CN104732050A - Method for estimating distribution of electromagnetism in flying targets made of carbon fiber materials under lightning pulses - Google Patents

Abstract

The invention discloses a method for estimating distribution of electromagnetism in flying targets made of carbon fiber materials under lightning pulses. The method comprises the following steps of simulating the lightning pulses with an ultra-wide spectrum range by using time domain plane waves; establishing a time domain analysis module of the flying objects made of the carbon fiber materials under the lightning pulses; performing transient far field high-efficiency calculation by using an algorithm of plane wave time domain (PWTD); quickly calculating an impedance matrix of a time stepping time domain volume integral equation MOT by using an equivalent electric dipole modal; solving a time domain matrix equation; and extracting electromagnetism characteristic in a broadband. By the method, only the flying targets made of the carbon fiber materials are dispersed, a free space green function is used, the equation is simple, uneven targets can be analyzed, the calculation precision is quite high, and an unknown quantity is small; and moreover, the equation is solved by a time domain method, and the electromagnetic characteristic of all frequency points in a frequency band can be calculated at one step. Compared with a frequency domain method requiring sweep frequency operation, the method has the advantages that time consumed on solving is greatly shortened.

Description

Electromagnetism distribution predictor method under lightening pulse in carbon fibre material airbound target

Technical field

The emulational computation, particularly high dielectric parameter that the invention belongs to the Electromagnetic Scattering Characteristics calculated fast under lightening pulse in carbon fibre material airbound target in certain frequency band, the emulational computation of electromagnetic characteristic of scattering having the carbon fibre material of consumption to form.

Background technology

Carbon fiber is that under adopting the inert gas of high-temperature decomposition 1000 ~ 3000 DEG C of high temperature by organic precursors fiber (viscose rayon, polyacrylonitrile or pitch etc.), carbonization is made, having the features such as intensity is large, modulus is high, density is low, linear expansion coefficient is little, is a kind of material of excellent in mechanical performance.A kind of special fibre that carbon fiber is mainly made up of carbon, its carbon content is different with kind difference, generally more than 90%.It is made up through techniques such as pre-oxidation, carbonization, graphitizations of organic precursors fiber (the carbon content man-made fiber that is higher, not melting in heat treatment process such as viscose glue, pitch, polyacrylonitrile).Its main application is and the matrix compounds such as resin, metal, pottery, cement, makes structured material.Carbon fiber enhancement resin base composite material (CFRP) is Typical Representative, and its performance such as specific strength, specific modulus is the highest in existing structure material.

Along with aircraft is gradually to lightness development, the part enclosure of aircraft adopts the compound substances such as carbon fiber.But the electromagnet shield effect of carbon fibre material is not as metal, and this makes the sophisticated electronics in body more easily be subject to the impact of external electromagnetic environment, so the electromagnetic environment safety analysis in aircraft flight has become important research topic.And thunder and lightning is as a kind of common spontaneous phenomenon, can produce the rise time in discharge process is exceedingly fast, the initial heavy current pulse that the duration is extremely short.Therefore thunder and lightning can produce very strong transient electromagnetic field in discharge process, and the electromagnetic field that this peak value is high and current impulse can cause high risks to being in aloft air electronics.Electromagnetism distribution under research lightening pulse in carbon fibre material airbound target has important realistic meaning to the design effort of reality.

At present, in aerospace field application, carbon fibre material, as a building material, utilizes high temperature resistant, the mechanical characteristic such as specific strength is high and specific modulus is high of carbon fiber to use as the structured material of Aeronautics and Astronautics, aircraft, airship etc.A building material as aircraft: main wing, empennage and body etc.; Secondary building material: the blade etc. of aileron, bearing circle, elevating rudder, built-in material, flooring board, brake block and helicopter; The exhaust cone, engine (lid, housing, firing chamber, jet pipe, larynx lining, diffuser), booster case etc. of rocket; Improve more greatly antifatigue, the performance such as corrosion-resistant, obvious loss of weight effect can be played.Carbon fibre composite is widely used in the aerospace fields such as rocket, guided missile and high-speed aircraft.Carbon fiber is little due to its quality, so power consumption is few, can save a large amount of fuel.The load-carrying construction, thermal protection system, solar cell substrate, complex-curved antenna, link etc. of artificial satellite; The aerofoil plate of spaceship and supporting member etc.Some critical components on space station and earth to orbit and return transportation system also often adopt RR45RR carbon fibre composite to be main material.At present, the use amount of carbon fibre composite on small-sized business aircraft and helicopter accounts for 70% ~ 80%, military aircraft accounts for 30% ~ 40%, airliner accounts for 15% ~ 50%.

