CN106354910B - A kind of structure master mode towards active phase array antenna determines method - Google Patents
A kind of structure master mode towards active phase array antenna determines method Download PDFInfo
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Abstract
The invention discloses a kind of, and the structure master mode towards active phase array antenna determines method, comprising: 1) parameter for determining active phase array antenna establishes the finite element model of antenna；2) natural antenna frequency, Mode Shape are obtained by model analysis；3) antenna deformation under load is analyzed；4) the corresponding output energy of antenna structure mode is calculated；5) antenna structure mode is truncated according to energy required precision；6) mode corresponds to energy proportion after finding out truncation；7) the corresponding state space equation of mode after being truncated is established；8) 2 norms of transmission function corresponding to mode after calculating truncation according to the state space equation parameter of mode after truncation；9) the synthesis norm of mode after being truncated is calculated；10) the synthesis norm of mode after truncation is arranged from big to small and carries out master mode selection, obtain the structure master mode of active phase array antenna.The present invention can instruct the Dynamic Modeling of active phase array antenna and be directed toward to control, to ensure antenna military service performance.
Description
Technical field
The invention belongs to microwave antenna art fields, and in particular to a kind of structure master mode towards active phase array antenna
Determine method.The present invention can be used for determining the structure master mode of active phase array antenna, be the dynamic of subsequent active phase array antenna
Mechanical modeling lays the foundation with control is directed toward, to ensure antenna military service performance.
Background technique
Active phase array antenna is quickly to be scanned with antenna beam, wave beam just in the new technology of accelerated development in recent years
The technologies such as flexible shapes, signal power space combination are that radar development opens broader space.Active phased array day at present
Line is widely used in the fields such as airborne early warning, spaceborne imaging, ground air defense, becomes the mainstream of current radar development.
With the continuous development and variation of military requirement, active phase array antenna is mainly towards ultra wide band, multi-functional, lightweight
Develop with high performance direction.Active phase array antenna itself is a complicated flexible structure, as antenna is towards lightweight side
To development, when it is acted on by extraneous load, active phase array antenna is more easy to produce vibration, vibrates to active phased array day
Line influence is also more and more obvious.Flexible deformation thus must be taken into consideration when carrying out Dynamic Modeling to active phase array antenna
Influence, focus on how flexible deformation being described.Currently, being directed to large and complex structure, mainly sat using mode
Its flexible deformation is described in mark method.But for active phase array antenna, since its structure is complicated, discretization posterior nodal point
Very more with number of unit, corresponding modal components can also become complex, therefore, how choose from complicated mode set
The structure master mode of Dynamic Modeling is influenced, lays the foundation for subsequent kinetic model of establishing, is the common face of domestic and international researcher
One of the problem of facing.
Currently, domestic and foreign scholars are when structure master mode is chosen, there are mainly two types of methods: (1) utilizing 2 models of transmission function
Number is used as performance indicator, carries out the selection of structure master mode, such as Gawronski, Modeling and control of antenna
The structure master mode introduced in and telescope, springer, 2008. determines method, is exactly 2 norms with transmission function
As performance indicator, Analysis Mode and its correlation carry out the selection of structure master mode to the influence degree of the index accordingly, but
This method does not consider that mode corresponds to energy proportion.(2) it is chosen using the structure master mode that energy criterion carries out antenna, such as
Cui Lingli, Zhang Jianyu, Gao Lixin, Xiao Zhiquan, the flexible mechanical arm modal reduction based on energy criterion, Journal of System Simulation,
2007,19 (5) establish the energy criterion based on energy norm in 1011-1014, are truncated energy criterion as system mode
Standard, the judgment criteria being truncated as structural modal, but the party are contributed using the degree of convergence of energy response information or energy
Method does not consider the influence size that mode exports system.
Therefore, it is necessary to which mode is corresponded to influence that energy proportion and mode export system while being carried out comprehensive
It closes and measures, the method that energy proportion is combined with 2 norms of transmission function is corresponded to using mode to determine active phased array
The structure master mode of antenna lays the foundation for the Dynamic Modeling of active phase array antenna with control is directed toward.
Summary of the invention
Based on the above issues, the present invention mutually ties the corresponding energy proportion of mode and 2 norm of transmission function of mode
Conjunction forms the corresponding comprehensive norm of mode, by calculating the synthesis norm of mode, to determine the structure master of active phase array antenna
Mode lays the foundation for the Dynamic Modeling of active phase array antenna with control is directed toward.
