensional model; and S is the sensitivity of the natural vibration frequency of the two-dimensional dynamic model to the rigidity parameter EI.
According to the scheme, the corrected rigidity parameter EI of the two-dimensional dynamic model is determined in the step 6) according to the following formulae：
EIe＝EI0+δEI；
Wherein, EI0And delta EI is the initial bending rigidity of the ith node layer, and is the rigidity parameter correction quantity of the two-dimensional dynamic model.
The invention also provides a two-dimensional dynamic model analysis system of the towering television tower structure, which comprises the following steps:
the node layer position and quantity analysis module of the two-dimensional dynamic model is used for establishing a three-dimensional finite element model of the towering structure, centralizing the quality of all structural members and non-structural members of the towering television tower in a preset node layer, and determining the set position and the set quantity of the node layer of the two-dimensional dynamic model;
the initial rigidity analysis module of the node layer is used for separating the finite element sub-models corresponding to the node layers from the integral three-dimensional finite element model, equivalent the finite element sub-models into a single-degree-of-freedom system and determining the rigidity parameters of the finite element sub-models;
the rigidity matrix and quality matrix analysis module of the two-dimensional dynamic model is used for establishing a rigidity matrix of each node layer by adopting the rigidity parameters of the node layers; then forming an integral rigidity matrix of the two-dimensional dynamic model through grouping, and establishing a concentrated mass matrix of the two-dimensional dynamic model;
the structure dynamic characteristic analysis module is used for respectively solving the natural vibration frequency of the original structure and the natural vibration frequency of the two-dimensional model by adopting a three-dimensional finite element model and a two-dimensional dynamic model;
the rigidity parameter objective function analysis module is used for establishing a rigidity parameter weighting objective function and a natural vibration frequency weighting objective function and further establishing a rigidity parameter objective function of the two-dimensional dynamic model;
and the rigidity parameter correction module of the two-dimensional dynamic analysis model is used for carrying out iterative optimization on the objective function. Recalculating the natural vibration frequency of the two-dimensional dynamic model according to the obtained corrected stiffness parameter EI, and comparing the natural vibration frequency with a target frequency, thereby determining the stiffness parameter variation of the two-dimensional dynamic model obtained after iteration;
and the two-dimensional dynamic analysis model building module is used for building a rigidity matrix of the two-dimensional dynamic model by adopting the corrected rigidity parameters and quickly solving the dynamic characteristics and dynamic response of the towering structure based on the structural characteristic equation and the motion equation.
The invention has the following beneficial effects:
1. the two-dimensional dynamic model analysis method for the towering television tower structure, provided by the invention, has the advantages of clear physical concept, strong operability, quickness and accuracy in analysis and calculation, wide application range and the like. The dynamic model analysis method and the dynamic model analysis system have applicability, and are suitable for dynamic analysis and calculation of the towering television tower structures with different heights, different structural forms and different physical parameters.
2. At present, the two-dimensional series connection multi-degree-of-freedom model of the existing high-rise television tower structure is obtained by inverting a flexibility matrix based on a three-dimensional finite element model, and a rigidity matrix is a full matrix and is an asymmetric matrix, so that the calculation and analysis workload is large, and the analysis precision is limited. Meanwhile, the model parameters of the two-dimensional series multi-degree-of-freedom model cannot be corrected based on the real structural dynamic characteristic parameters, and the precision of the model is completely dependent on the precision of the original three-dimensional finite element model. Once the original drawing model and the actually measured structure have great difference, the precision of the two-dimensional serial multi-degree-of-freedom model can not be ensured completely. The two-dimensional dynamic model analysis method for the towering television tower structure considers the correctability of the structural rigidity parameters, and can establish a target function and carry out iterative correction on the structural real dynamic characteristic parameters, so that the model has high calculation precision.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a three-dimensional finite element model diagram of a towering television tower structure according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a two-dimensional power model of a high-rise television tower structure according to an embodiment of the present invention;
FIG. 4 is a node level equivalent single degree of freedom model according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of solving for a node layer stiffness parameter according to an embodiment of the invention;
FIG. 6 shows the first 3 order mode of the structure based on the two-dimensional dynamic model according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in FIG. 1, an embodiment of the present invention begins by building a three-dimensional finite element model of the tower structure of a high-rise television. And further determining the number and the positions of the node layers of the two-dimensional dynamic analysis model. And determining the initial stiffness coefficient of each node layer, and establishing a stiffness matrix and a quality matrix of the two-dimensional dynamic analysis model. And determining the natural vibration frequency of different models based on the three-dimensional finite element model and the two-dimensional dynamic model. And establishing a target function for correcting the rigidity parameters of the node layer, and correcting the rigidity parameters of the two-dimensional dynamic model. And establishing a two-dimensional dynamic model based on the corrected node layer rigidity parameters, and quickly determining the dynamic characteristics of the high-rise television tower structure and the dynamic response under the action of an external load.