Traditional time domain approach such as FDTD precision is very restricted, can not meet day by day increase to high-precision needs.And the impedance matrix of each frequency of the method for frequency domain is different, the electromagnetic property calculating some frequency bands must frequency sweep, and frequency domain to carry out frequency sweep very time-consuming, ivory-towered demand.

Summary of the invention

The object of the present invention is to provide a kind of numerical method of carbon fibre material airbound target scattering properties, thus realize the method obtaining Electromagnetic Scattering Characteristics parameter in broadband fast.

The technical scheme realizing the object of the invention is: the electromagnetism distribution predictor method under a kind of lightening pulse in carbon fibre material airbound target, and step is as follows:

The first step, time domain time stepping electric field volume divides the foundation of equation, and in based target body, resultant field is incident electric fields and scattering electric field sum.Incident electric fields is Time Domain Planar ripple, and modulation Gauss pulse is usually used to as incident electric fields, and scattering electric field can represent with unknown polarization body electric current to be asked.

Second step, is converted to dielectric (flux) density by unknown quantity by polarization body electric current, and provides the time domain expression-form of polarization body electric current in lossy medium.Dielectric (flux) density space basis function and time base function expansion, use here and be defined in tetrahedron to upper SWG and second order Lagrange time basis function.And in spatial domain, carry out the gold test of gal the Liao Dynasty, time domain is carried out Point matching and obtain time-domain matrix equation.

3rd step, time domain model matrix computations, Time Domain Planar ripple algorithm PWTD improves the speed of traditional MOT impedance matrix filling in conjunction with equivalent electric dipole model method, and efficient calculation obtains time-domain matrix.Application PWTD algorithm realization transient state far field efficient calculation, reduces the quantity needing the MOT impedance matrix elements of filling, improves the efficiency of MOT algorithm.The present invention is treated with a certain discrimination needing the MOT impedance matrix elements of filling in PWTD algorithm, the impedance matrix elements that field source basis function in 3 time steps is formed adopts traditional MOT to fill, other is greater than the element application equivalent electric dipole model method approximate treatment of 3 time steps apart, improves MOT efficiency further.

4th step, time-domain matrix equation solution and the electromagnetism distribution situation calculated in objective body.

The present invention compared with prior art, its remarkable advantage: (1) establishing equation is simple, and relative to other Time Domain Analysis as FDTD, unknown quantity is few, and computational accuracy is high.(2) relative to frequency domain method, required computational resource is few.Because the present invention inherits Time Domain Analysis, once can obtain the characteristic of electromagnetic scattering in a broadband, avoid the modeling of repetition and fill calculating without the need to frequency sweep.And frequency-domain analysis method once calculates the characteristic of the electromagnetic scattering that can only obtain a frequency, compared to the time-domain analysis model that the present invention proposes, when analyzing the practical problems of carbon fibre material airbound target, frequency-domain analysis method computing time, oversize and required amount of ram was large.Simultaneously when meeting the condition of Time Domain Planar ripple PWTD algorithm, computational resource can be saved further under the requirement meeting computational accuracy.

Accompanying drawing explanation

Fig. 1 carbon fibre material target of the present invention geometric model schematic diagram.

Fig. 2 carbon fibre material airbound target of the present invention schematic diagram.

Fig. 3 example temporal current of the present invention coefficient is schemed over time.

Fig. 4 example of the present invention is schemed over time at the electric field x component value near field observation point (0.05m, 0.00m, 0.00m) place.

Embodiment

Electromagnetism distribution predictor method under lightening pulse of the present invention in carbon fibre material airbound target, step is as follows:

The first step, if airbound target housing is made up of carbon fibre material, irradiates airbound target with time domain plane-wave simulation lightening pulse, produces polarization body electric current J in airbound target housing _v(r, t), because the total electric field in airbound target housing equals incident electric fields and scattering electric field sum, the time domain time stepping improved Electric Field Integral Equation form obtaining airbound target housing is as follows:

Wherein represent incident electric fields, represent scattering electric field, represent total electric field, expression is:

Wherein A _vrepresent vector magnetic potential and Φ _vrepresent electric scalar potential, v represents the body unit of carbon fibre material, and ε represents the specific inductive capacity of carbon fibre material, represents dielectric (flux) density, r represents a point, and t represents the time;

Second step, the unknown quantity polarization body electric current in the improved Electric Field Integral Equation set up in the first step is converted to dielectric (flux) density, and provides the time domain expression-form of polarization body electric current in lossy medium, its concrete representation is as follows:

$J(r,t)=\mathrm{\κ}\left(r\right)\·\frac{\∂D(r,t)}{\∂t}+v\left(r\right)\·D(r,t)$ (3)

$\mathrm{\κ}\left(r\right)=\frac{\mathrm{\ϵ}\left(r\right)-{\mathrm{\ϵ}}_0\left(r\right)}{\mathrm{\ϵ}\left(r\right)},v\left(r\right)=\mathrm{\σ}\left(r\right)/\mathrm{\ϵ}\left(r\right)$

