CN102890741B - Method for predicting influence of vibration deformation on electric performance of array antenna - Google Patents

Method for predicting influence of vibration deformation on electric performance of array antenna Download PDF

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CN102890741B
CN102890741B CN201210414471.8A CN201210414471A CN102890741B CN 102890741 B CN102890741 B CN 102890741B CN 201210414471 A CN201210414471 A CN 201210414471A CN 102890741 B CN102890741 B CN 102890741B
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array antenna
antenna
array
radiating element
random vibration
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CN102890741A (en
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王从思
李兆
普涛
王伟
康明魁
王猛
段宝岩
黄进
保宏
王艳
宋立伟
李鹏
李娜
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Xidian Univ
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Abstract

The invention discloses a method for predicting influence of vibration deformation on electric performance of an array antenna. The method comprises the following steps of: 1) determining a geometric model file of the array antenna; 2) establishing a finite element model of the array antenna in ANSYS; 3) presetting an acceleration power spectrum, calculating random vibration deformation, and extracting position offset of each radiation unit; 4) calculating a pattern function of the array antenna; and 5) judging whether the pattern function satisfies design requirements. According to the conventional method, whether the structure strength of the antenna satisfies the requirement is analyzed according to the acceleration power spectrum, and the electrical performance cannot be determined according to array plane deformation errors. The method provided by the invention can realize the prediction on the electrical performance of the antenna according to the offset caused by random vibration; the method provided by the invention is more succinct, can introduce the offset into an electromechanical coupling model to calculate the electrical performance, and does not need to repeat electromagnetic modeling according to the change of the offset; and the method provided by the invention is used for analyzing the influence of vibration on the antenna and finding main structural factors, thereby ensuring that the antenna is protected from being damaged, and the electrical performance of the antenna in a working state is improved.

Description

A kind of Forecasting Methodology of vibration deformation pair array antenna electric performance impact
Technical field
The present invention relates to antenna technical field, the Forecasting Methodology of specifically a kind of vibration deformation pair array antenna electric performance impact.
Background technology
Array antenna technique is the state-of-the-art technology developed in recent years.Array antenna changes the antenna of pattern shapes by the current feed phase of radiating element in control array antenna.Control phase can change the sensing of antenna radiation pattern maximal value, to reach the object of beam scanning.Under special circumstances, the shape of minor level, minimum value position and whole directional diagram can also be controlled.Mechanically during rotating antenna, inertia is large, speed is slow, and array antenna overcomes this shortcoming, and the sweep velocity of wave beam is high.As active phase array antenna the most advanced in array antenna, just there is this outstanding feature of array antenna.Its current feed phase generally uses the computer controlled system of electronics, phase place pace of change fast (millisecond magnitude), and namely the change of the sensing of antenna radiation pattern maximal value or other parameters is rapid.Be the maximum feature of active phase array antenna to sweep that alternative machine sweeps mutually, this mertialess beam scanning, gives active phase array antenna many excellent properties.
When airborne array antenna real work, because aircraft platform motion causes antenna generation random vibration, and then cause front structure to deform, antenna electric performance finally must be caused to change.In existing research, mechanical aspects mainly concentrates on the research of random vibration to antenna structure Effect on Mechanical Properties, and calculate stochastic error when antenna electric performance is affected, Most scholars thinks that the stochastic error of antenna obeys certain probability distribution, can not affect produced error by actual response antenna structure by random vibration.
Therefore, be necessary to propose exactly the requirement of Antenna Construction Design according to the index request of antenna electric performance to overcome the impact of random vibration.After carrying out array antenna random vibration analysis, grasp antenna structure random vibration to the impact of antenna electric performance.By setting up the relation influencing each other, mutually restrict between array antenna structure design and Electromagnetic Design, utilize mechanical-electric coupling method to predict the antenna electric performance under the various organization plans under airborne vibration effect.
Summary of the invention
The object of this invention is to provide the Forecasting Methodology of a kind of vibration deformation pair array antenna electric performance impact, the method is by setting up the electromechanical Coupling Model of array antenna, grasp the impact of array antenna structure random vibration pair array antenna electric performance, to realize the electrical property prediction based on dynamo-electric two couplings of array antenna, in order to instruct its structural design.
