CN110020467A - A kind of annular spread Dynamic Load Identification method - Google Patents
A kind of annular spread Dynamic Load Identification method Download PDFInfo
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Abstract
The invention discloses a kind of annular spread Dynamic Load Identification methods, and this method comprises the following steps: S1, obtaining acceleration responsive of the ring section structure under the excitation of practical basis acceleration；S2, the finite element model for establishing ring section structure；S3, it determines B-spline basic function expression formula, applies the distribution pulse excitation of basic function form respectively to model, obtain acceleration responsive measuring point unit impulse response function and establish transfer function matrix；S4, distribution dynamic loading is solved using actual measureed value of acceleration response and transfer function matrix.The present invention solves the problems, such as to provide a kind of means of dynamic loading indirect gain using the spatial distribution and time history of annular spread dynamic loading in actual measurement structure dynamic response identification structure in time domain for the engineering structure under the excitation of annular spread dynamic loading.
Description
Technical field
The invention belongs to Structural Dynamics indirect problem technical field more particularly to a kind of annular spread Dynamic Load Identification sides
Method.
Background technique
Dynamic loading information in engineering structure is the foundation of structure design and security evaluation.In many cases, dynamic loading is difficult
To be obtained by directly measurement, often the dynamic response directly in measurement structure, is obtained dynamic in structure by the means of indirect identification
Load information.
Traditional Dynamic Load Identification method is to cause the secondary dynamic response using the structure dynamic response data identification of single actual measurement
Excitation information, be certainty Dynamic Load Identification method.Existing certainty Dynamic Load Identification method be used to obtain engineering knot
Concentration dynamic loading on structure, the information such as mobile load and distributed dynamic loading.It is worth noting that, distributed Dynamic Load Identification
Problem is equivalent to identification, and difficulty is bigger, generally requires and solves distributed Dynamic Load Identification problem dimensionality reduction.
The dynamic loading acted on engineering structure, it is often annular in shape to be distributed such as the dynamic loading on ring flange butt joint interface,
Therefore spatial distribution and its time history information for how accurately identifying dynamic loading are most important to the dynamic design of structure.It utilizes
Orthogonal polynomial goes the spatial distribution of fitting load that can not expire although the simple dynamic loading of distribution form can be identified preferably
The continuous feature of sufficient annular spread dynamic loading ending, and the load of mutant form can not be identified effectively, it is therefore desirable to one
Kind is directed to the new method of ring-shape distribution Dynamic Load Identification.
Summary of the invention
Goal of the invention: it in view of the above problems, the present invention proposes a kind of annular spread Dynamic Load Identification method, solves in time domain
Interior the problem of identifying the dynamic loading spatial distribution and time-histories characteristic acted in structure using actual measurement structure dynamic response, for by annular
The Structural Design and security evaluation for being distributed dynamic loading provide a kind of means of dynamic loading indirect gain.
Technical solution: to achieve the purpose of the present invention, the technical scheme adopted by the invention is that: a kind of annular distribution dynamic load
Lotus recognition methods, which is characterized in that this method comprises the following steps:
S1. acceleration responsive of the ring section structure under the excitation of practical basis acceleration is obtained；
S2. the finite element model of ring section structure is established；
S3. it determines B-spline basic function expression formula, applies the distribution pulse excitation of basic function form respectively to model, obtain
Acceleration responsive measuring point unit impulse response function simultaneously establishes transfer function matrix；
S4. distribution dynamic loading is solved using actual measureed value of acceleration response and transfer function matrix；
The annular distribution Dynamic Load Identification method based on B-spline function, foundation annular described in step S2 are cut
The specific method of the finite element model of face structure includes:
S21: the initial finite element model of practical ring section structure is established；
S22: it is based on modal test, obtains the modal data of practical structures；
S23: Modifying model is carried out to initial finite element model based on the modal data of modal test, acquisition is revised to be had
Limit meta-model.