Wherein ε (r) be medium specific inductive capacity, ε ₀r () is free space specific inductive capacity, μ ₀for permeability of free space, σ (r) is conductivity;

To (2) formula improved Electric Field Integral Equation discrete and carry out in spatial domain gal the Liao Dynasty gold test, time domain is carried out Point matching and obtains time-domain matrix equation:

$Z_0{I}_j=V_j^{\mathrm{inc}}-\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{Z}_{i-j}{I}_{j}j=1,...,N_t---\left(4\right)$

Wherein represent the excitation of a jth time step, N _trepresent the number of time step, I _jthe coefficient to be asked of a jth time step, be the time domain model matrix of time delay (i-j) individual time step, i, j=1,2,3..., i>=j, i-j represents time delay (i-j) Δ t, and Δ t represents a time step, Δ t=1/ (10*f _max), f _maxrepresent the highest frequency of incident wave;

3rd step, in conjunction with Time Domain Planar ripple algorithm PWTD and equivalent electric dipole model method, calculates time-domain matrix;

4th step, solves time-domain matrix equation, obtains the electromagnetism distribution in broadband in airbound target housing.

In described 3rd step, scattered field is decomposed into polymerizing factor, transfer factor and the projection factor in far-field region, and to the two basis function application equivalent dipole models being greater than 3 time steps apart near field region, concrete steps are as follows:

Step 3.1, sets up the tree structure of airbound target housing;

Step 3.2, supposes there is a field point r in arbitrary group of m, has a source point r' in arbitrary group of n, the central point of field point group and source point group respectively; The space vector of two non-NULL group midfield points and source point is designated as: $R=r-r^{\′}=(r-r_o^c)+(r_o^c-r_s^c)-(r^{\′}-r_s^c)$

Far field scattered field is write as following form:

Wherein A (r, t') represents vector magnetic potential, representation unit dyad;

Step 3.3, is decomposed into the projection factor by the scattered field expression formula in far-field region, the form of polymerizing factor and transfer factor three convolution, the projection factor, and the expression of polymerizing factor and transfer factor is as follows:

$l_m^{-,v}(\hat{k},t)=\underset{v}{\∫}\mathrm{dv}\·\hat{k}\×f_m^v\left(r\right)\·\mathrm{\δ}[t-\hat{k}(r-r_o^c)/c]$

$l_n^{+,v}(\hat{k},t)={\∂}_t\underset{v}{\∫}{\mathrm{dv}}^{\′}\·\mathrm{\κ}\left(r^{\′}\right)\hat{k}\×f_n^v\left(r\right)\·\mathrm{\δ}[t+\hat{k}(r^{\′}-r_s^c)/c]---\left(6\right)$

$T(\hat{k},t)=\frac{{\mathrm{\η}}_0}{{8\mathrm{\π}}^2{c}^2}{\∂}_t^3\mathrm{\δ}(t-\hat{k}\·(r_o^c-r_s^c)/c)$

Wherein represent the projection factor, represent polymerizing factor, represent transfer factor

Step 3.4, when the spacing of two near field effect basis functions is greater than 3 time steps, application equivalent dipole approximate treatment impedance element;

The expression formula of the equivalent dipole that SWG is formed is as follows:

$m_{v,n}={\∫}_{T_n^{\±}}\mathrm{\κ}\left(r^{\′}\right)\·f_{v,n}(r,t){\mathrm{dV}}^{\′}\≈a_{v,n}{\mathrm{\κ}}^{+}\left(r^{\′}\right)\·(r_{\mathrm{ns}}^c-r_{v,n}^{c+})+a_{v,n}{\mathrm{\κ}}^{-}\left(r^{\′}\right)\·(r_{v,n}^{c-}-r_{\mathrm{ns}}^c)---\left(7\right)$

Wherein represent upper and lower tetrahedral central point, represent the central point of medium gore, a _v,nrepresent medium triangle area, V represents dielectric, κ (r)=(ε (r)-ε ₀(r))/ε (r);

The electric field expression formula that the electric dipole obtaining the formation of single SWG basis function produces in far field is as follows:

$E_n^{\mathrm{sca}}=\frac{\mathrm{\η}}{4\mathrm{\π}}[(M_{v,n}-m_{v,n})\frac{1}{\mathrm{cR}}{\∂}_t^{2}T(t-R/c)+\frac{1}{R^2}(\frac{c}{R}T(t-R/c)+{\∂}_{t}T(t-R/c))\·({3M}_{v,n}-m_{v,n})]---\left(8\right)$

