CN107590309B - Net-shaped antenna electrical performance time domain characteristic analysis method based on approximate calculation formula - Google Patents
Net-shaped antenna electrical performance time domain characteristic analysis method based on approximate calculation formula Download PDFInfo
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Abstract
The invention discloses a method for analyzing the electrical performance time domain characteristics of a mesh antenna based on an approximate calculation formula, which comprises the following steps: (1) inputting geometric parameters, material parameters and electrical parameters of an antenna; (2) establishing an antenna structure finite element model; (3) extracting node, unit and shape function information; (4) calculating a first-order and second-order coefficient matrix of the electrical property; (5) applying a dynamic load; (6) calculating node displacement information; (7) calculating node speed information; (8) calculating node acceleration information; (9) approximately calculating the time domain information of the electric field change speed of the antenna far zone; (10) approximately calculating the time domain information of the electric field change acceleration of the far zone; (11) judging whether the electrical property meets the requirement; (12) outputting the antenna structure design scheme; (13) and updating the antenna parameters. The invention can realize the calculation of the electric field change speed and the acceleration time domain information of the far area of the mesh antenna on the premise of ensuring the calculation precision, and performs the electromechanical integration optimization design of the antenna structure.
Description
Technical Field
The invention belongs to the technical field of radar antennas, and particularly relates to an electrical property time domain characteristic analysis method of a mesh antenna based on an approximate calculation formula.
Background
The mesh reflector antenna is widely applied to the fields of space detection, reconnaissance and the like due to the advantages of high gain, light weight and low storage ratio. As the size of the mesh antenna structure increases, the mesh antenna is more easily affected by the space environment due to factors such as structural nonlinearity and the like. Dynamic loads such as space radiant heat, impact and the like can cause the antenna structure to deform, the electrical property to deteriorate and the normal work of the antenna to be influenced. Under the influence of dynamic loading, the antenna electrical performance changes over time. Therefore, it is necessary to analyze and calculate the change of the electrical property of the mesh antenna with time according to the influence of the dynamic load, obtain the information such as the speed and acceleration of the change, and provide an electrical property time domain characteristic analysis method.
Wang Yun Si et al put forward a prediction method for analyzing the influence of vibration deformation on the electrical property of an array antenna in a Chinese patent 'a prediction method for the influence of vibration deformation on the electrical property of an array antenna'. The method takes the array antenna as an object, and analyzes the influence of random vibration on the electrical property of the array antenna; however, in the analysis process, the calculation amount is large, and meanwhile, the time domain information of the electrical property change speed and the acceleration is difficult to obtain quickly. The influence of dynamic load on the mechanical and electrical performance of the structure-function integrated antenna is analyzed in the literature of Zhongjin pillar, Song standing Wei and the like, the mechanical engineering report of which is volume 52, 9 th, 2016, 5 months and 105-; the analysis method also has the problem that the time domain information of the electrical property change speed and the acceleration is difficult to obtain quickly. Therefore, aiming at the time domain information requirements of the mesh antenna for analyzing and calculating the electrical property change speed and the acceleration of the antenna under the influence of the dynamic load, the electrical property time domain characteristic analysis method of the mesh antenna based on the approximate calculation formula is provided, and on the premise of ensuring the calculation time, the electrical property change speed and the acceleration time domain information can be obtained quickly, and the electromechanical integration optimization design of the antenna structure is carried out.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an electrical property time domain characteristic analysis method of a mesh antenna based on an approximate calculation formula. The method is based on an approximate calculation formula, analyzes the electrical property change speed and acceleration time domain information of the mesh antenna under the action of dynamic load, and performs electromechanical integration optimization design of the antenna structure.