Realizing the technical solution of the object of the invention is, a kind of structure master mode towards active phase array antenna is determining
Method, this method include the following steps:
(1) structural parameters and material properties for determining active phase array antenna establish active phased array using ANSYS software
The finite element model of antenna；
(2) model analysis is carried out using finite element model of the ANSYS software to active phase array antenna, and according to mode point
Analysis is as a result, extracting includes natural antenna frequency wiMode Shape corresponding with itsPreceding 100 rank mode；
(3) using ANSYS software to active phase array antenna carry out deformation under load analysis, and according to loading analysis as a result,
Extract the displacement z (t) of each node of active phase array antenna after having deformation；
(4) load acquired in conjunction with the structural parameters of active phase array antenna, step (3) acts on lower active phase array antenna
The corresponding Mode Shape of natural antenna frequency that the displacement of each node and step (2) acquire, it is corresponding to find out antenna structure mode
Export energy；
(5) energy required precision is combined, the structural modal of active phase array antenna is truncated；
(6) energy according to corresponding to mode after truncation, mode corresponds to energy proportion after acquiring truncation；
(7) the corresponding state space equation of mode after being truncated is established；
(8) according to the state space equation parameter of mode after truncation, 2 of transmission function corresponding to mode after being truncated are calculated
Norm；
(9) 2 norms of transmission function, and the corresponding energy institute accounting of mode after truncation are corresponded in conjunction with mode after truncation
Weight calculates the synthesis norm of mode after truncation；
(10) by the synthesis norm of mode after truncation according to arranging from big to small, according to the numerical value of modal synthesis norm
It is required that carrying out master mode selection, the structure master mode of active phase array antenna is obtained.
In the step (1), the structural parameters of active phase array antenna, the row including antenna aperture, front radiating element
Number, columns, cell spacing and T/R component, cold plate, front frame and mounting framework；The material of the active phase array antenna
Attribute includes density, elasticity modulus and Poisson's ratio.
In the step (3), determine the load f (t) that active phase array antenna is subject to, institute is loaded include antenna self weight,
Vibration and wind lotus.
The corresponding output energy of antenna structure mode is calculated in the step (4), is included the following steps:
The active phase array antenna finite element model that (4a) utilizes ANSYS to establish, extracts the knot of active phase array antenna
Structure stiffness matrix, K structure mass matrix M and structural damping battle array C；
(4b) is intrinsic according to the structural stiffness matrix K of active phase array antenna, architecture quality matrix M and with the i-th rank of antenna
Frequency wiCorresponding Mode ShapeThe corresponding rigidity k of antenna the i-th rank mode can be obtainediWith quality mi:
In formula, T is matrix transposition symbol；
(4c) acts on the displacement z (t) of lower each node of antenna according to obtained load, corresponding with antenna the i-th rank intrinsic frequency
Mode ShapeLoad can be obtained and act on the lower corresponding modal displacement z of the i-th rank of antenna modei(t) and speed
(4d) is according to the corresponding rigidity k of antenna the i-th rank modei, quality miAnd load acts on lower the i-th rank of antenna mode pair
The modal displacement z answeredi(t) and speedPreceding n (1 n≤100 <) the corresponding energy of rank mode and J can be obtainedn:
(4e) is according to the corresponding energy of n rank mode and J before antennanAnd the corresponding energy of preceding n-1 rank mode and Jn-1, can
Find out the corresponding ENERGY E of active phase array antenna n-th order moden:
In formula, kn、mnThe respectively corresponding rigidity of n-th order mode and quality, zn(t)、Respectively under load effect
The corresponding modal displacement of antenna n-th order mode and speed.
According to energy required precision in the step (5), the structural modal of active phase array antenna is truncated, including
Following step:
N before (5a) is calculated, (1 n≤100 <) the corresponding energy of rank mode and JnAnd the (n+1)th corresponding energy of rank mode
En+1；
(5b) is if the corresponding ENERGY E of the (n+1)th rank moden+1Energy corresponding with preceding n rank mode and JnCompared to less than 1%,
I.e.Then think that n is exactly the rank number of mode n for needing to be truncatedj；Otherwise n=n+1 repeats (5a)~(5b), until looking for
To the rank number of mode n of truncationj, the structural modal of active phase array antenna is truncated.