Wherein represent the mid point of the equivalent electric dipole of field point SWG, represent the mid point of the equivalent electric dipole of source point SWG, R represents the distance between two electric dipoles, and k represents wave number, represent the electric field that No. n-th basis function produces, $M_{v,n}=(\stackrel{\→}{R}\·m_{v,n})\stackrel{\→}{R}/R^2.$

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Composition graphs 2, the present invention is based on a kind of time stepping time-domain integration numerical computation method analyzing carbon fibre material airbound target, step is as follows:

The first step, proposes the time-domain analysis model of a kind of carbon fibre material flight housing, sets up time domain time stepping electric field volume and divide equation.Suppose that a medium carbon fibre material target I is arranged in unbounded space 2, the specific inductive capacity of medium 1 is ε (r), and magnetic permeability is μ ₀, the specific inductive capacity of unbounded space 2 is ε ₀, magnetic permeability is μ ₀, when dielectric object I is subject to incident electric fields during excitation, polarization body current density will be produced in dielectric object according to equivalence principle, dielectric, to the scattering of incident field, can be equivalent to the body polarization current density in its respective regions in free space the scattering produced.Because total electric field equals incident field and scattered field sum, that is:

Wherein represent incident electric fields, represent scattering electric field, represent total electric field

Time Domain Planar ripple irradiates carbon fibre material target surface, shown in the scattered field can known in target according to Maxwell equation can be expressed as:

In formula, v represents medium body unit, A _vrepresent vector magnetic potential and Φ _vrepresent electric scalar potential;

Electric field meets following formula at medium:

on medium (3)

Be added with incident field by scattered field, we obtain electric field expression formula as follows:

(4) formula is exactly the derivation result of time domain volume integral equations fundamental formular.

Wherein:

$R=|\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}|$

$\mathrm{\τ}=t-\frac{R}{c}$

Have again:

$J_v(\stackrel{\→}{r},t)=\mathrm{\κ}\left(\stackrel{\→}{r}\right)\frac{\∂}{\∂t}\stackrel{\→}{D}(\stackrel{\→}{r},t)$

$\mathrm{\κ}\left(\stackrel{\→}{r}\right)=\frac{\mathrm{\ϵ}\left(\stackrel{\→}{r}\right)-{\mathrm{\ϵ}}_0}{\mathrm{\ϵ}\left(\stackrel{\→}{r}\right)}$

Wherein A _vrepresent vector magnetic potential and Φ _vrepresent electric scalar potential, v represents the body unit of carbon fibre material, represent dielectric (flux) density, r represents a point, and r' represents source point, and t represents the time; The specific inductive capacity that ε (r) is medium, ε ₀r () is free space specific inductive capacity, μ ₀for permeability of free space, σ (r) is conductivity, represent polarization body current density;

Excitation when selecting modulation Gauss plane-wave to calculate as time domain electromagnetic:

${\stackrel{\→}{E}}^{\mathrm{inc}}(\stackrel{\→}{r},t)={\hat{u}}^i\exp [-0.5{(t-t_p-\stackrel{\→}{r}\·k^i/c)}^2/{\mathrm{\σ}}^2]\cos \left[{2\mathrm{\πf}}_0(t-\stackrel{\→}{r}\·k^i/c)\right]---\left(5\right)$

Wherein f ₀represent incident wave centre frequency, σ indicating impulse width, k ⁱrepresent the incident wave direction of propagation, C represents the light velocity, and tp represents time delay;

Second step, is converted to dielectric (flux) density by unknown quantity by polarization body electric current, and provides the time domain expression-form of polarization body electric current in lossy medium.The present invention choose SWG basis function as space basis function, second order Lagrange's interpolation basis function as time basis function to dielectric (flux) density discrete representation.

SWG basis function concrete form is as follows:

${\stackrel{\→}{f}}_n^V\left(r\right)=\left\{\begin{array}{cc}\frac{a_n}{{3V}_n^{+}}{\stackrel{\→}{\mathrm{\ρ}}}_n^{+V}& \stackrel{\→}{r}\mathrm{in}{T}_n^{+}\\ \frac{a_n}{{3V}_3^{-}}{\stackrel{\→}{\mathrm{\ρ}}}_n^{-V}& \stackrel{\→}{r}\mathrm{in}{T}_n^{-}\\ 0& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

It is as follows that time basis function chooses concrete form:

Wherein v represents the body unit of layer of carbon fiber material, gets be any point in two tetrahedrons, with represent base vector, summit corresponding to common sides, needs explanation only exist there is value tetrahedron inside.

By dielectric (flux) density obtain by after base function expansion:

$D(\stackrel{\→}{r},t)\≅\underset{\text{n=1}}{\overset{N_s}{\mathrm{\Σ}}}\underset{l=1}{\overset{N_t}{\mathrm{\Σ}}}{I}_n^l{f}_n^v\left(\stackrel{\→}{r}\right)T_l\left(t\right)---\left(8\right)$

Wherein Ns is the number of the SWG basis function that scatterer comprises, and Nt is the number of time step.