The technical scheme of the invention is as follows: the electrical property time domain characteristic analysis method of the mesh antenna based on the approximate calculation formula comprises the following steps:
(1) inputting geometric parameters, material parameters and electrical parameters of the antenna
Inputting geometric parameters, material parameters and electrical parameters of the spatial mesh antenna provided by a user; the geometric parameters comprise caliber, focal length, offset distance and minimum distance of front and back net surfaces; the material parameters comprise the material density, the cross-sectional area, the Young's modulus of elasticity and the Poisson ratio of the cable structure, the truss structure and the wire mesh structure; the electrical parameters comprise working wavelength, feed source parameters, a feed source primary directional diagram and electrical performance requirements including antenna gain, lobe width, side lobe level, pointing accuracy, far-zone electric field change speed and acceleration time domain information;
(2) establishing antenna structure finite element model
Establishing an antenna structure finite element model according to antenna geometric parameters and material parameters provided by a user, wherein a cable structure is modeled by adopting a rod unit which is only pulled, a truss structure is modeled by adopting a beam unit, and a wire mesh structure is modeled by adopting a shell unit;
(3) extracting node, cell and shape function information
Extracting node, unit and shape function information of the reflecting surface part under the irradiation of the electromagnetic wave in the finite element model based on the established structure finite element model;
(4) calculating a first-order and second-order coefficient matrix of the electrical property;
(5) applying dynamic loads
Applying dynamic load changing along with time aiming at the finite element model of the antenna structure;
(6) calculating node displacement information;
(7) calculating node speed information;
(8) calculating node acceleration information;
(9) approximate calculation of time domain information of electric field change speed of antenna far zone
And (3) combining the node displacement information obtained in the step (6) and the node speed information obtained in the step (7), calculating time domain information of the electric field change speed of the antenna far zone by adopting an approximate calculation formula, and calculating by the following formula:
wherein E represents the change amount of the far-zone electric field under the action of a load, dE represents the differential operation of the far-zone electric field, t is a time factor, dt represents the differential operation of the time factor, j represents an imaginary unit, and k represents free spaceThe number of m-waves, η, represents the free-space wave impedance, exp represents the exponential operation of the natural logarithm, R represents the far-field viewpoint location vector magnitude, pi represents the circumferential ratio,
the unit of the dyadic vector is expressed,
representing unit vectors
The vector delta is the node shift column vector, the superscript T represents the transposition operation,
g represents the electrical property first-order coefficient matrix obtained in the step (4) and H represents the electrical property second-order coefficient matrix obtained in the step (4) for the node velocity column vector;
(10) approximate calculation of far-zone electric field change acceleration time domain information
And (3) calculating electric field change acceleration time domain information of the antenna far zone by adopting an approximate calculation formula by combining the node displacement information obtained in the step (6), the node speed information obtained in the step (7) and the node acceleration information obtained in the step (8), and calculating by the following formula:
wherein E represents the change of the electric field in the far zone under the action of the load, and d2E represents two differential operations to the far-zone electric field, t is a time factor, dt2Representing two differential operations on the time factor, j representing an imaginary unit, k representing a free-space wavenumber, η representing a free-space wave impedance, exp representing an exponential operation on the natural logarithm, R representing the far-field viewpoint location vector magnitude, pi representing the circumferential ratio,
the unit of the dyadic vector is expressed,
representing unit vectors
Dyadic of (d, delta, d),
Respectively carrying out node displacement, velocity and acceleration column vectors obtained in the steps (6), (7) and (8), wherein the superscript T represents transposition operation, G represents an electrical property first-order coefficient matrix obtained in the step (4), and H represents an electrical property second-order coefficient matrix obtained in the step (4);
(11) judging whether the electrical property meets the requirement
Judging whether the electric field change speed and the acceleration time domain information of the antenna far zone obtained in the step (10) meet the electrical performance requirements of the antenna gain, the lobe width, the side lobe level, the pointing accuracy, the electric field change speed of the far zone and the acceleration time domain information, if so, turning to the step (12), otherwise, turning to the step (13);
(12) design scheme of output antenna structure
When the antenna far-zone electric field meets the antenna electrical property requirement, outputting antenna structure design data;
(13) updating antenna parameters
And (3) when the electric field of the antenna far zone does not meet the electrical performance requirement of the antenna, updating the antenna parameters and turning to the step (1).