Mode corresponds to energy proportion after calculating truncation in the step (6), includes the following steps:
Energy corresponding to i-th rank mode after (6a) calculating truncation:
Wherein, rank number of mode i is less than the rank number of mode n of truncationj(i≤nj), ki、miRespectively the i-th rank mode is corresponding just
Degree and quality, zi(t)、The lower corresponding modal displacement of the i-th rank of antenna mode and speed are acted on for load.
The corresponding energy proportion of i-th rank mode of (6b) truncation:
In formula, EiFor the corresponding energy of the i-th rank mode of truncation,For preceding njThe corresponding energy of rank mode and.
The corresponding state space equation of mode after being truncated is established in the step (7), is included the following steps:
(7a) establishes the corresponding state space equation of the i-th rank mode after truncation:
Y=Cix(t)
In formula, x (t) is state vector；U (t) is the structural excitation vector that antenna is subject to, the load f (t) etc. that antenna is subject to
In structural excitation vector u (t) and input matrix B that antenna is subject to0Product (f (t)=B0u(t))；Y is the antenna section to be obtained
The displacement of point；Ai、BiAnd CiThe corresponding sytem matrix of respectively the i-th rank modal vibration equation, input matrix and output matrix；
The state vector of (7b) selection state space equationzi(t)、For load work
With the corresponding modal displacement of lower the i-th rank of antenna mode and speed, then the state space equation parameter of the i-th rank mode, sytem matrix
Ai, input matrix Bi, output matrix CiIt respectively indicates are as follows:
In formula, I is unit battle array, wiFor the corresponding natural antenna frequency of the i-th rank mode, ζiFor the damping ratio system of the i-th rank mode
Number；
In formula,It is the corresponding Mode Shape of the i-th rank intrinsic frequency, matrix B0It is and the relevant input loaded of antenna institute
Matrix；T is matrix transposition symbol；BmiFor the corresponding mode input matrix of the i-th rank mode；
Coq、CovRefer respectively to the displacement output matrix and speed output matrix of active phase array antenna；Cmqi、CmviPoint
It Wei not the corresponding displacement output matrix of the i-th rank mode and speed output matrix.
According to the state space equation parameter of mode after truncation in the step (8), calculate after being truncated corresponding to mode
2 norms of transmission function, include the following steps:
According to the state space equation parameter of the i-th rank mode of truncation, transmitting corresponding to the i-th rank mode of truncation is calculated
2 norms of function:
||Gi(wi)2=| | Ci(jwiI-Ai)-1Bi||2
In formula, I is unit battle array, Ai、BiAnd CiIt is the sytem matrix of the corresponding modal state space equation of respectively the i-th rank, defeated
Enter matrix and output matrix；J is imaginary symbols；wiFor antenna the i-th rank intrinsic frequency.
The synthesis norm of the i-th rank mode in the step (9) after truncation is calculate by the following formula:
γi=λi||Gi(wi)||2
Wherein, λiFor the corresponding energy proportion of the i-th rank mode after truncation；||Gi(wi)||2For i-th after truncation
Corresponding 2 norm of transmission function of rank mode.
The structure master mode that active phase array antenna is determined in the step (10), includes the following steps:
(10a) arranges the synthesis norm of mode from big to small:
γa1≥γa2≥γa3...≥γan (a1,a2,a3...an≤nj)
(10b) is according to comprehensive norm numerical requirements, according to the sequence of comprehensive norm from big to small, k comprehensive model before choosing
Number: γa1, γa2, γa3...γakStructure master mode of the corresponding mode as active phase array antenna.
Compared with prior art, the present invention having the following characteristics that
It is combined 1. mode is corresponded to 2 norm of transmission function and corresponds to energy proportion with mode, introduces modal synthesis model
Number can determine the structure master mode of active phase array antenna according to the size of the corresponding comprehensive norm of mode.This method effectively solves
Traditional modal fails completely to consider the problems of modal synthesis influence factor in choosing.
2. mode truncation is carried out to active phase array antenna structure, then by mode pair first by energy required precision
2 norm of transmission function answered corresponds to energy proportion with mode and combines, and determines the structure master mode of active phase array antenna.
Can further it be reduced by using the dimension of this method active phase array antenna structural model, model calculation later period, meeting time
Greatly reducing, computational efficiency is improved, and the Dynamic Modeling of active phase array antenna lays the foundation with control is directed toward for after,
To ensure antenna military service performance.