The expansion (8) of dielectric (flux) density being brought into carries out discrete to time domain volume integral equations in formula (4), character used in proper names and in rendering some foreign names the Liao Dynasty gold (Galerkin) method test on application space, Point matching on time, obtains time domain time stepping volume integral equations form as follows:

$Z_0{I}_j=V_j^{\mathrm{inc}}-\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{Z}_{i-j}{I}_{j}j=1,...,N_t---\left(9\right)$

Wherein represent the excitation of a jth time step, N _trepresent the number of time step, I _jbe the coefficient to be asked of a jth time step, i-j represents time delay (i-j) Δ t, and Δ t represents a time step.The time stepping volumetric method impedance matrix expression that the present invention uses is as follows:

3rd step, impedance matrix calculates, and Time Domain Planar ripple algorithm PWTD improves the speed of traditional MOT impedance matrix filling in conjunction with equivalent electric dipole model method, and efficient calculation obtains time-domain matrix.Application PWTD algorithm realization transient state far field efficient calculation, reduces the quantity needing the MOT impedance matrix elements of filling, improves the efficiency of MOT algorithm.The present invention is treated with a certain discrimination needing the MOT impedance matrix elements of filling in PWTD algorithm, the impedance matrix elements that field source basis function in 3 time steps is formed adopts traditional MOT to fill, other is greater than the element application equivalent electric dipole model method approximate treatment of 3 time steps apart, improves MOT efficiency further.

When calculating far zone field, the expression formula angular spectrum of vector magnetic potential A (r, t') launches to be write as following form by PWTD algorithm:

${\tilde{A}}_{n,l}(r,t)=-\frac{{\mathrm{\μ}}_0{\∂}_t}{{8\mathrm{\π}}^{2}c}\∫d^2\mathrm{\Ω}{\∫}_{v_n}{\mathrm{dv}}_n^{\′}{f}_n^v\left(r^{\′}\right)\mathrm{\δ}(t-\hat{k}\·(r-r^{\′})/c)*g_{n,l}\left(t\right)---\left(11\right)$

Wherein g _n,lt () represents a basic subsignal, time basis function T (t) is combined by L basic subsignal;

Formula (11) is substituted into scattered field formula, and detailed process is as follows:

$E^s(r,t)=-{\∫}_0^t{\mathrm{dt}}^{\′}({\∂}_{t^{\′}}^{2}I-c^2\▿\▿)\·A(r,t^{\′})$

$=-{\∫}_0^t{\mathrm{dt}}^{\′}({\∂}_{t^{\′}}^{2}I-c^2\▿\▿)\·(-\frac{u_0{\∂}_{t^{\′}}}{{8\mathrm{\π}}^{2}c}\∫d^2\mathrm{\Ω}{\∫}_{v_n}\mathrm{\κ}\left(r^{\′}\right)f_n^v\left(r^{\′}\right)\·\mathrm{\δ}(t^{\′}-\hat{k}\·(r-r^{\′}))*{\∂}_{t^{\′}}{g}_{n,l}\left(t^{\′}\right){\mathrm{dv}}^{\′})$

Due to for plane wave, there is operator $\▿=-{\∂}_t\hat{k}/c$

$={\∫}_0^t{\mathrm{dt}}^{\′}\·\frac{u_0{\∂}_{t^{\′}}}{{8\mathrm{\π}}^{2}c}\·({\∂}_{t^{\′}}^2\stackrel{=}{I}-c^2\·{\∂}_{t^{\′}}^2\hat{k}\·\hat{k}/c^2)\·({\∫d}^2\mathrm{\Ω}{\∫}_{v_n}\mathrm{\κ}\left(r^{\′}\right)f_n^v\left(r^{\′}\right)\·\mathrm{\δ}(t^{\′}-\hat{k}\·((r-r_0)-(r^{\′}-r_s)+(r_0-r_s))*{\∂}_{t^{\′}}{g}_{n,l}\left(t^{\′}\right){\mathrm{dv}}^{\′})$

$={\∫}_0^t{\mathrm{dt}}^{\′}\·\frac{u_0{\∂}_t^3}{{8\mathrm{\π}}^{2}c}\·(\stackrel{=}{I}-\hat{k}\·\hat{k})\·\left({\∫d}^2\mathrm{\Ω}{\∫}_{v_n}{f}_n^v\left(r^{\′}\right)\left\{\begin{array}{c}\mathrm{\δ}(t^{\′}-\hat{k}\·(r-r_0))*\mathrm{\δ}(t^{\′}+\hat{k}\·(r^{\′}-r_s))*\\ \mathrm{\δ}(t^{\′}-\hat{k}\·(r_0-r_s))*g_{n,l}\left(t^{\′}\right)\end{array}\right\}{\mathrm{dv}}^{\′}\right)$