The step (4) of calculating the first-order and second-order coefficient matrixes of the electrical property is carried out according to the following steps:
4a) calculating a first order coefficient matrix of cell electrical properties by:
wherein the content of the first and second substances,
a matrix of first order coefficients of electrical properties of element e is shown, superscript e indicates a certain element in the finite element model of the structure extracted in step (3), subscript i indicates a node number located on element e,
the ith component of the electrical property first order coefficient matrix representing cell e, the symbol e represents the dependency, NUM represents the total number of nodes on cell e,
a normal vector representing the unit e is shown,
representing a position vector of a reflecting surface
The incident magnetic field of the magnetic field of (c),
representing the reflector position vector, exp representing the exponential operation of the natural logarithm, j representing the unit of an imaginary number, k representing the free space wavenumber,
unit vector, Q, representing far field observation pointiRepresenting the shape function, theta, extracted in step (3) with respect to the ith nodesRepresenting position vectors
The subscript s represents the feed coordinate system, theta represents the far field observation point pitch angle, and sigma represents the feed coordinate systemeRepresenting the projected area of the element e in the aperture plane;
4b) calculating a cell electrical property second order coefficient matrix by:
wherein the content of the first and second substances,
representing an electrical property second order coefficient matrix of the element e, wherein a superscript e represents a certain element in the structural finite element model extracted in the step (3), u and v respectively represent node numbers positioned on the element e,
representing the electrical second order coefficient matrix component of cell e, consisting of nodes u and v, with the symbol e representing dependency, NUM representing the total number of nodes on cell e, k representing the free space wavenumber,
a normal vector representing the unit e is shown,
representing a position vector of a reflecting surface
The incident magnetic field of the magnetic field of (c),
representing the reflector position vector, exp representing the exponential operation of the natural logarithm, j representing the unit of an imaginary number,
unit vector, Q, representing far field observation pointuRepresenting the shape function, Q, extracted in step (3) with respect to the u-th nodevRepresenting the shape function, theta, extracted in step (3) with respect to the v-th nodesRepresenting position vectors
The angle of pitch in the feed coordinate system, subscript s denotes the feed seatScale, theta denotes the far field viewpoint pitch angle, sigmaeRepresenting the projected area of the element e in the aperture plane;
4c) the overall electrical performance first order coefficient matrix is assembled by:
wherein G represents a matrix of first order coefficients of the overall electrical properties,
representing an electrical property first-order coefficient matrix of an element e, wherein a superscript e represents a certain element in the structural finite element model extracted in the step (3), m represents the total number of the elements, and A represents finite element set operation;
4d) the overall electrical performance second order coefficient matrix is assembled by:
wherein H represents a matrix of second order coefficients of the overall electrical performance,
and (3) representing an electrical property second-order coefficient matrix of the element e, wherein a superscript e represents a certain element in the structural finite element model extracted in the step (3), m represents the total number of the elements, and A represents finite element set operation.
In the step (6), node displacement information is obtained by solving the following structural dynamics equation:
m, C, K represents the antenna structure total mass array, total damping array and total rigidity array corresponding to the finite element model, delta (t),
Respectively node displacement, velocity and acceleration column vectorP (t) is the dynamic load column vector applied in step (5), and t is a time factor.
In the step (7), the node speed information is calculated by the following formula:
wherein the content of the first and second substances,
the node velocity column vector is represented by δ (t), the node displacement column vector is represented by d δ, the node displacement is differentiated by d δ, the time factor is differentiated by dt, and the time factor is represented by t.
In the step (8), the node acceleration information is calculated by the following formula:
wherein the content of the first and second substances,
is a nodal acceleration column vector, δ (t) is a nodal displacement column vector, d2Delta denotes two differential operations on the node displacement, dt2It represents that two differential operations are carried out on the time factor, and t is the time factor.