The present invention is by realizing with following technical proposals:
The Forecasting Methodology of vibration deformation pair array antenna electric performance impact, the method comprises the steps:
1) according to structural parameters and the material properties of array antenna, the geometric model parameter of array antenna is determined;
2) in ANSYS, build the structural finite element model of array antenna;
3) constraint condition of given array antenna structure finite element model and airborne random vibration acceleration power spectrum, computing array antenna random vibration deflection, extract the position offset of each radiating element Centroid on x, y, z direction of array antenna finite element model respectively;
4) according to array antenna finite element model radiating element Centroid position offset, utilize electromechanical Coupling Model, obtain array aerial direction figure function, and draw array aerial direction figure;
5) according to the electrical performance indexes requirement of array antenna, judge whether the array antenna electrical property calculated meets the demands, if met the demands, then array antenna structure design is qualified; Otherwise, the structural parameters of amendment array antenna, and repeat step 1) to step 4), until meet the demands.
The structural parameters of described step 1) array antenna comprise the parameter of cold drawing, radiating element, T/R assembly and front framework.
The material properties of described step 1) array antenna comprises elastic modulus, Poisson ratio and density.
The position offset of each radiating element Centroid on x, y, z direction of described step 3) array antenna finite element model is (Δ x 0,0, Δ y 0,0, Δ z 0,0) ... (Δ x mn, Δ y mn, Δ z mn), wherein M × each radiating element N number of is by equidistant rectangular grid battle array arrangement, and m is the natural number between 0 ~ M-1, and represent the numbering of array antenna M row radiating element, n is the natural number between 0 ~ N-1, represents the numbering of the capable radiating element of array antenna N.
Calculate array aerial direction figure function in described step 4) to carry out according to the following formula:
4a) establish array antenna to have M × N number of radiating element to arrange by equidistant rectangular grid battle array, spacing horizontal and vertical between unit is respectively d xwith d y; Observation point P is relative to the direction at rectangular coordinate system xyz place (cos α is expressed as with direction cosine x, cos α y, cos α z), obtain the angle of observation point P relative to coordinate axis and the relation of direction cosine thus:
4b) order is (Δ x by the position offset of (m, n) radiating element on x, y, z direction in M × N number of radiating element of equidistant rectangular grid battle array arrangement mn, Δ y mn, Δ z mn), the position offset of (0,0) radiating element on x, y, z direction is (Δ x 0,0, Δ y 0,0, Δ z 0,0), then the phase difference φ of (m, n) radiating element relative (0,0) radiating element mnfor:
Δφ mn=k(md x+Δx mn-Δx 0,0)cosα x+k(nd y+Δy mn-Δy 0,0)cosα y
+k(Δz mn-Δz 0,0)cosα zmn
In formula, for the wave constant of array antenna, λ is the operation wavelength of array antenna, β mnbe (m, n) radiating element battle array in phase differential;
4c) according to array antenna superposition principle, by 4b) obtain array aerial direction figure function and be:
+ ( nd y + Δ y mn - Δ y 0,0 ) cos α y + ( Δ z mn - Δ z 0,0 ) cos α z ] + j β mn }
In formula, E efor the pattern function of antenna element, I mnit is element excitation electric current.
Described step 4) draws array aerial direction figure, antenna gain, E face minor level, E face half power lobe width and E face beam position side-play amount is obtained from array aerial direction figure, and H face minor level, H face half power lobe width and H face beam position side-play amount.
The present invention compared with prior art, has following characteristics:
1. utilize the structural finite element model of array antenna to carry out finite element analysis, determine the position offset that array antenna random vibration causes, and then realize the prediction of pair array antenna electric performance.Whether classic method can only meet not destroyed requirement according to the structural strength of the acceleration power spectrumanalysis array antenna of random vibration, and the wavefront distortion error that cannot cause according to random vibration determines array antenna electrical property in working order.Compare classic method, the position offset that this method can be caused by random vibration realizes the prediction of the electrical property of pair array antenna;
2. to compare classic method process more simple and direct for the method, obtained random vibration position offset directly can be introduced electromechanical Coupling Model, thus calculate the electrical property of array antenna, do not need the change according to random vibration position offset, repeat to carry out Electromagnetic Modeling to calculate electrical property to antenna;
3. by the mechanical-electric coupling problem of research array antenna, analyze random vibration to the impact of Antenna Operation performance, wherein main structural reason revising can be found out, not only can ensure that structure is not destroyed, the electrical property under Antenna Operation state can also be improved on the basis of improving structure.