Due to vector operation identical relation

$(\stackrel{=}{I}-\hat{k}\hat{k})\·f_n=f_n-\hat{k}(\hat{k}\·f_n)=-\hat{k}\×(\hat{k}\×f_n)$

$f_m\·[\hat{n}\×(\hat{k}\×f_n)]=(\hat{k}\×f_n)\·(f_m\×\hat{n})=-(\hat{k}\×f_n)\·(\hat{n}\×f_m)$

$f_m\·(\stackrel{=}{I}-\hat{k}\hat{k})\·f_n=f_m\·[-\hat{k}\×(\hat{k}\×f_n)]=(-1)f_m\·[\hat{k}\×(\hat{k}\×f_n)]=(-1)[-(\hat{k}\×f_n)\·(\hat{k}\×f_m)]$

$=(\hat{k}\×f_n)\·(\hat{k}\×f_m)=(\hat{k}\×f_m)\·(\hat{k}\×f_n)$

Bring into $<f_m^v\left(r\right),L_e\left\{J_{n,l}^v(r^{\&prime;},t)\right\}>$ Expression formula obtain following expression:

$<f_m^v\left(r\right),L_e\left\{J_{n,l}^v(r^{\&prime;},t)\right\}>=\frac{{\mathrm{\&eta;}}_0}{{8\mathrm{\&pi;}}^2{c}^2}\&Integral;d^2\mathrm{\&Omega;}\underset{0}{\overset{t}{\&Integral;}}{\mathrm{dt}}^{\&prime;}{\&Integral;}_{v_m}\hat{k}\&times;f_m^v\left(r\right)*\mathrm{\&delta;}(t^{\&prime;}-\hat{k}\&CenterDot;(r-r_0))\mathrm{dv}$ (12)

$*\left\{{\&PartialD;}_{t^{\&prime;}}^3\mathrm{\&delta;}(t-\hat{k}\&CenterDot;(r_0-r_s)/c)\right\}*{\&Integral;}_{v_n}\hat{k}\&times;f_n^v\left(r^{\&prime;}\right)\&CenterDot;\mathrm{\&delta;}(t^{\&prime;}-\hat{k}\&CenterDot;(r-r^{\&prime;}))*g_{n,l}\left(t^{\&prime;}\right){\mathrm{dv}}^{\&prime;}$

Wherein represent polarization body electric current, represent the angular spectrum component in certain direction, η ₀represent free space wave impedance, r represents a point, and r' represents source point, r _o, r _sthe central point of field point group and source point group respectively, representation unit dyad;

From formula (12), isolate the projection factor, the expression of polymerizing factor and transfer factor is as follows:

$l_m^{-,v}(\hat{k},t)=\underset{v}{\&Integral;}\mathrm{dv}\&CenterDot;\hat{k}\&times;f_m^v\left(r\right)\&CenterDot;\mathrm{\&delta;}[t-\hat{k}(r-r_o^c)/c]$

$l_n^{+,v}(\hat{k},t)={\&PartialD;}_t\underset{v}{\&Integral;}{\mathrm{dv}}^{\&prime;}\&CenterDot;\mathrm{\&kappa;}\left(r^{\&prime;}\right)\hat{k}\&times;f_n^v\left(r\right)\&CenterDot;\mathrm{\&delta;}[t+\hat{k}(r^{\&prime;}-r_s^c)/c]---\left(13\right)$

$T(\hat{k},t)=\frac{{\mathrm{\&eta;}}_0}{{8\mathrm{\&pi;}}^2{c}^2}{\&PartialD;}_t^3\mathrm{\&delta;}(t-\hat{k}\&CenterDot;(r_o^c-r_s^c)/c)$

Wherein represent the projection factor, represent polymerizing factor, represent transfer factor;

Step 3.4, when two near field effect element distances are greater than 3 time steps, the approximate treatment of application equivalent dipole.The expression formula of the equivalent dipole that SWG is formed

$m_{v,n}={\&Integral;}_{T_n^{\&PlusMinus;}}\mathrm{\&kappa;}\left(r^{\&prime;}\right)\&CenterDot;f_n^v\left(r^{\&prime;}\right){\mathrm{dV}}^{\&prime;}\&ap;a_{v,n}{\mathrm{\&kappa;}}^{+}\left(r^{\&prime;}\right)\&CenterDot;(r_{\mathrm{ns}}^c-r_{v,n}^{c+})+a_{v,n}{\mathrm{\&kappa;}}^{-}\left(r^{\&prime;}\right)\&CenterDot;(r_{v,n}^{c-}-r_{\mathrm{ns}}^c)---\left(14\right)$

Wherein represent upper and lower tetrahedral central point, represent the central point of medium gore, a _v,nrepresent medium triangle area, V represents medium, κ (r)=(ε (r)-ε ₀(r))/ε (r).