The two-dimensional dynamic model analysis method in the embodiment provides a new simplified dynamic model establishment technical means for the towering television tower structure, and can be effectively applied to the modeling process of the actual large towering television tower structure. Specifically, a two-dimensional dynamic model analysis method for a towering television tower structure is established through the following steps:
the method comprises the following steps: determining node layer positions and number of two-dimensional dynamic model
First, a three-dimensional finite element model of the towering structure is built, as shown in fig. 2. And further determining the position where the main horizontal component and the additional mass of the structure are concentrated based on the three-dimensional model. These locations may be provided as a node level of the structure. The main contradiction can be caught in the process of establishing the two-dimensional dynamic model, the secondary factors are omitted, and a model order reduction method is adopted. The mass of structural and non-structural members of a high-rise television tower is first concentrated on a selected limited node level. The node layer mainly selects the platform with larger mass and more main components and auxiliary components. Fig. 3 shows the arrangement positions of the node layers.
Step two: determining initial stiffness of each node layer
According to the selected node layers, the finite element sub-models corresponding to the node layers can be separated from the whole three-dimensional finite element model. The quality of the i-th node layer submodel is concentrated on the top of the submodel, and other parts are simplified into a vertical rod piece without quality and rigidity, so that an equivalent single-degree-of-freedom system is formed, as shown in fig. 4. And (4) constraining the bottom of the ith node layer finite element sub model by establishing a three-dimensional finite element model of the sub model. Let the number of upper plane nodes of the sub-model be niApplying a total horizontal load F on top of the submodeliThen horizontal force f applied by each nodeiComprises the following steps:
in the formula: n istThe number of node layers of the two-dimensional dynamic model; f. ofiIs the horizontal force component applied to a node on top of the sub-model.
Further determining horizontal displacement x of each node on the top of the sub-model under the action of horizontal load through calculationi：
fi＝Kixi(2)
In the formula: kiA three-dimensional finite element model rigidity matrix of the i-th layer sub-model; f. ofiFor horizontal load vector applied, all elements thereofThe sum of elements being Fi。
After the horizontal displacement of each node is obtained through analysis and calculation, the average displacement of the ith node layer can be determined
From this, it can be determined that the initial horizontal stiffness of the ith node layer is:
since the upper and lower parts of the ith node layer of an actual tv tower are constrained, it can be assumed that the stiffness of the substructure model can be approximately expressed as:
in the formula: EI (El)0Is the initial equivalent bending stiffness; l isiIs the height of the node level.
From this, it can be determined that the initial bending stiffness of the ith node layer is:
step three: establishing rigidity matrix and quality matrix of two-dimensional dynamic model
On the basis of determining the initial stiffness coefficient of each node layer of the two-dimensional dynamic model, the cross sectional area of each node layer member can be further counted, and the equivalent cross sectional area A can be obtained by accumulationi. Therefore, each node layer can be regarded as an equivalent beam unit, and the rigidity matrix of each node layer is established by adopting finite element expression of the beam unit:
in the formula:
is a beam element stiffness matrix expressed by an implicit function.
Further, an initial two-dimensional dynamic model stiffness matrix of the towering television tower structure can be obtained by grouping stiffness matrices of each node layer:
for a two-dimensional dynamic model of a towering television tower structure, the mass matrix is usually given as n according to the lumped mass methodtA diagonal matrix is maintained, wherein each diagonal element value is the mass of structural and non-structural members concentrated on each floor:
in the formula: m isiIs the aggregate quality of the ith node level.