The invention has the beneficial effects that: firstly, inputting geometric parameters, material parameters and electrical parameter information of an antenna, and establishing a finite element model of an antenna structure according to the geometric parameters and the material parameter information; secondly, extracting node, unit and shape function information according to the finite element model of the antenna structure, and calculating first-order and second-order coefficient matrixes of electrical property; thirdly, on the basis of the antenna structure finite element model, applying dynamic load to the structure finite element model, calculating node displacement information according to a structure dynamics equation, and sequentially obtaining node speed and acceleration information; and finally, combining the first-order and second-order coefficient matrixes of the electrical performance and node displacement, speed and acceleration information, and respectively and approximately calculating the electric field change speed and acceleration time domain information of the antenna far zone so as to carry out electromechanical integration optimization design on the antenna structure.
Compared with the prior art, the invention has the following advantages:
1. based on an approximate calculation formula, the method can reduce the calculation time and improve the calculation efficiency on the premise of ensuring the calculation accuracy;
2. the invention can obtain the electric field change speed and acceleration time domain information of the antenna far zone more quickly and make up for the defects of the prior art.
The present invention will be described in further detail below with reference to the accompanying drawings.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a mesh antenna structure;
FIG. 3 is a graph of maximum deformation amplitude of the antenna surface over time;
fig. 4 is a diagram showing the variation speed of the antenna main axis direction coefficient.
Detailed Description
The following detailed description of embodiments of the invention is provided in conjunction with the appended drawings:
referring to fig. 1, the invention provides a method for analyzing electrical performance time domain characteristics of a mesh antenna based on an approximate calculation formula, comprising the following steps:
step 1, inputting geometric parameters, material parameters and electrical parameters of a spatial mesh antenna provided by a user; the geometric parameters comprise caliber, focal length, offset distance and minimum distance of front and back net surfaces; the material parameters comprise the material density, the cross-sectional area, the Young's modulus of elasticity and the Poisson ratio of the cable structure, the truss structure and the wire mesh structure; the electrical parameters comprise working wavelength, feed source parameters, a feed source primary directional diagram and electrical performance requirements including antenna gain, lobe width, side lobe level, pointing accuracy, far-zone electric field change speed and acceleration time domain information;
step 3, extracting node, unit and shape function information of the reflecting surface part under the irradiation of the electromagnetic wave in the finite element model on the basis of the established structural finite element model;
step 4, calculating first-order and second-order coefficient matrixes of electrical property
4a) Calculating a first order coefficient matrix of cell electrical properties by:
wherein the content of the first and second substances,
a matrix of first order coefficients of electrical properties of element e is shown, superscript e indicates a certain element in the finite element model of the structure extracted in step 3, subscript i indicates a node number located on element e,
the ith component of the electrical property first order coefficient matrix representing cell e, the symbol e represents the dependency, NUM represents the total number of nodes on cell e,
a normal vector representing the unit e is shown,
representing a position vector of a reflecting surface
The incident magnetic field of the magnetic field of (c),
denotes a reflecting surface position vector, exp denotes an exponential operation of a natural logarithm, j denotes an imaginary unit, and k denotesThe wave number in free space is the number of,
unit vector, Q, representing far field observation pointiRepresenting the shape function, θ, extracted in step 3 with respect to the ith nodesRepresenting position vectors
The subscript s represents the feed coordinate system, theta represents the far field observation point pitch angle, and sigma represents the feed coordinate systemeRepresenting the projected area of the element e in the aperture plane;
4b) calculating a cell electrical property second order coefficient matrix by:
wherein the content of the first and second substances,
an electrical property second order coefficient matrix of the element e is shown, the superscript e shows a certain element in the structural finite element model extracted in the step 3, u and v respectively show node numbers positioned on the element e,
representing the electrical second order coefficient matrix component of cell e, consisting of nodes u and v, with the symbol e representing dependency, NUM representing the total number of nodes on cell e, k representing the free space wavenumber,
a normal vector representing the unit e is shown,
representing a position vector of a reflecting surface
The incident magnetic field of the magnetic field of (c),