$m_n(r,t)=\underset{V}{\&Integral;}{J}_n^v(r^{\&prime;},t){\mathrm{dv}}^{\&prime;}=\underset{V}{\&Integral;}{\&PartialD;}_t\mathrm{\&kappa;}\left(r^{\&prime;}\right)\&CenterDot;f_n^v\left(r^{\&prime;}\right)\&CenterDot;T\left(t\right){\mathrm{dv}}^{\&prime;}=m_{v,n}\&CenterDot;T\left(t\right)---\left(15\right)$

The electric field expression formula that the time domain electric dipole that n basis function is formed produces in far field is as follows:

$E_n^s=\frac{{\mathrm{\&eta;}}_0}{4\mathrm{\&pi;}}[(M_{v,n}-m_{v,n})\frac{1}{\mathrm{cR}}{\&PartialD;}_t^{2}T(t-R/c)+\frac{1}{R^2}(\frac{c}{R}T(t-R/c)+{\&PartialD;}_{t}T(t-R/c))\&CenterDot;({3M}_{v,n}-m_{v,n})]---\left(16\right)$

Wherein represent the mid point of the equivalent electric dipole of field point SWG, represent the mid point of the equivalent electric dipole of source point SWG, R represents the distance between two electric dipoles, and k represents wave number, represent the electric field that No. n-th basis function produces, $M_{v,n}=(\stackrel{\&RightArrow;}{R}\&CenterDot;m_{v,n})\stackrel{\&RightArrow;}{R}/R^2;$

4th step, time-domain matrix equation solution and the electromagnetism distribution situation calculated in objective body.In order to verify correctness and the validity of the inventive method, shown below is the example calculating carbon fibre material target.The essential information of example is as follows: the inside and outside length of side of carbon fibre material cube shell is respectively 0.6m, 0.7m, the conductivity of carbon fibre material is 0.001 relative dielectric parameter is 100, the centre frequency of time domain incident wave is set to 15MHZ, incident modulation Gauss pulse direction of wave travel is z-axis positive dirction, x direction polarization.As seen from Figure 3, the temporal current coefficient that the present invention obtains over time with frequency domain frequency sweep after through inverse Fourier transform result coincide very well, and near field observation point (0.05m, 0.00m, 0.00m) electric field x component value in place coincide with the simulation result of CST over time as shown in Figure 4.

Claims (2)

1. the electromagnetism distribution predictor method under lightening pulse in carbon fibre material airbound target, is characterized in that step is as follows:

The first step, if airbound target housing is made up of carbon fibre material, irradiates airbound target with time domain plane-wave simulation lightening pulse, produces polarization body electric current J in airbound target housing _v(r, t), because the total electric field in airbound target housing equals incident electric fields and scattering electric field sum, the time domain time stepping improved Electric Field Integral Equation form obtaining airbound target housing is as follows:

Wherein represent incident electric fields, represent scattering electric field, represent total electric field, expression is:

Wherein A _vrepresent vector magnetic potential and Φ _vrepresent electric scalar potential, v represents the body unit of carbon fibre material, and ε represents the specific inductive capacity of carbon fibre material, represents dielectric (flux) density, r represents a point, and t represents the time;

Second step, the unknown quantity polarization body electric current in the improved Electric Field Integral Equation set up in the first step is converted to dielectric (flux) density, and provides the time domain expression-form of polarization body electric current in lossy medium, its concrete representation is as follows:

$J(r,t)=\mathrm{\&kappa;}\left(r\right)\&CenterDot;\frac{\&PartialD;D(r,t)}{\&PartialD;t}+v\left(r\right)\&CenterDot;D(r,t)$ (3)

$\mathrm{\&kappa;}\left(r\right)=\frac{\mathrm{\&epsiv;}\left(r\right)-{\mathrm{\&epsiv;}}_0\left(r\right)}{\mathrm{\&epsiv;}\left(r\right)},v\left(r\right)=\mathrm{\&sigma;}\left(r\right)/\mathrm{\&epsiv;}\left(r\right)$

Wherein ε (r) be medium specific inductive capacity, ε ₀r () is free space specific inductive capacity, μ ₀for permeability of free space, σ (r) is conductivity;

To (2) formula improved Electric Field Integral Equation discrete and carry out in spatial domain gal the Liao Dynasty gold test, time domain is carried out Point matching and obtains time-domain matrix equation:

$Z_0{I}_j=V_j^{\mathrm{inc}}-\underset{i=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{Z}_{i-j}{I}_{j}j=1,...,N_t---\left(4\right)$

Wherein represent the excitation of a jth time step, N _trepresent the number of time step, I _jthe coefficient to be asked of a jth time step, be the time domain model matrix of time delay (i-j) individual time step, i, j=1,2,3..., i>=j, i-j represents time delay (i-j) Δ t, and Δ t represents a time step, Δ t=1/ (10*f _max), f _maxrepresent the highest frequency of incident wave;

3rd step, in conjunction with Time Domain Planar ripple algorithm PWTD and equivalent electric dipole model method, calculates time-domain matrix;

4th step, solves time-domain matrix equation, obtains the electromagnetism distribution in broadband in airbound target housing.