Accompanying drawing explanation
Fig. 1 is array antenna mechanical-electric coupling analysis process figure of the present invention.
Fig. 2 is array antenna radiating element arrangement schematic diagram.
Fig. 3 observation point P is relative to the space geometry graph of a relation of coordinate system xyz.
Fig. 4 is active phase array antenna geometric model figure.
Fig. 5 is active phase array antenna structural finite element model figure.
Fig. 6 active phase array antenna random vibration acceleration power spectrum.
Fig. 7 active phase array antenna random vibration time history sample.
Fig. 8 active phase array antenna malformation cloud atlas.
Fig. 9 (a) half-wave a period of time E face directional diagram.
Fig. 9 (b) half-wave a period of time H face directional diagram.
Active phase array antenna electrical property comparison diagram before and after Figure 10 (a) E facial disfigurement.
Active phase array antenna electrical property comparison diagram before and after Figure 10 (b) H facial disfigurement.
Embodiment
Below in conjunction with drawings and Examples, the present invention will be further described.
With reference to shown in Fig. 1, the Forecasting Methodology of vibration deformation pair array antenna electric performance impact of the present invention, step is as follows:
Step one, determines the geometric model file of array antenna
According to structural parameters and the material properties of array antenna, determine the geometric model parameter of array antenna, wherein, the structural parameters of array antenna comprise the parameter of cold drawing, radiating element, T/R assembly and front framework, and the material properties of array antenna comprises elastic modulus, Poisson ratio and density.
Step 2, builds its finite element model in ANSYS
In ANSYS, build its finite element model, the structural unit types of cold drawing and T/R assembly is solid element SOLID45, and the structural unit types of radiating element and front framework is face cell S HELL63.Wherein, be interconnected between cold drawing and front framework, between cold drawing and T/R assembly, between T/R assembly and radiating element, between there is no relative displacement.
Step 3, extracts array antenna finite element model radiating element Centroid displacement
According to given array antenna structure finite element model constraint condition and airborne random vibration acceleration power spectrum, application harmony superposition, converts L load step to by airborne random vibration acceleration power spectrum, final acquisition random vibration time history sample.Wherein, L be greater than 10 natural number.Utilize random vibration time history sample computing array antenna random vibration deflection by ANSYS, extract the position offset of each radiating element geometric center node on x, y, z direction (the Δ x of array antenna finite element model respectively 0,0, Δ y 0,0, Δ z, 0) ... (Δ x mn, Δ y mn, Δ z mn), wherein m is the natural number between 0 ~ M-1, represents the numbering of array antenna M row radiating element; N is the natural number between 0 ~ N-1, represents the numbering of the capable radiating element of array antenna N.
Step 4, the pattern function of computing array antenna
According to array antenna finite element model radiating element geometric center nodal displacement amount, utilize electromechanical Coupling Model, computing array antenna radiation pattern function.
The electrical property of computing array antenna carries out according to the following formula:
4a) establish array antenna to have M × N number of radiating element to arrange by equidistant rectangular grid battle array, spacing horizontal and vertical between unit is respectively d xwith d y, as shown in Figure 2; Observation point P is relative to the direction at rectangular coordinate system xyz place (cos α is expressed as with direction cosine x, cos α y, cos α z), as shown in Figure 3; Obtain the angle of observation point P relative to coordinate axis and the relation of direction cosine thus:
4b) order is (Δ x by the position offset of (m, n) unit on x, y, z direction in M × N number of radiating element of equidistant rectangular grid battle array arrangement mn, Δ y mn, Δ z mn), the position offset of (0,0) unit on x, y, z direction is (Δ x 0,0, Δ y 0,0, Δ z 0,0), then the phase difference φ of (m, n) unit relative (0,0) unit mnfor:
Δφ mn = k ( md x + Δ x mn - Δ x 0,0 ) cos α x + k ( nd y + Δ y mn - Δ y 0,0 ) cos α y
+ k ( Δ z mn - Δ z 0,0 ) cos α z + β mn
In formula, for the wave constant of array antenna, λ is the operation wavelength of array antenna, β mnbe (m, n) radiating element battle array in phase differential;
4c) according to array antenna superposition principle, by 4b) obtain array aerial direction figure function and be:
+ ( nd y + Δ y mn - Δ y 0,0 ) cos α y + ( Δ z mn - Δ z 0,0 ) cos α z ] + j β mn }
In formula, E efor the pattern function of antenna element, I mnit is element excitation electric current.