representing the reflector position vector, exp representing the exponential operation of the natural logarithm, j representing the unit of an imaginary number,
unit vector, Q, representing far field observation pointuRepresenting the shape function, Q, extracted in step 3 with respect to the u-th nodevRepresenting the shape function, θ, extracted in step 3 with respect to the v-th nodesRepresenting position vectors
The subscript s represents the feed coordinate system, theta represents the far field observation point pitch angle, and sigma represents the feed coordinate systemeRepresenting the projected area of the element e in the aperture plane;
4c) the overall electrical performance first order coefficient matrix is assembled by:
wherein G represents a matrix of first order coefficients of the overall electrical properties,
representing an electrical property first-order coefficient matrix of the element e, wherein a superscript e represents a certain element in the structural finite element model extracted in the step 3, m represents the total number of the elements, and A represents finite element set operation;
4d) the overall electrical performance second order coefficient matrix is assembled by:
wherein H represents a matrix of second order coefficients of the overall electrical performance,
representing an electrical property second order coefficient matrix of a unit e, wherein a superscript e represents a certain unit in the structure finite element model extracted in the step 3, m represents the total number of the units, and A represents finite element set operation;
step 6, obtaining node displacement information by solving the following structural dynamics equation:
m, C, K represents the antenna structure total mass array, total damping array and total rigidity array corresponding to the finite element model, delta (t),
Respectively are node displacement, velocity and acceleration column vectors, P (t) is the dynamic load column vector applied in the step 5, and t is a time factor;
step 7, calculating node speed information by the following formula
Wherein the content of the first and second substances,
the node velocity column vector is adopted, delta (t) is the node displacement column vector, d delta represents the differential operation of the node displacement, dt represents the differential operation of a time factor, and t is the time factor;
step 8, calculating node acceleration information through the following formula
Wherein the content of the first and second substances,
is a nodal acceleration column vector, δ (t) is a nodal displacement column vector, d2Delta denotes two differential operations on the node displacement, dt2The method comprises the following steps of (1) performing differential operation twice on a time factor, wherein t is the time factor;
and 9, combining the node displacement information obtained in the step 6 and the node speed information obtained in the step 7, calculating time domain information of the electric field change speed of the antenna far zone by adopting an approximate calculation formula, and calculating by the following formula:
wherein E represents the variation of the far-zone electric field under the action of a load, dE represents the differential operation of the far-zone electric field, t is a time factor, dt represents the differential operation of the time factor, j represents an imaginary unit, k represents a free space wave number, η represents the free space wave impedance, exp represents the exponential operation of a natural logarithm, R represents the vector magnitude of a far-field observation point, and pi represents a circumferential ratio,
the unit of the dyadic vector is expressed,
representing unit vectors
The vector delta is the node shift column vector, the superscript T represents the transposition operation,
g represents the electrical property first-order coefficient matrix obtained in the step 4, and H represents the electrical property second-order coefficient matrix obtained in the step 4;
wherein E represents the change of the electric field in the far zone under the action of the load, and d2E represents two differential operations to the far-zone electric field, t is a time factor, dt2Representing two differential operations on the time factor, j representing an imaginary unit, k representing a free-space wavenumber, η representing a free-space wave impedance, exp representing an exponential operation on the natural logarithm, R representing the far-field viewpoint location vector magnitude, pi representing the circumferential ratio,
the unit of the dyadic vector is expressed,
representing unit vectors
Dyadic of (d, delta, d),
Respectively representing the node displacement, the velocity and the acceleration column vectors obtained in the steps 6, 7 and 8, wherein the superscript T represents transposition operation, G represents an electrical property first-order coefficient matrix obtained in the step 4, and H represents an electrical property second-order coefficient matrix obtained in the step 4;
step 11, judging whether the antenna far-zone electric field obtained in the step 10 meets the electrical performance requirements of antenna gain, lobe width, side lobe level, pointing accuracy, far-zone electric field change speed and acceleration time domain information, if so, turning to the step 12, otherwise, turning to the step 13;
step 12, outputting antenna structure design data when the antenna far-zone electric field meets the antenna electrical property requirement;
and step 13, when the electric field of the antenna far zone does not meet the electrical property requirement of the antenna, updating the antenna parameters, and turning to the step 1.