Detailed description of the invention
Fig. 1 is the flow chart that a kind of structure master mode towards active phase array antenna of the present invention determines method；
Fig. 2 is the unit arrangement schematic diagram of active phase array antenna；
Fig. 3 is the structural schematic diagram of active phase array antenna；
Fig. 4 is the grid model of active phase array antenna in ANSYS software；
Fig. 5 is the constrained schematic diagram of active phase array antenna；
Fig. 6 is active phase array antenna random vibration acceleration power spectrum；
Fig. 7 is the random vibration Aberration nephogram of active phase array antenna.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments
Referring to Fig.1, the present invention is that a kind of structure master mode towards active phase array antenna determines method, and specific steps are such as
Under:
Step 1, the structural parameters and material properties for determining active phase array antenna establish active phase using ANSYS software
Control the finite element model of array antenna.
1.1. the structural parameters of active phase array antenna, including antenna aperture, (direction x, y) length L in front are determinedxWith
Width Ly, in front radiating element spacing d on the direction x, y of line number M, columns N, antenna elementx,dy(as shown in Figure 2),
Antenna element form, T/R component, cold plate, front frame and parameter of mounting framework etc..
1.2. determining active phase array antenna T/R component, the material properties of front frame, mounting framework and antenna element,
Including density, elasticity modulus and Poisson's ratio etc..
1.3. according to the structural parameters of active phase array antenna and material properties, active phase is established using ANSYS software
The finite element model of array antenna.
Step 2, active phase array antenna model analysis obtains natural antenna frequency, Mode Shape.
Model analysis is carried out to active phase array antenna using ANSYS software, and according to model analysis as a result, extracting day
100 rank mode before line, the intrinsic frequency w including antennaiAnd Mode Shape corresponding to intrinsic frequencyWherein i=1,
2,...100。
Step 3, active phase array antenna deformation under load is analyzed.
3.1 determine the load f (t) that active phase array antenna is subject to, and institute loaded includes antenna self weight, vibration, wind lotus etc..
3.2 carry out deformation under load analysis to active phase array antenna using mechanical analysis software ANSYS, and according to load point
Analysis is as a result, extract the displacement z (t) of each node of active phase array antenna after deformation.
Step 4, the corresponding output energy of antenna structure mode is calculated.
4.1. the active phase array antenna finite element model established using ANSYS, extracts the knot of active phase array antenna
Structure mass matrix M, structural stiffness matrix K and structural damping battle array C.
After being analyzed and processed using ANSYS software to active phase array antenna finite element model, active phased array can be obtained
The architecture quality matrix M and structural stiffness matrix K of antenna；Its damping ratio of general aluminium alloy structure, steel construction is in 0.02-
Between 0.05, since active phase array antenna structural material type is more, and to will affect structure whole for the connection between front and frame
The damping of body, thus it is 0.05 that this patent, which takes damping ratio, the structural damping Matrix C of active phase array antenna is then that matrix element is equal
For 0.05 diagonal matrix.
4.2. intrinsic according to the structural stiffness matrix K of active phase array antenna, architecture quality matrix M and with the i-th rank of antenna
Frequency wiCorresponding Mode ShapeThe corresponding rigidity k of antenna the i-th rank mode can be obtainediWith quality mi:
In formula, T is matrix transposition symbol.
4.3. the displacement z (t) that lower each node of antenna is acted on according to the load that step (3) obtains, with the intrinsic frequency of the i-th rank of antenna
The corresponding Mode Shape of rateLoad can be obtained and act on the lower corresponding modal displacement z of the i-th rank of antenna modei(t) and speed
4.4. according to the corresponding rigidity k of antenna the i-th rank modei, quality miAnd load acts on lower the i-th rank of antenna mode pair
The modal displacement z answeredi(t) and speedPreceding n (1 n≤100 <) the corresponding energy of rank mode and J can be obtainedn:
4.5. according to the corresponding energy of n rank mode and J before antennanAnd the corresponding energy of preceding n-1 rank mode and Jn-1, can
Find out the corresponding ENERGY E of active phase array antenna n-th order moden:
In formula, kn、mnThe respectively corresponding rigidity of n-th order mode and quality, zn(t)、Respectively under load effect
The corresponding modal displacement of antenna n-th order mode and speed.
Step 5, according to energy required precision, the structural modal of active phase array antenna is truncated.