Step four: determining dynamic characteristics of three-dimensional finite element model and two-dimensional dynamic model
The characteristic equation of the towering television tower structure based on the three-dimensional finite element model can be expressed as follows:
in the formula: m3DAnd K3DRespectively a mass matrix and a rigidity matrix of the three-dimensional finite element model;
the mode shape of the three-dimensional model is taken as the mode shape; omega3DIs the circular frequency of the three-dimensional model.
The characteristic equation of the two-dimensional dynamic model can be obtained in the same way:
in the formula: m and K0Respectively a mass matrix and an initial stiffness matrix of the two-dimensional dynamic model;
the vibration mode is a two-dimensional dynamic model; omega2DThe circular frequency of the two-dimensional dynamic model.
The circular frequency and the natural vibration frequency of the three-dimensional finite element model and the two-dimensional dynamic model can be obtained by solving the characteristic equation:
in the formula: f. of3DAnd ω3DRespectively a natural vibration frequency vector and a circular frequency vector of the three-dimensional finite element model; f. of2DAnd ω2DThe natural vibration frequency vector and the circular frequency vector of the two-dimensional dynamic model based on the initial stiffness parameters are respectively.
Step five: establishing an objective function for stiffness parameter correction
Because the rigidity of each node layer in the two-dimensional model is obtained by estimation according to related physical parameters, the natural frequency of the two-dimensional model established based on the rigidity is different from the natural frequency of the real structure to a certain extent, and the difference can be expressed as:
δR＝f2D-f3D(14)
self-vibration frequency f adopting two-dimensional power model based on perturbation method2DAnd the structural rigidity parameter EI and the rigidity sensitivity represent the natural vibration frequency of the two-dimensional dynamic model after the ith rigidity correction:
in the formula:
the initial natural vibration frequency of the two-dimensional dynamic model is obtained;
the two-dimensional dynamic model is subjected to the stiffness correction for i times; and S is the sensitivity of the natural vibration frequency of the two-dimensional dynamic model to the rigidity parameter EI.
The stiffness parameter correction process is actually a parameter optimization process and can be performed by adopting a mathematical optimization algorithm. The key is to establish an optimized objective function. The invention provides a stiffness parameter correction objective function J for forming a two-dimensional dynamic model, which can be expressed as a stiffness parameter weighting objective function J1And the natural frequency weighted objective function J2And (3) the sum:
J1(δEI)＝δEITWPδEI (16)
J2(δEI)＝(δR-SδEI)TWR(δR-SδEI) (17)
δEI＝EIi-EI0(18)
in the formula: wPWeighting a matrix for the stiffness parameters; wRIs a self-oscillation frequency weighting matrix.
Step six: stiffness parameter correction for two-dimensional dynamic analysis model
After the objective function is established, iterative optimization can be performed on the objective function:
Min J(δEI)＝Min{J1(δEI)+J2(δEI)} (19)
through multiple iterative optimization, the corrected rigidity parameter EI is obtainediRecalculating the natural vibration frequency of the two-dimensional dynamic model and comparing the calculated natural vibration frequency with the target frequency f3DComparing, repeating the steps until the obtained frequency difference norm meets the set convergence tolerance, and ending the iteration process:
in the formula: tol is a predetermined convergence tolerance greater than zero.
Therefore, the stiffness parameter variation of the two-dimensional dynamic model obtained after n iterations is determined to be delta EI:
step seven: establishing two-dimensional dynamic analysis model based on corrected stiffness parameters
After the variation delta EI of the stiffness parameter of the two-dimensional dynamic model is obtained, the stiffness parameter of the two-dimensional dynamic model can be determined as follows:
EIe＝EI0+δEI (22)
on the basis of determining the initial stiffness parameters of each node layer of the two-dimensional dynamic model, a stiffness matrix of each node layer can be established:
further, a rigidity matrix of the final two-dimensional dynamic model can be obtained by grouping rigidity matrixes of all node layers:
the characteristic equation of the two-dimensional dynamic model can be established as follows:
in the formula: keRespectively representing the rigidity matrixes of the final two-dimensional dynamic model;
the vibration mode of the final two-dimensional dynamic model is obtained; omegaeThe circular frequency of the final two-dimensional dynamic model.
And solving the equation to obtain the power characteristics of the high-rise television tower structure based on the two-dimensional power model. The dynamic response of the high-rise structure can be rapidly obtained based on the following motion equation:
in the formula: m, C and KeThe method comprises the steps that a quality matrix, a damping matrix and a rigidity matrix of a towering television tower structure based on a two-dimensional dynamic model are respectively provided; x (t),
And
is the displacement, velocity and acceleration response of the system; f (t) is the external load acting on the structure.