The advantages of the present invention can be further illustrated by the following simulation experiments:
1. simulation conditions are as follows:
taking a circularly symmetric umbrella-shaped mesh-shaped reflector antenna as an example, the aperture of the antenna is 0.5m, the rib focal length is 0.25m, the working frequency is 35.75GHz, the number of ribs is 30, the feed source adopts a Cosine-Q type feed source, the polarization mode is y linear polarization, and the parameter of the feed source is Qx＝Qy2.2538. The schematic diagram of the antenna structure is shown in fig. 2, where the thick solid line represents the antenna rib, the thin solid line represents the edge of the umbrella-shaped antenna patch, and the dotted line represents the aperture circle. The antenna is placed on the top of the sky, and dynamic load is applied to the whole foundation of the antenna. Assuming that the displacement of the antenna under this dynamic load can be described as the following expression
Wherein, Δ z is z-direction displacement of the reflection surface node of the antenna, λ is the working wavelength, d is the aperture of the antenna, ρ' is the distance from the reflection surface node to the origin of coordinates, ω ═ 0.8 π is the oscillation period of the dynamic deformation, τ ═ 0.3 is the attenuation factor, and t is the time factor.
2. And (3) simulation results:
the method of the invention is adopted to analyze and calculate the electrical property time domain characteristics of the mesh antenna under the dynamic deformation, and the time domain information of the electrical property change speed and the acceleration is obtained. Fig. 3 is a graph of maximum deformation amplitude of the antenna surface as a function of time. Fig. 4 is a graph of the change speed of the electrical performance of the antenna versus the coefficient of the direction of the main axis, in which a curve marked with x represents a change speed curve obtained by using a conventional finite difference method, and a curve marked with · represents a change speed curve obtained by using the method of the present invention. As can be seen from fig. 3 and 4, the electrical property variation speed curve is consistent with the variation trend of the maximum deformation amplitude curve of the antenna surface, and the calculation result obtained by the method of the present invention is consistent with the result obtained by the conventional finite difference method.
In summary, the invention firstly inputs the geometric parameters, material parameters and electrical parameter information of the antenna, and establishes a finite element model of the antenna structure according to the geometric parameters and the material parameter information; secondly, extracting node, unit and shape function information according to the finite element model of the antenna structure, and calculating first-order and second-order coefficient matrixes of electrical property; thirdly, on the basis of the antenna structure finite element model, applying dynamic load to the structure finite element model, calculating node displacement information according to a structure dynamics equation, and sequentially obtaining node speed and acceleration information; and finally, combining the first-order and second-order coefficient matrixes of the electrical performance and node displacement, speed and acceleration information, and respectively and approximately calculating the electric field change speed and acceleration time domain information of the antenna far zone so as to carry out electromechanical integration optimization design on the antenna structure.
Compared with the prior art, the invention has the following advantages:
1. based on an approximate calculation formula, the method can reduce the calculation time and improve the calculation efficiency on the premise of ensuring the calculation accuracy;
2. the invention can obtain the electric field change speed and acceleration time domain information of the antenna far zone more quickly and make up for the defects of the prior art.
The parts of the present embodiment not described in detail are common means known in the art, and are not described here. The above examples are merely illustrative of the present invention and should not be construed as limiting the scope of the invention, which is intended to be covered by the claims and any design similar or equivalent to the scope of the invention.