Obtain the electrical property of array antenna thus, according to the array aerial direction figure that array aerial direction figure function is drawn, obtain the gain of array antenna, E face maximum sidelobe levels, E face half power lobe width and E face beam position side-play amount, and H face maximum sidelobe levels, H face half power lobe width and H face beam position side-play amount.Wherein, E face is plane when array antenna θ under polar coordinates (θ, φ) is 0 °, φ gets-90 ° ~ 90 °, and H face is plane when array antenna φ under polar coordinates (θ, φ) is 0 °, θ gets-90 ° ~ 90 °.Can be found out by array antenna E face directional diagram, E face maximum sidelobe levels is the level of antenna first secondary lobe in the drawings, E face half power lobe width in the drawings for gain maximum decline 3 decibels time corresponding main lobe both sides angular range width, E face beam position side-play amount be antenna main lobe direction with distance between direction; Can be found out by array antenna H face directional diagram, H face maximum sidelobe levels is the level of antenna first secondary lobe in the drawings, H face half power lobe width in the drawings for gain maximum decline 3 decibels time corresponding main lobe both sides angular range width, H face beam position side-play amount is the distance between antenna main lobe direction and ° direction, θ=0.
Step 5, judges whether to meet design requirement
According to the electrical performance indexes requirement of array antenna, judge whether the array antenna electrical property calculated meets the demands, if met the demands, then array antenna structure design is qualified; Otherwise, the structural parameters of amendment array antenna, and repeat step one to step 4, until meet the demands.
The present invention can be further illustrated by emulation experiment:
1. emulate active phase array antenna parameter
For verifying the correctness of electromechanical Coupling Model, be applied in the active phase array antenna working in X-band 10GHz.The material properties of active phase array antenna is as shown in table 1.
The material properties of table 1 active phase array antenna
Radiating element arranges with equidistant rectangular grid in xoy plane, gets M=10, N=10, amounts to 100 radiating element composition active phase array antenna arrays; Get active phase array antenna operation wavelength λ=30mm, then d x=0.5 λ=15mm, d y=0.6 λ=18mm.
2. calculate the electrical property of active phase array antenna
The electrical property of active phase array antenna can be obtained by following four steps:
1) the geometric model file of active phase array antenna is determined
According to structural parameters and the material properties of active phase array antenna, determine the geometric model parameter of active phase array antenna, the structural parameters of active phase array antenna comprise the parameter of cold drawing, radiating element, T/R assembly and front framework, and the material properties of active phase array antenna comprises elastic modulus, Poisson ratio and density.The geometric model of active phase array antenna as shown in Figure 4.
2) in ANSYS, active phase array antenna finite element model is built
The finite element model built in ANSYS, structural unit types is solid element SOLID45, and the structural unit types of radiating element and front framework is SHELL63.Wherein, be interconnected between cold drawing and front framework, between cold drawing and T/R assembly, between T/R assembly and radiating element, between there is no relative displacement.The free grid of ANSYS software set is adopted to divide geometric model.Active phase array antenna finite element model as shown in Figure 5.
3) active phase array antenna finite element model radiating element geometric center nodal displacement amount is extracted
According to given active phase array antenna finite element model constraint condition and airborne random vibration acceleration power spectrum, wherein airborne random vibration acceleration power spectrum draws according to active phase array antenna actual working environment, as shown in Figure 6, horizontal ordinate is the frequency range of pumping signal, from 15Hz to 2000Hz, ordinate is acceleration power spectral density, and its scope is 0.003 ~ 0.025g 2/ Hz, wherein g is acceleration of gravity.Application harmony superposition, converts 100 load steps to by airborne random vibration acceleration power spectrum, final acquisition random vibration time history sample, active phase array antenna random vibration time history sample as shown in Figure 7.Because active phase array antenna structural vibration pumping signal comes from the vibration environment of aircraft itself, can in Fig. 5 antenna structure finite element model, random vibration power spectrum signal is applied to the pedestal journal stirrup position of antenna structure, and on X, Y and Z tri-coordinate directions, is applied with airborne random vibration acceleration power spectrum respectively.Calculate active phase array antenna random vibration deflection by ANSYS software, draw active phase array antenna malformation cloud atlas, as shown in Figure 8.Extract the position offset of each radiating element geometric center node on x, y, z direction (the Δ x of active phase array antenna finite element model respectively 0,0, Δ y 0,0, Δ z 0,0) ... (Δ x mn, Δ y mn, Δ z mn), wherein M × each radiating element N number of is by equidistant rectangular grid battle array arrangement, and m is the natural number between 0 ~ M-1, as the numbering representing active phase array antenna M row radiating element, n is the natural number between 0 ~ N-1, represents the numbering of the capable radiating element of active phase array antenna N.