The annular distribution Dynamic Load Identification method, determination B-spline basic function expression formula described in step S3, to mould
Type applies the distribution pulse excitation of basic function form respectively, obtains acceleration responsive measuring point unit impulse response function and establishes biography
The specific method of delivery function matrix includes:
S31: determining B-spline basic function number and control point number and position, considers the periodical side of annular distribution load
Boundary's condition, in section [x0,xn) on obtain k B-spline basic function expression formula, x0It is section starting point, xnIt is section terminal, it can
To indicate are as follows:
Ni+1,p(x)=Ni,p(x+Δx) (3)
In formula, p is the number of B-spline basic function；Ni,p(x) it is i-th p times B-spline basic function；xiIt is controlled for i-th
The abscissa of point, it is contemplated that periodic boundary condition, xn+i=xi, Δ x is the distance between control point, and Δ x is arranged and fixes
It is constant；
S32: finite element method is utilized, panel load is converted by the distribution pulse excitation of each B-spline basic function form and applies
It is added on finite element model, the impulse response function g of acceleration responsive measuring point is calculated using finite element softwarek,i(t), have
Steps are as follows for body；
The distribution pulse excitation N of B-spline basic function formi(x, t) may be expressed as:
Ni(x, t)=Ni,p(x)·s0(t) (4)
In formula, Ni(x, t) is i-th of distribution pulse excitation；s0It (t) is unit pulse excitation, i.e., zero moment amplitude is 1,
The transient state that remaining moment amplitude is 0 motivates.
Using finite element method, pulse excitation N will be distributedi(x, t) is converted into the panel load of structure, cell node load
Fe(t) it can be integrated and be obtained by shape function:
In formula, l is element length, NeIt (x) is unit shape function.
S33: by the impulse response function g of acceleration responsive measuring pointk,i(t) it is assembled into transfer function matrix G, and establishes knot
The calculated relationship of structure response and excitation, can indicate are as follows:
In formula, ymIt indicates to respond y at m-th of measuring pointmIn the column vector that the value at each time point forms；sn(t) it indicates n-th
S is motivated at control pointn(t) column vector composed by the value at each time point；Gm,nIt is structure in n-th p times B-spline basic function
Nn,pUnder the pulse excitation effect of form, the impulse response function g that is obtained at m-th of measuring pointm,n(t) impulse response square composed by
Battle array, BnIt is the coefficient for representing n-th of B-spline basic function.
The annular distribution Dynamic Load Identification method based on B-spline function is added described in step S4 using actual measurement
Speed responsive and the specific method of transfer function matrix solution distribution dynamic loading include:
S41: utilizing least square method and regularization method, solves B-spline basic function coefficient BiWith basic excitation time-histories s
(t) product, the specific steps are as follows:
Formula (6) is turned to:
{ Bs (t) }=(GTG)-1GT{Y} (7)
In formula, Y is the acceleration responsive y of m measuring pointkThe column vector of composition；G is the transmitting that impulse response matrix is assembled into
Matrix；Bs (t) is B-spline basic function coefficient BiWith excitation each time point value si(t) column vector of product composition.
S42: according to the following formula, by B-spline basic function coefficient BiWith product vector Bs (t) inverting of basic excitation time-histories s (t)
Annular distribution dynamic loading q (x, t):
The utility model has the advantages that compared with prior art, technical solution of the present invention has following advantageous effects:
1, existing Dynamic Load Identification technology generally can only identify that the concentration in structure is moved by actual measurement structure dynamic response data
Load, the identification for the dynamic loading that the distribution Dynamic Load Identification method occurred at present can not be distributed suitable for non-stationary, and due to
Existing method can not be applied to the annular spread Dynamic Load Identification with periodic characteristic by the characteristics of orthogonal basis function, and
Distribution dynamic loading time domain identification technology provided in the present invention can be known using the actual measurement structure dynamic response data at limited measure node
The spatial distribution and its time-histories characteristic of other annular spread dynamic loading have certain advantage.
2, the annular spread load recognition method based on B-spline function does not need excessive basic function item number, than based on just
Handing over the distribution Dynamic Load Identification method of basic function has higher computational efficiency, generally reduces the time of load identification.
Detailed description of the invention
Fig. 1 is the logical procedure diagram of the method for the present invention；
Fig. 2 is dummy satellite schematic diagram under annular spread dynamic load effect；
Fig. 3 is load history recognition result at annular spread dynamic loading position；
Fig. 4 is annular spread dynamic loading spatial distribution recognition result.
Specific embodiment
Below by the mode of embodiment, technical solution of the present invention is described in detail, but embodiment is only the present invention
Preferred embodiment, it should be pointed out that: for those skilled in the art, do not departing from the principle of the invention
Under the premise of, can be made several improvements in the form of to structure and dynamic loading and equivalent replacement, these to the claims in the present invention into
Technical solution after row improvement and equivalent replacement, each falls within protection scope of the present invention.