A two-dimensional dynamic model analysis system for a towering television tower structure is characterized by comprising the following components:
the node layer position and quantity analysis module of the two-dimensional dynamic model is used for concentrating the quality of all structural members and non-structural members of the high-rise television tower on the selected limited node layer and determining the set positions and the set quantity of the node layers;
the initial rigidity analysis module of the node layer is used for separating the finite element sub-models corresponding to the node layers from the integral three-dimensional finite element model, equivalent the finite element sub-models into a single-degree-of-freedom system and determining the rigidity coefficient of the finite element sub-models;
the rigidity matrix and quality matrix analysis module of the two-dimensional dynamic model is used for establishing a rigidity matrix of each node layer by adopting the rigidity coefficients of the node layers; then forming an integral rigidity matrix of the two-dimensional dynamic model through grouping, and establishing a concentrated mass matrix of the two-dimensional dynamic model;
the structure dynamic characteristic analysis module is used for respectively solving the natural vibration frequency of the original structure and the natural vibration frequency of the two-dimensional dynamic model based on the three-dimensional finite element model and the two-dimensional dynamic model;
and the rigidity parameter objective function analysis module is used for establishing a rigidity parameter weighting objective function and a natural vibration frequency weighting objective function and further establishing a rigidity parameter objective function of the two-dimensional dynamic model.
And the rigidity parameter correction module of the two-dimensional dynamic analysis model is used for carrying out iterative optimization on the objective function. Recalculating the natural vibration frequency of the two-dimensional dynamic model according to the obtained corrected stiffness parameter EI, and calculating the natural vibration frequency of the two-dimensional dynamic model and the target frequency f3DA comparison is made. And determining the rigidity parameter variation of the two-dimensional dynamic model obtained after iteration.
And the two-dimensional dynamic analysis model building module is used for building a rigidity matrix of the two-dimensional dynamic model by adopting the corrected rigidity parameters and quickly solving the dynamic characteristics and dynamic response of the towering structure based on the structural characteristic equation and the motion equation.
The following describes the specific implementation of the present patent in the case of a practical high-rise tv tower structure:
fig. 2 is a schematic structural diagram of a large-scale high-rise television tower, which is 340 m high and has comprehensive functions of broadcast television transmission and transmission, microwave communication, tour and sightseeing. The height of the tower is 255 m below a regular hexagonal space truss system, the height of the tower is a regular quadrilateral antenna mast above the regular hexagonal space truss system, and spherical tower descending and tower ascending are arranged at the positions with the elevation of more than 60 m and 220 m. The mass and rigidity of the television tower structure are extremely unevenly distributed along the height direction, most of the mass and rigidity of the structure are concentrated at the upper tower and the lower tower, the rigidity of an antenna mast which is connected with the upper tower and is as high as 80 meters is very small, and the whip tip effect is obvious. Firstly, a coordinate system of the towering television tower structure is established, wherein the two horizontal directions are respectively an X direction and a Y direction, and the vertical direction is a Z direction. The spatial finite element model of the structure has about 2000 nodes, 8000 units of division and 12000 degrees of freedom.
Firstly, according to the step 1), the mass of all structural components and non-structural components of the structure is concentrated on the selected 18 node layers, and the positions where the node layers are arranged are determined.
Separating the finite element sub-models corresponding to the node layers from the integral three-dimensional finite element model according to a formula (6), enabling the node layers to be equivalent to a single-degree-of-freedom system, and determining the initial value of equivalent stiffness of each node layer by solving the equivalent flexibility;
determining a rigidity matrix of each node layer in the two-dimensional power model according to a formula (8), forming an integral rigidity matrix of the two-dimensional power model according to a formula (9) set, and establishing a concentrated quality matrix of the two-dimensional power model according to a formula (10); determining the natural vibration frequency of the three-dimensional finite element model and the two-dimensional dynamic model according to the formulas (12) and (13);
determining a stiffness parameter weighting objective function and a natural vibration frequency weighting objective function according to formulas (16) and (17), and further establishing a stiffness parameter objective function of the two-dimensional dynamic model;
and writing a computer program according to the formula (19) and performing iterative optimization on the objective function. According to the obtained corrected rigidity parameter EIiRecalculating the natural vibration frequency of the two-dimensional dynamic model and comparing the calculated natural vibration frequency with the target frequency f3DA comparison is made. And repeating the steps until the obtained frequency difference norm meets the set convergence tolerance, and ending the iteration process. Determining the variable quantity of the stiffness parameter of the two-dimensional dynamic model obtained after iteration;
and (3) determining the corrected node layer rigidity parameters according to a formula (22), and establishing a rigidity matrix of the two-dimensional dynamic model by using the corrected rigidity parameters, thereby forming a two-dimensional dynamic analysis model of the towering television tower structure.