4) pattern function of active phase array antenna is calculated
According to active phase array antenna finite element model radiating element geometric center nodal displacement amount, utilize electromechanical Coupling Model, calculate the electrical property of active phase array antenna.
The electrical property calculating active phase array antenna carries out according to the following formula:
4a) establish active phase array antenna to have M × N number of radiating element to arrange by equidistant rectangular grid battle array, spacing horizontal and vertical between unit is respectively d xwith d y.Observation point P is relative to the direction at coordinate system xyz place (cos α is expressed as with direction cosine x, cos α y, cos α z).Obtain the angle of observation point P relative to coordinate axis and the relation of direction cosine thus:
4b) order is (Δ x by the position offset of (m, n) radiating element on x, y, z direction in M × N number of radiating element of equidistant rectangular grid battle array arrangement mn, Δ y mn, Δ z mn), the position offset of (0,0) radiating element on x, y, z direction is (Δ x 0,0, Δ y 0,0, Δ z 0,0), then the phase difference φ of (m, n) unit relative (0,0) radiating element mnfor:
Δφ mn=k(md x+Δx mn-Δx 0,0)cosα x+k(nd y+Δy mn-Δy 0,0)cosα y
+k(Δz mn-Δz 0,0)cosα zmn
In formula, for the wave constant of array antenna, λ is the operation wavelength of array antenna, β mnbe (m, n) radiating element battle array in phase differential;
4c) according to array antenna superposition principle, by 4b) obtain array aerial direction figure function and be:
+ ( nd y + Δ y mn - Δ y 0,0 ) cos α y + ( Δ z mn - Δ z 0,0 ) cos α z ] + j β mn }
In formula, E efor the pattern function of antenna radiation unit, the pattern function of each radiating element is identical with the pattern function in half-wave a period of time, as shown in Fig. 9 (a) and Fig. 9 (b); I mnbe element excitation electric current, suppose that active phase array antenna obeys the same Entropy density deviation of constant amplitude, namely each radiating element amplitude of active phase array antenna is equal, and the phase differential between each radiating element is 0, I herein mnvalue is 1, β mnvalue is 0.
Obtain the pattern function of active phase array antenna thus, according to the antenna radiation pattern that the electrical property of active phase array antenna is drawn, obtain antenna gain, E face maximum sidelobe levels, E face half power lobe width, E face beam position side-play amount and H face maximum sidelobe levels, H face half power lobe width, H face beam position side-play amount.
3. simulation result
Utilize above five steps to obtain the pattern function of active phase array antenna, comparative result is as shown in Figure 10 (a), Figure 10 (b) He table 2.Wherein Figure 10 (a) dotted line represents the antenna E face directional diagram of active phase array antenna when there being random vibration to be out of shape, and solid line represents active phase array antenna antenna E face directional diagram in the ideal case; Figure 10 (b) represents the antenna H face directional diagram of active phase array antenna when there being random vibration to be out of shape, and solid line represents active phase array antenna antenna H face directional diagram in the ideal case.As can be seen from Table 2: the loss of (1) antenna gain obviously, reaches 0.7139dB, and reducing number percent is 2.9059%.(2) main lobe broadens, and E face broadens 0.1158deg, and the number percent that broadens is 1.0192%; H face broadens 0.4906deg, and the number percent that broadens is 4.2136%.(3) minor level integral raising, E face maximum sidelobe levels has raised 2.8508dB, and raising number percent is that 15.1554%, H face maximum sidelobe levels has raised 1.0962dB, raises than being 5.7286%.(4) beam position offsets, and this will cause the reduction of radar antenna tracking power.