5.1. n (1 n≤100 <) the corresponding energy of rank mode and J before calculatingnAnd the (n+1)th corresponding energy of rank mode
En+1。
5.2. if the corresponding ENERGY E of the (n+1)th rank moden+1Energy corresponding with preceding n rank mode and JnCompared to less than 1%,
I.e.Then think that n is exactly the rank number of mode n for needing to be truncatedj；Otherwise n=n+1 repeats (5.1)~(5.2), until looking for
To the rank number of mode n of truncationj, the structural modal of active phase array antenna is truncated.
Step 6, mode corresponds to energy proportion after calculating truncation.
6.1. energy corresponding to the i-th rank mode after being truncated is calculated:
Wherein, rank number of mode i is less than the rank number of mode n of truncationj(i≤nj), ki、miRespectively the i-th rank mode is corresponding just
Degree and quality, zi(t)、The lower corresponding modal displacement of the i-th rank of antenna mode and speed are acted on for load.
6.2. the corresponding energy proportion of the i-th rank mode being truncated:
In formula, EiFor the corresponding energy of the i-th rank mode of truncation,For preceding njThe corresponding energy of rank mode and.
Step 7, the corresponding state space equation of mode after being truncated is established.
7.1. the corresponding state space equation of the i-th rank mode after being truncated is established:
In formula, x (t) is state vector；U (t) is the structural excitation vector that antenna is subject to, the load f (t) etc. that antenna is subject to
In structural excitation vector u (t) and input matrix B that antenna is subject to0Product (f (t)=B0u(t))；Y is the antenna section to be obtained
The displacement of point；Ai、BiAnd CiThe corresponding sytem matrix of respectively the i-th rank modal vibration equation, input matrix and output matrix.
7.2. the state vector of state space equation is selectedzi(t)、For load effect
The corresponding modal displacement of lower the i-th rank of antenna mode and speed, then the state space equation parameter of the i-th rank mode, sytem matrix Ai、
Input matrix Bi, output matrix CiIt respectively indicates are as follows:
In formula, I is unit battle array, wiFor the corresponding natural antenna frequency of the i-th rank mode, ζiFor the damping ratio system of the i-th rank mode
Number, value 0.05.
In formula,It is the corresponding Mode Shape of the i-th rank intrinsic frequency, matrix B0It is and the relevant input loaded of antenna institute
Matrix；T is matrix transposition symbol；BmiFor the corresponding mode input matrix of the i-th rank mode.
In formula, Coq、CovRefer respectively to the displacement output matrix and speed output matrix of active phase array antenna；Cmqi、
CmviThe corresponding displacement output matrix of respectively the i-th rank mode and speed output matrix.
Step 8, according to the state space equation parameter of mode after truncation, transmission function corresponding to mode after being truncated is calculated
2 norms.
According to the state space equation parameter of the i-th rank mode of truncation, transmitting corresponding to the i-th rank mode of truncation is calculated
2 norms of function:
||Gi(wi)2=| | Ci(jwiI-Ai)-1Bi||2 (13)
In formula, I is unit battle array, Ai、BiAnd CiIt is the sytem matrix of the corresponding modal state space equation of respectively the i-th rank, defeated
Enter matrix and output matrix；J is imaginary unit；wiFor antenna the i-th rank intrinsic frequency.
Step 9, the synthesis norm of mode after being truncated is calculated.
According to corresponding 2 norm of transmission function of the i-th rank mode after truncation | | Gi(wi)||2And the i-th rank after truncation
The corresponding energy proportion λ of modei, the synthesis norm of the i-th rank mode after calculating truncation:
γi=λi||Gi(wi)||2 (14)
Step 10, by the synthesis norm of mode after truncation according to arranging from big to small, according to modal synthesis norm
Numerical requirements carry out master mode selection, obtain the structure master mode of active phase array antenna.
10.1. the synthesis norm of mode is arranged from big to small:
γa1≥γa2≥γa3...≥γan (a1,a2,a3...an≤nj)
10.2 according to comprehensive norm numerical requirements, according to the sequence of comprehensive norm from big to small, k comprehensive model before choosing
Number: γa1, γa2, γa3...γakStructure master mode of the corresponding mode as active phase array antenna.