Claims (5)
1. The electrical property time domain characteristic analysis method of the mesh antenna based on the approximate calculation formula is characterized by comprising the following steps of:
(1) inputting geometric parameters, material parameters and electrical parameters of the antenna
Inputting geometric parameters, material parameters and electrical parameters of the spatial mesh antenna provided by a user; the geometric parameters comprise caliber, focal length, offset distance and minimum distance of front and back net surfaces; the material parameters comprise the material density, the cross-sectional area, the Young's modulus of elasticity and the Poisson ratio of the cable structure, the truss structure and the wire mesh structure; the electrical parameters comprise working wavelength, feed source parameters, a feed source primary directional diagram and electrical performance requirements including antenna gain, lobe width, side lobe level, pointing accuracy, far-zone electric field change speed and acceleration time domain information;
(2) establishing antenna structure finite element model
Establishing an antenna structure finite element model according to antenna geometric parameters and material parameters provided by a user, wherein a cable structure is modeled by adopting a rod unit which is only pulled, a truss structure is modeled by adopting a beam unit, and a wire mesh structure is modeled by adopting a shell unit;
(3) extracting node, cell and shape function information
Extracting node, unit and shape function information of the reflecting surface part under the irradiation of the electromagnetic wave in the finite element model based on the established structure finite element model;
(4) calculating a first-order and second-order coefficient matrix of the electrical property;
(5) applying dynamic loads
Applying dynamic load changing along with time aiming at the finite element model of the antenna structure;
(6) calculating node displacement information;
(7) calculating node speed information;
(8) calculating node acceleration information;
(9) approximate calculation of time domain information of electric field change speed of antenna far zone
And (3) combining the node displacement information obtained in the step (6) and the node speed information obtained in the step (7), calculating time domain information of the electric field change speed of the antenna far zone by adopting an approximate calculation formula, and calculating by the following formula:
wherein E represents the variation of the far-zone electric field under the action of a load, dE represents the differential operation of the far-zone electric field, t is a time factor, dt represents the differential operation of the time factor, j represents an imaginary unit, k represents a free space wave number, η represents the free space wave impedance, exp represents the exponential operation of a natural logarithm, R represents the vector magnitude of a far-field observation point, and pi represents a circumferential ratio,
the unit of the dyadic vector is expressed,
representing unit vectors
The vector delta is the node shift column vector, the superscript T represents the transposition operation,
g represents the electrical property first-order coefficient matrix obtained in the step (4) and H represents the electrical property second-order coefficient matrix obtained in the step (4) for the node velocity column vector;
(10) approximate calculation of far-zone electric field change acceleration time domain information
And (3) calculating electric field change acceleration time domain information of the antenna far zone by adopting an approximate calculation formula by combining the node displacement information obtained in the step (6), the node speed information obtained in the step (7) and the node acceleration information obtained in the step (8), and calculating by the following formula:
wherein E represents the change of the electric field in the far zone under the action of the load, and d2E represents two differential operations to the far-zone electric field, t is a time factor, dt2Representing two differential operations on the time factor, j representing an imaginary unit, k representing a free-space wavenumber, η representing a free-space wave impedance, exp representing an exponential operation on the natural logarithm, R representing the far-field viewpoint location vector magnitude, pi representing the circumferential ratio,
the unit of the dyadic vector is expressed,
representing unit vectors
Dyadic of (d, delta, d),
Respectively carrying out node displacement, velocity and acceleration column vectors obtained in the steps (6), (7) and (8), wherein the superscript T represents transposition operation, G represents an electrical property first-order coefficient matrix obtained in the step (4), and H represents an electrical property second-order coefficient matrix obtained in the step (4);
(11) judging whether the electrical property meets the requirement
Judging whether the electric field change speed and the acceleration time domain information of the antenna far zone obtained in the step (10) meet the electrical performance requirements of the antenna gain, the lobe width, the side lobe level, the pointing accuracy, the electric field change speed of the far zone and the acceleration time domain information, if so, turning to the step (12), otherwise, turning to the step (13);
(12) design scheme of output antenna structure
When the antenna far-zone electric field meets the antenna electrical property requirement, outputting antenna structure design data;
(13) updating antenna parameters
And (3) when the electric field of the antenna far zone does not meet the electrical performance requirement of the antenna, updating the antenna parameters and turning to the step (1).