Table 2 ideal situation and antenna electric performance result when there is distortion
Be out of shape antenna electric performance influence degree as can be seen from active phase array antenna random vibration, the random vibration of Antenna Operation environment causes the change in location of radiating element, produce phase place and range error, the electrical property of antenna is declined, and especially the change of minor level is more obvious compared with the change of other electrical performance indexes.Therefore in the present embodiment, the distortion of active phase array antenna random vibration to cause antenna electric performance and affects more greatly, needs amendment antenna structure parameter, to meet antenna electric performance index request.

Claims (4)

1. the Forecasting Methodology of vibration deformation pair array antenna electric performance impact, it is characterized in that, the method comprises the steps:
1) according to structural parameters and the material properties of array antenna, the geometric model parameter of array antenna is determined;
2) in ANSYS, build the structural finite element model of array antenna;
3) constraint condition of given array antenna structure finite element model and airborne random vibration acceleration power spectrum, computing array antenna random vibration deflection, extract the position offset of each radiating element Centroid on x, y, z direction of array antenna finite element model respectively;
4) according to array antenna finite element model radiating element Centroid position offset, utilize electromechanical Coupling Model, obtain array aerial direction figure function, and draw array aerial direction figure;
5) according to the electrical performance indexes requirement of array antenna, judge whether the array antenna electrical property calculated meets the demands, if met the demands, then array antenna structure design is qualified; Otherwise, the structural parameters of amendment array antenna, and repeat step 1) to step 4), until meet the demands;
Described step 3), according to given array antenna structure finite element model constraint condition and airborne random vibration acceleration power spectrum, application harmony superposition, converts L load step to by airborne random vibration acceleration power spectrum, final acquisition random vibration time history sample;
Wherein, L be greater than 10 natural number; The position offset of each radiating element Centroid on x, y, z direction of array antenna finite element model is (Δ x 0,0, Δ y 0,0, Δ z 0,0) (Δ x mn, Δ y mn, Δ z mn), wherein M × each radiating element N number of is by equidistant rectangular grid battle array arrangement, and m is the natural number between 0 ~ M-1, and represent the numbering of array antenna M row radiating element, n is the natural number between 0 ~ N-1, represents the numbering of the capable radiating element of array antenna N;
Described step 4) in calculate array aerial direction figure function and carry out according to the following formula:
4a) establish array antenna to have M × N number of radiating element to arrange by equidistant rectangular grid battle array, spacing horizontal and vertical between unit is respectively d xwith d y; Observation point P is relative to the direction at rectangular coordinate system xyz place (cos α is expressed as with direction cosine x, cos α y, cos α z), obtain the angle of observation point P relative to coordinate axis and the relation of direction cosine thus:
4b) order is (Δ x by the position offset of (m, n) radiating element on x, y, z direction in M × N number of radiating element of equidistant rectangular grid battle array arrangement mn, Δ y mn, Δ z mn), the position offset of (0,0) radiating element on x, y, z direction is (Δ x 0,0, Δ y 0,0, Δ z 0,0), then the phase difference φ of (m, n) radiating element relative (0,0) radiating element mnfor:
Δφ mn=k(md x+Δx mn-Δx 0,0)cosα x+k(nd y+Δy mn-Δy 0,0)cosα y
+k(Δz mn-Δz 0,0)cosα zmn
In formula, for the wave constant of array antenna, λ is the operation wavelength of array antenna, β mnbe (m, n) radiating element battle array in phase differential;
4c) according to array antenna superposition principle, by 4b) obtain array aerial direction figure function and be:
In formula, E efor the pattern function of antenna element, I mnit is element excitation electric current.
2. the Forecasting Methodology of vibration deformation pair array antenna electric performance impact according to claim 1, it is characterized in that, described step 4) draw array aerial direction figure, antenna gain, E face minor level, E face half power lobe width and E face beam position side-play amount is obtained from array aerial direction figure, and H face minor level, H face half power lobe width and H face beam position side-play amount.
3. the Forecasting Methodology of vibration deformation pair array antenna electric performance according to claim 1 impact, is characterized in that, described step 1) structural parameters of array antenna comprise the parameter of cold drawing, radiating element, T/R assembly and front framework.
4. the Forecasting Methodology of vibration deformation pair array antenna electric performance according to claim 1 impact, is characterized in that, described step 1) material properties of array antenna comprises elastic modulus, Poisson ratio and density.
CN201210414471.8A 2012-10-25 2012-10-25 Method for predicting influence of vibration deformation on electric performance of array antenna Expired - Fee Related CN102890741B (en)

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