Advantages of the present invention can be further illustrated by following emulation experiment:
One, the structural parameters of active phase array antenna are determined
In this example with rectangular grid equidistant in front arrangement, center operating frequency be f=2.5GHz (wavelength X=
For active phase array antenna 120mm), as shown in Figure 3.The line number and columns of the antenna element in the direction x and the direction y in front
M=N=3, spacing d of the antenna element on the direction x, yx=dy=0.5 λ=60mm.
The geometrical model parameter of 1 active phase array antenna of table
The material properties of 2 active phase array antenna of table
Two, the structure master mode of active phase array antenna is determined
1. establishing the structural finite element model of active phase array antenna
Active phase is established in ANSYS software according to the geometrical model size of active phase array antenna, material properties parameter
Control the structural finite element model of array antenna.Wherein, according to engineering reality, antenna is set according to the material parameter of aluminium alloy in table 2
The material properties of the carrier layers such as front frame and mounting bracket, according to the material of the material parameter setting antenna element of printed circuit board
Expect attribute.Carrier layer cell type is solid element SOLID92, and array element structure cell type is face cell S HELL63, carrier layer
It is connected with each other between array element, without relative displacement.To the geometric model of active phase array antenna, using ANSYS software
The free grid of setting carries out grid dividing, and the grid model for obtaining source phased array antenna is as shown in Figure 4.
2. applying constraint and load, natural antenna frequency, Mode Shape and the displacement for deforming each node of aft antenna are obtained
2.1 will be had according to the installation site of engineering bracket in practice using cantilever beam structure force analysis as shown in Figure 5
One end of source phased array antenna is fixed, as constraint condition；
2.2 carry out model analysis to active phase array antenna using ANSYS software, and according to model analysis as a result, mentioning
Take 100 rank mode before antenna, the intrinsic frequency w including antennaiAnd Mode Shape corresponding to intrinsic frequencyWherein i=
1,2,...100。
The 2.3 finite element model constraint conditions according to active phase array antenna and given random vibration acceleration power
Spectrum draws active phased array as shown in fig. 6, mechanical analysis software ANSYS carries out deformation under load analysis to active phase array antenna
The malformation cloud atlas of antenna, as shown in fig. 7, obtaining the displacement of each node of active phase array antenna after deformation.
3. mode truncation
3.1, according to formula (6) and step (3), can obtain energy corresponding to the i-th rank mode:
Wherein, ki、miThe corresponding rigidity of respectively the i-th rank mode and quality, zi(t)、Lower antenna the is acted on for load
The corresponding modal displacement of i rank mode and speed.
3.2, according to formula (6), (7), (15) and step (6), find the rank number of mode n of truncationj, to active phased array day
The structural modal of line is truncated.
4. determining structure master mode
4.1, according to formula (8), (13), calculate the synthesis norm of the i-th rank mode after being truncated:
In formula, njFor the rank number of mode of truncation；ki、miThe corresponding rigidity of respectively the i-th rank mode and quality；zi(t)、The lower corresponding modal displacement of the i-th rank of antenna mode and speed are acted on for load；I is unit battle array；Ai、BiAnd CiRespectively
Sytem matrix, input matrix and the output matrix of the corresponding modal state space equation of i rank.
4.2 arrange the synthesis norm of mode from big to small:
γa1≥γa2≥γa3...≥γan (a1,a2,a3...an≤nj)
4.3 according to comprehensive norm numerical requirements, according to the sequence of comprehensive norm from big to small, k comprehensive norm before choosing:
γa1,γa2,γa3...γakStructure master mode of the corresponding mode as active phase array antenna.
Three, result and analysis
The corresponding output energy of mode is obtained according to formula (15), in conjunction with step (3), the rank number of mode n that can must be truncatedj, right
The structural modal of active phase array antenna is truncated；The synthesis model for the i-th rank mode for recycling formula (16) to calculate after truncation
Number, is arranged the synthesis norm of mode after truncation according to sequence from big to small by step (11), according to modal synthesis
The numerical requirements of norm carry out master mode selection, obtain the structure master mode of active phase array antenna.
Table 3 is mode energy contrast table, wherein EnFor the corresponding energy of n-th order mode, JnFor the corresponding energy of preceding n rank mode
Amount and,It is expressed as the corresponding ENERGY E of the (n+1)th rank moden+1Energy corresponding with preceding n rank mode and JnRatio, from table 3
It can obtain the rank number of mode n of active phase array antenna truncationj=9.
Corresponding 2 norm of transmission function of mode is truncated, the synthesis norm of mode is truncated as shown in table 4, table 5.