Table 1 gives the mass of the 18 nodal layers of the television tower structure and table 2 gives the initial stiffness of each nodal layer. Table 3 gives a comparison of the natural frequency of vibration for the three-dimensional finite element model and the initial two-dimensional dynamic model. The analysis result shows that: the initial rigidity of each node layer can reflect the rigidity characteristic of the high-rise television tower, but the initial rigidity is different from the accurate result. The first two order natural frequencies of the initial two-dimensional dynamic model differed from the three-dimensional finite element results by 15% and 54%. Obviously, the initial two-dimensional model has different rigidity, and a large error is generated if the initial two-dimensional model is used for analyzing the structural dynamic response. By adopting the two-dimensional dynamic model analysis method for the towering television tower structure, which is established by the invention, the rigidity of each node layer of the structure can be obtained through multiple iterative corrections, and a two-dimensional dynamic analysis model is established and the dynamic characteristics of the structure are calculated, as shown in table 4. Fig. 6 shows the structural first 3 order mode results based on a two-dimensional dynamic model. The analysis result shows that: the two-dimensional dynamic model obtained by the method has the natural frequency very close to the result of the three-dimensional finite element model. The dynamic characteristics of the structure can be accurately and effectively reflected, so that the accuracy and the effectiveness of the dynamic response analysis of the towering television tower structure can be ensured.
TABLE 1 television tower node layer concentration quality (kg)
Table 2 initial stiffness (n.m) of each node layer of the tv tower2)
TABLE 3 TV TOWER-FRONT 5 th order frequency comparison (Hz)
TABLE 4 two-dimensional Power model frequency comparison (Hz)
The concrete functions of each module in the high-rise television tower structure two-dimensional dynamic model analysis system can be realized by adopting the method.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (4)
1. A two-dimensional dynamic model analysis method for a towering television tower structure is characterized by comprising the following steps:
1) establishing a three-dimensional finite element model of the towering structure, determining the mass concentration positions of main structural components and non-structural components of the structure based on the three-dimensional finite element model, taking the mass concentration positions as node layers, and determining a two-dimensional dynamic model and the node layer positions and number of the two-dimensional dynamic model;
2) determining the initial rigidity of each node layer: separating the finite element sub-models corresponding to the node layers from the integral three-dimensional finite element model, and enabling the finite element sub-models to be equivalent to a single-degree-of-freedom system and determining the equivalent stiffness of the single-degree-of-freedom system;
determining the initial rigidity of the ith node layer in the step 2) by the following formula:
wherein the content of the first and second substances,
wherein, KiThe initial rigidity of the ith node layer;
is the average displacement of the ith node layer; fiApplying a total horizontal load to the upper part of the finite element sub-model of the ith node layer; n isiThe number of plane nodes on the upper part of the finite element sub model of the ith node layer is counted; x is the number ofmHorizontally displacing each node on the top of the sub-model under the action of horizontal load;
initial bending stiffness EI of i-th node layer0Comprises the following steps:
wherein: l isiIs the height of the node layer, KiThe initial rigidity of the ith node layer;
3) determining a rigidity matrix and a quality matrix of the two-dimensional dynamic model according to the initial rigidity of each node layer;
4) determining the dynamic characteristics of the three-dimensional finite element model and the two-dimensional dynamic model;
the dynamic characteristics of the three-dimensional finite element model and the two-dimensional dynamic model in the step 4) are as follows:
in the formula: m3DAnd K3DRespectively a mass matrix and a rigidity matrix of the three-dimensional finite element model;
the mode shape of the three-dimensional model is taken as the mode shape; omega3DIs the circular frequency of the three-dimensional model; m and K0Respectively a mass matrix and an initial stiffness matrix of the two-dimensional dynamic model;
the vibration mode is a two-dimensional dynamic model; omega2DIs the circular frequency of the two-dimensional dynamic model;
5) establishing a stiffness parameter correction objective function;
the objective function of stiffness parameter correction in the step 5) is established as follows:
J1(δEI)＝δEITWPδEI
J2(δEI)＝(δR-SδEI)TWR(δR-SδEI)
in the formula: wPWeighting a matrix for the stiffness parameters; wRWeighting matrix for self-oscillation frequency; δ R is a self-vibration frequency error vector of the two-dimensional model and the three-dimensional model; s is the sensitivity of the natural vibration frequency of the two-dimensional dynamic model to the rigidity parameter EI;
6) correcting the rigidity parameter of the two-dimensional dynamic analysis model;
the stiffness parameter correction quantity delta EI of the two-dimensional dynamic model in the step 6) is determined by adopting the following formula:
in the formula: wPWeighting a matrix for the stiffness parameters; wRWeighting matrix for self-oscillation frequency; δ R is a self-vibration frequency error vector of the two-dimensional model and the three-dimensional model; s is the sensitivity of the natural vibration frequency of the two-dimensional dynamic model to the rigidity parameter EI;
7) and establishing a two-dimensional dynamic analysis model based on the corrected stiffness parameters, and solving the dynamic characteristics and dynamic response of the towering structure based on a structural characteristic equation and a motion equation.
2. The method for analyzing the two-dimensional dynamic model of the tower structure of the towering television as claimed in claim 1, wherein the stiffness matrix K of the two-dimensional dynamic model in the step 3) is0And the quality matrix M is formulated as follows:
M＝diag[m1,m2...mi...mnt]
in the formula: m isiIs the collective quality of the ith node level, ntNumber of node layers, K, for a two-dimensional power modeliIs the initial stiffness of the ith node layer.
3. The method for analyzing two-dimensional dynamic model of towering television tower structure as claimed in claim 1, wherein the corrected stiffness parameter EI of the two-dimensional dynamic model is determined in step 6) according to the following formulae：
EIe＝EI0+δEI；
Wherein, EI0And delta EI is the initial bending rigidity of the ith node layer, and is the rigidity parameter correction quantity of the two-dimensional dynamic model.
4. A two-dimensional dynamic model analysis system for a towering television tower structure is characterized by comprising the following components:
the node layer position and quantity analysis module of the two-dimensional dynamic model is used for establishing a three-dimensional finite element model of the towering structure, centralizing the quality of all structural members and non-structural members of the towering television tower in a preset node layer, and determining the set position and the set quantity of the node layer of the two-dimensional dynamic model;
the initial rigidity analysis module of the node layer is used for separating the finite element sub-models corresponding to the node layers from the integral three-dimensional finite element model, equivalent the finite element sub-models into a single-degree-of-freedom system and determining the rigidity parameters of the finite element sub-models;
the rigidity matrix and quality matrix analysis module of the two-dimensional dynamic model is used for establishing a rigidity matrix of each node layer by adopting the rigidity parameters of the node layers; then forming an integral rigidity matrix of the two-dimensional dynamic model through grouping, and establishing a concentrated mass matrix of the two-dimensional dynamic model;
the structure dynamic characteristic analysis module is used for respectively solving the natural vibration frequency of the original structure and the natural vibration frequency of the two-dimensional model by adopting a three-dimensional finite element model and a two-dimensional dynamic model;
the rigidity parameter objective function analysis module is used for establishing a rigidity parameter weighting objective function and a natural vibration frequency weighting objective function and further establishing a rigidity parameter objective function of the two-dimensional dynamic model;
the stiffness parameter correction module of the two-dimensional dynamic analysis model is used for carrying out iterative optimization on the objective function; recalculating the natural vibration frequency of the two-dimensional dynamic model according to the obtained corrected stiffness parameter EI, and comparing the natural vibration frequency with a target frequency, thereby determining the stiffness parameter variation of the two-dimensional dynamic model obtained after iteration;
and the two-dimensional dynamic analysis model building module is used for building a rigidity matrix of the two-dimensional dynamic model by adopting the corrected rigidity parameters and quickly solving the dynamic characteristics and dynamic response of the towering structure based on the structural characteristic equation and the motion equation.
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