2. the electromagnetism distribution predictor method under lightening pulse according to claim 1 in carbon fibre material airbound target, it is characterized in that: in described 3rd step, scattered field is decomposed into polymerizing factor, transfer factor and the projection factor in far-field region, and to the two basis function application equivalent dipole models being greater than 3 time steps apart near field region, concrete steps are as follows:

Step 3.1, sets up the tree structure of airbound target housing;

Step 3.2, supposes there is a field point r in arbitrary group of m, has a source point r' in arbitrary group of n, the central point of field point group and source point group respectively; The space vector of two non-NULL group midfield points and source point is designated as: $R=r-r^{\&prime;}=(r-r_o^c)+(r_o^c-r_s^c)-(r^{\&prime;}-r_s^c)$

Far field scattered field is write as following form:

Wherein A (r, t') represents vector magnetic potential, representation unit dyad;

Step 3.3, is decomposed into the projection factor by the scattered field expression formula in far-field region, the form of polymerizing factor and transfer factor three convolution, the projection factor, and the expression of polymerizing factor and transfer factor is as follows:

$l_m^{-,v}(\hat{k},t)=\underset{v}{\&Integral;}\mathrm{dv}\&CenterDot;\hat{k}\&times;f_m^v\left(r\right)\&CenterDot;\mathrm{\&delta;}[t-\hat{k}(r-r_o^c)/c]$

$l_n^{+,v}(\hat{k},t)={\&PartialD;}_t\underset{v}{\&Integral;}{\mathrm{dv}}^{\&prime;}\&CenterDot;\mathrm{\&kappa;}\left(r^{\&prime;}\right)\hat{k}\&times;f_n^v\left(r\right)\&CenterDot;\mathrm{\&delta;}[t+\hat{k}(r^{\&prime;}-r_s^c)/c]---\left(6\right)$

$T(\hat{k},t)=\frac{{\mathrm{\&eta;}}_0}{{8\mathrm{\&pi;}}^2{c}^2}{\&PartialD;}_t^3\mathrm{\&delta;}(t-\hat{k}\&CenterDot;(r_o^c-r_s^c)/c)$

Wherein represent the projection factor, represent polymerizing factor, represent transfer factor

Step 3.4, when the spacing of two near field effect basis functions is greater than 3 time steps, application equivalent dipole approximate treatment impedance element;

The expression formula of the equivalent dipole that SWG is formed is as follows:

$m_{v,n}={\&Integral;}_{T_n^{\&PlusMinus;}}\mathrm{\&kappa;}\left(r^{\&prime;}\right)\&CenterDot;f_{v,n}(r,t){\mathrm{dV}}^{\&prime;}\&ap;a_{v,n}{\mathrm{\&kappa;}}^{+}\left(r^{\&prime;}\right)\&CenterDot;(r_{\mathrm{ns}}^c-r_{v,n}^{c+})+a_{v,n}{\mathrm{\&kappa;}}^{-}\left(r^{\&prime;}\right)\&CenterDot;(r_{v,n}^{c-}-r_{\mathrm{ns}}^c)---\left(7\right)$

Wherein represent upper and lower tetrahedral central point, represent the central point of medium gore, a _v,nrepresent medium triangle area, V represents dielectric, κ (r)=(ε (r)-ε ₀(r))/ε (r);

The electric field expression formula that the electric dipole obtaining the formation of single SWG basis function produces in far field is as follows:

$E_n^{\mathrm{sca}}=\frac{\mathrm{\&eta;}}{4\mathrm{\&pi;}}[(M_{v,n}-m_{v,n})\frac{1}{\mathrm{cR}}{\&PartialD;}_t^{2}T(t-R/c)+\frac{1}{R^2}(\frac{c}{R}T(t-R/c)+{\&PartialD;}_{t}T(t-R/c))\&CenterDot;({3M}_{v,n}-m_{v,n})]---\left(8\right)$

Wherein represent the mid point of the equivalent electric dipole of field point SWG, represent the mid point of the equivalent electric dipole of source point SWG, R represents the distance between two electric dipoles, and k represents wave number, represent the electric field that No. n-th basis function produces, $M_{v,n}=(\stackrel{\&RightArrow;}{R}\&CenterDot;m_{v,n})\stackrel{\&RightArrow;}{R}/R^2.$