2. The method of analyzing the time-domain characteristics of the electrical properties of a mesh antenna based on an approximate calculation formula as claimed in claim 1, wherein: the step (4) of calculating the first-order and second-order coefficient matrixes of the electrical property is carried out according to the following steps:
4a) calculating a first order coefficient matrix of cell electrical properties by:
wherein the content of the first and second substances,
a matrix of first order coefficients of electrical properties of element e is shown, superscript e indicates a certain element in the finite element model of the structure extracted in step (3), subscript i indicates a node number located on element e,
the ith component of the electrical property first order coefficient matrix representing cell e, the symbol e represents the dependency, NUM represents the total number of nodes on cell e,
a normal vector representing the unit e is shown,
representing a position vector of a reflecting surface
The incident magnetic field of the magnetic field of (c),
representing the reflector position vector, exp representing the exponential operation of the natural logarithm, j representing the unit of an imaginary number, k representing the free space wavenumber,
unit vector, Q, representing far field observation pointiRepresenting the shape function, theta, extracted in step (3) with respect to the ith nodesRepresenting position vectors
The subscript s represents the feed coordinate system, theta represents the far field observation point pitch angle, and sigma represents the feed coordinate systemeRepresenting the projected area of the element e in the aperture plane;
4b) calculating a cell electrical property second order coefficient matrix by:
wherein the content of the first and second substances,
representing an electrical property second order coefficient matrix of the element e, wherein a superscript e represents a certain element in the structural finite element model extracted in the step (3), u and v respectively represent node numbers positioned on the element e,
representing the electrical second order coefficient matrix component of cell e, consisting of nodes u and v, with the symbol e representing dependency, NUM representing the total number of nodes on cell e, k representing the free space wavenumber,
a normal vector representing the unit e is shown,
representing a position vector of a reflecting surface
The incident magnetic field of the magnetic field of (c),
representing the reflector position vector, exp representing the exponential operation of the natural logarithm, j representing the unit of an imaginary number,
unit vector, Q, representing far field observation pointuRepresenting the shape function, Q, extracted in step (3) with respect to the u-th nodevRepresenting the nodes extracted in step (3) relative to the v-th nodeForm function of thetasRepresenting position vectors
The subscript s represents the feed coordinate system, theta represents the far field observation point pitch angle, and sigma represents the feed coordinate systemeRepresenting the projected area of the element e in the aperture plane;
4c) the overall electrical performance first order coefficient matrix is assembled by:
wherein G represents a matrix of first order coefficients of the overall electrical properties,
representing an electrical property first-order coefficient matrix of an element e, wherein a superscript e represents a certain element in the structural finite element model extracted in the step (3), m represents the total number of the elements, and A represents finite element set operation;
4d) the overall electrical performance second order coefficient matrix is assembled by:
wherein H represents a matrix of second order coefficients of the overall electrical performance,
and (3) representing an electrical property second-order coefficient matrix of the element e, wherein a superscript e represents a certain element in the structural finite element model extracted in the step (3), m represents the total number of the elements, and A represents finite element set operation.
3. The method of analyzing the time-domain characteristics of the electrical properties of a mesh antenna based on an approximate calculation formula as claimed in claim 1, wherein: in the step (6), node displacement information is obtained by solving the following structural dynamics equation:
m, C, K represents the antenna structure total mass array, total damping array and total rigidity array corresponding to the finite element model, delta (t),
Respectively are node displacement, velocity and acceleration column vectors, P (t) is the dynamic load column vector applied in the step (5), and t is a time factor.
4. The method of analyzing the time-domain characteristics of the electrical properties of a mesh antenna based on an approximate calculation formula as claimed in claim 1, wherein: in step (7), the node speed information is calculated by the following formula:
wherein the content of the first and second substances,
the node velocity column vector is represented by δ (t), the node displacement column vector is represented by d δ, the node displacement is differentiated by d δ, the time factor is differentiated by dt, and the time factor is represented by t.
5. The method of analyzing the time-domain characteristics of the electrical properties of a mesh antenna based on an approximate calculation formula as claimed in claim 1, wherein: in the step (8), node acceleration information is calculated according to the following formula:
wherein the content of the first and second substances,
is a nodal acceleration column vector, δ (t) is a nodal displacement column vector, d2Delta denotes two differential operations on the node displacement, dt2It represents that two differential operations are carried out on the time factor, and t is the time factor.
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