3 mode energy contrast table of table
Corresponding 2 norm of transmission function of mode is truncated in table 4
The corresponding comprehensive norm of mode is truncated in table 5
According to the data (table 5) in the corresponding comprehensive norm contrast table of truncation mode, by the synthesis norm of mode after truncation
γiIt is arranged according to sequence from big to small: γ2> γ7> γ5> γ9> γ3> γ4> γ1> γ8> γ6, and according to
Comprehensive norm numerical requirements are greater than 6e-13, according to the sequence of comprehensive norm from big to small, choose preceding 7 comprehensive norm (γ2,
γ7,γ5,γ9,γ3,γ4,γ1) corresponding 2nd rank, the 7th rank, the 5th rank, the 9th rank, the 3rd rank, the 4th rank, the 1st rank mode conduct
The structure master mode of active phase array antenna.
Above-mentioned emulation experiment can be seen that and can carry out active phase array antenna mode using the present invention and correspond to energy, mould
State corresponds to the calculating of 2 norm of transmission function and the corresponding comprehensive norm of mode, can be used for determining the structure master of active phase array antenna
Mode, and then instruct the Dynamic Modeling of active phase array antenna.
Claims (9)
1. a kind of structure master mode towards active phase array antenna determines method, comprise the following processes:
(1) structural parameters and material properties for determining active phase array antenna establish active phase array antenna using ANSYS software
Finite element model；
(2) model analysis is carried out using finite element model of the ANSYS software to active phase array antenna, and according to model analysis knot
Fruit, extracting includes natural antenna frequency wiMode Shape corresponding with itsPreceding 100 rank mode；
(3) deformation under load analysis is carried out to active phase array antenna using ANSYS software, and according to loading analysis as a result, extracting
There is the displacement z (t) of each node of active phase array antenna after deforming；
(4) load acquired in conjunction with the structural parameters of active phase array antenna, step (3) acts on lower active phase array antenna and respectively saves
The corresponding Mode Shape of natural antenna frequency that the displacement and step (2) of point acquire, finds out the corresponding output of antenna structure mode
Energy；
(5) energy required precision is combined, the structural modal of active phase array antenna is truncated；
(6) energy according to corresponding to mode after truncation, mode corresponds to energy proportion after acquiring truncation；
(7) the corresponding state space equation of mode after being truncated is established；
(8) according to the state space equation parameter of mode after truncation, 2 models of transmission function corresponding to mode after being truncated are calculated
Number；
(9) 2 norms of transmission function, and the corresponding energy proportion of mode after truncation, meter are corresponded in conjunction with mode after truncation
Calculate the synthesis norm of mode after being truncated；
(10) by the synthesis norm of mode after truncation according to arranging from big to small, according to the numerical requirements of modal synthesis norm
Master mode selection is carried out, the structure master mode of active phase array antenna is obtained；
Step (7) carries out according to the following procedure:
(7a) establishes the corresponding state space equation of the i-th rank mode after truncation:
Y=Cix(t)
In formula, x (t) is state vector；U (t) is the structural excitation vector that antenna is subject to, and the load f (t) that antenna is subject to is equal to day
The structural excitation vector u (t) and input matrix B that line is subject to0Product (f (t)=B0u(t))；Y is the antenna node to be obtained
Displacement；Ai、BiAnd CiThe corresponding sytem matrix of respectively the i-th rank modal vibration equation, input matrix and output matrix；
The state vector of (7b) selection state space equationzi(t)、Lower day is acted on for load
The corresponding modal displacement of line the i-th rank mode and speed, then the state space equation parameter of the i-th rank mode, sytem matrix Ai, input
Matrix Bi, output matrix CiIt respectively indicates are as follows:
In formula, I is unit battle array, wiFor the corresponding natural antenna frequency of the i-th rank mode, ζiFor the damping to coefficient of the i-th rank mode；
In formula,It is the corresponding Mode Shape of the i-th rank intrinsic frequency, matrix B0It is and antenna institute relevant input matrix loaded；
T is matrix transposition symbol；BmiFor the corresponding mode input matrix of the i-th rank mode；
Coq、CovRefer respectively to the displacement output matrix and speed output matrix of active phase array antenna；Cmqi、CmviRespectively
The corresponding displacement output matrix of i rank mode and speed output matrix.
2. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In in step (1), the structural parameters of active phase array antenna include antenna aperture, the line number of front radiating element, columns and list
First spacing and T/R component, cold plate, front frame and mounting framework；The material properties of the active phase array antenna include close
Degree, elasticity modulus and Poisson's ratio.
3. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In in step (3), determining the load f (t) that active phase array antenna is subject to, institute loaded includes antenna self weight, vibration and wind
Lotus.
4. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In step (4) carries out according to the following procedure:
The active phase array antenna finite element model that (4a) utilizes ANSYS to establish, the structure for extracting active phase array antenna are rigid
Spend matrix K, architecture quality matrix M and structural damping Matrix C；
(4b) according to the structural stiffness matrix K of active phase array antenna, architecture quality matrix M and with antenna the i-th rank intrinsic frequency wi
Corresponding Mode ShapeThe corresponding rigidity k of antenna the i-th rank mode can be obtainediWith quality mi:
In formula, T is matrix transposition symbol；
(4c) acts on the displacement z (t) of lower each node of antenna according to obtained load, with antenna the i-th rank intrinsic frequency wiCorresponding mould
The state vibration shapeLoad can be obtained and act on the lower corresponding modal displacement z of the i-th rank of antenna modei(t) and speed
(4d) is according to the corresponding rigidity k of antenna the i-th rank modei, quality miAnd lower the i-th rank of the antenna mode of load effect is corresponding
Modal displacement zi(t) and speedThe corresponding energy of n rank mode and J before can obtainingn, wherein 1 n≤100 <:
(4e) is according to the corresponding energy of n rank mode and J before antennanAnd the corresponding energy of preceding n-1 rank mode and Jn-1, can find out
The corresponding ENERGY E of active phase array antenna n-th order moden:
In formula, kn、mnThe respectively corresponding rigidity of n-th order mode and quality, zn(t)、Respectively load acts on lower antenna the
The corresponding modal displacement of n rank mode and speed.
5. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In step (5) carries out according to the following procedure:
The corresponding energy of n rank mode and J before (5a) is calculatedn, wherein 1 n≤100 <；And the (n+1)th corresponding energy of rank mode
En+1；
(5b) is if the corresponding ENERGY E of the (n+1)th rank moden+1Energy corresponding with preceding n rank mode and JnCompared to less than 1%, i.e.,Then think that n is exactly the rank number of mode n for needing to be truncatedj；Otherwise n=n+1 repeats (5a)~(5b), cuts until finding
Disconnected rank number of mode nj, the structural modal of active phase array antenna is truncated.
6. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In step (6) carries out according to the following procedure:
Energy corresponding to i-th rank mode after (6a) calculating truncation:
Wherein, rank number of mode i is less than the rank number of mode n of truncationj(i≤nj), ki、miThe corresponding rigidity of respectively the i-th rank mode and
Quality, zi(t)、The lower corresponding modal displacement of the i-th rank of antenna mode and speed are acted on for load；
The corresponding energy proportion of i-th rank mode of (6b) truncation:
In formula, EiFor the corresponding energy of the i-th rank mode of truncation,For preceding njEnergy corresponding to rank mode and.
7. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In step (8) is calculated corresponding to the i-th rank mode of truncation according to the state space equation parameter of the i-th rank mode of truncation
2 norms of transmission function:
||Gi(wi)||2=| | Ci(jwiI-Ai)-1Bi||2
In formula, I is unit battle array, Ai、BiAnd CiSytem matrix, the input square of the corresponding modal state space equation of respectively the i-th rank
Battle array and output matrix；J is imaginary unit；wiFor antenna the i-th rank intrinsic frequency.
8. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In in step (9), the synthesis norm of the i-th rank mode after truncation is calculate by the following formula:
γi=λi||Gi(wi)||2
Wherein, λiFor the corresponding energy proportion of the i-th rank mode after truncation；||Gi(wi)||2For the i-th rank mode after truncation
Corresponding 2 norm of transmission function.
9. a kind of structure master mode towards active phase array antenna according to claim 1 determines that method, feature exist
In step (10) carries out according to the following procedure:
(10a) arranges the synthesis norm of mode from big to small:
γa1≥γa2≥γa3...≥γan
Wherein, a1, a2, a3...an≤nj；
(10b) is according to comprehensive norm numerical requirements, according to the sequence of comprehensive norm from big to small, k comprehensive norm before choosing:
γa1,γa2,γa3...γakStructure master mode of the corresponding mode as active phase array antenna.
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