Embodiment: to structure as shown in Figure 2, place's annular is docked with rocket in satellite using method recognition reaction of the invention
It is distributed dynamic loading.Satellite structural materials are aluminium, and elasticity modulus is 7 × 1010Pa, density are 2.7 × 103kg/m3, Poisson's ratio is
0.3, the damping of structure uses Rayleigh damping, and each rank damping ratios are ξi=0.02.Annular spread dynamic loading to be identified point
Cloth function are as follows:
S (t) is the time-varying component of annular spread dynamic loading to be identified, and the power spectrum according to Gaussian random process obtains s
(t) time-history curves:
In formula, Δ ω indicates frequency increment；ωk=ωmin+Δω(k-1)；NkIndicate section [ωmin,ωmax] on frequency
The total number of division, ωmin,ωmaRefer respectively to frequency limits.Nk=(ωmax-ωmin)/Δω；ψkExpression is uniformly distributed
Random phase angle in section [0,2 π]；The bilateral power spectral density of Φ (ω) expression zero-mean non-stationary Gaussian random process
Function has Φ (ω)=(1/2 π) (2/ ω2+1)。
Using technology of the invention by actual measurement structure dynamic response data identification annular spread dynamic loading spatial distribution and when
Journey curve, specifically includes the following steps:
S1. the acceleration responsive of 8 measuring point of the ring section structure under the excitation of practical basis acceleration is obtained, composition is rung
Answer array y；
S2. the finite element model for establishing ring section structure, includes the following steps；
S21: the initial finite element model of practical ring section structure is established；
S22: it is based on modal test, obtains the modal data of practical structures；
S23: Modifying model is carried out to initial finite element model based on the modal data of modal test, acquisition is revised to be had
Meta-model is limited, as shown in Figure 2.
S3. it determines B-spline basic function expression formula, applies the distribution pulse excitation of basic function form respectively to model, obtain
Acceleration responsive measuring point unit impulse response function simultaneously establishes transfer function matrix, comprising the following steps:
S31: will be divided into 8 sections at annular spread dynamic load effect, select 8 control points, consider annular distribution load
Periodic boundary condition, obtain 3 B-spline basic functions [0,8) calculation formula in section are as follows:
Ni+1,p(x)=Ni,p(x+1), (4) i=0,1,2,3,4
For borderline B-spline basic function, calculation formula is respectively as follows:
S32: finite element method is utilized, panel load is converted by the distribution pulse excitation of each B-spline basic function form and applies
It is added on finite element model, the impulse response function g of acceleration responsive measuring point is calculated using finite element softwarek,i(t), have
Steps are as follows for body:
The distribution pulse excitation N of B-spline basic function formi(x, t) may be expressed as:
Ni(x, t)=Ni,p(x)·s0(t) (8)
In formula, Ni(x, t) is i-th of distribution pulse excitation；s0It (t) is unit pulse excitation, i.e., zero moment amplitude is 1,
The transient state that remaining moment amplitude is 0 motivates.
Using finite element method, distributed pulse is motivated into Ni(x, t) is converted into the panel load of structure, and cell node carries
Lotus Fe(t) it can be integrated and be obtained by shape function:
In formula, l is element length, NeIt (x) is unit shape function.
S33: by the impulse response function g of acceleration responsive measuring pointk,i(t) it is assembled into transfer function matrix G, and establishes knot
The calculated relationship of structure response and excitation, can indicate are as follows:
In formula, ymIt indicates to respond y at m-th of measuring pointmIn the column vector that the value at each time point forms；sn(t) it indicates n-th
S is motivated at control pointn(t) column vector composed by the value at each time point；Gm,nIt is structure in n-th p times B-spline basic function
Nn,pUnder the pulse excitation effect of form, the impulse response function g that is obtained at m-th of measuring pointm,n(t) impulse response square composed by
Battle array, BnIt is the coefficient for representing n-th of B-spline basic function.
S4. distribution dynamic loading is solved using actual measureed value of acceleration response and transfer function matrix, comprising the following steps:
S41: utilizing least square method and regularization method, solves B-spline basic function coefficient BiWith basic excitation time-histories s
(t) product, the specific steps are as follows:
Formula (10) is turned to:
{ Bs (t) }=(GTG)-1GT{Y} (11)
In formula, Y is the acceleration responsive y of m measuring pointkThe column vector of composition；G is the transmitting that impulse response matrix is assembled into
Matrix；Bs (t) is B-spline basic function coefficient BiWith excitation each time point value si(t) column vector of product composition.
S42: according to the following formula, by B-spline basic function coefficient BiWith product vector Bs (t) inverting of basic excitation time-histories s (t)
Annular distribution dynamic loading q (x, t):
Load history discre value and true value at the annular spread dynamic loading position that identification obtains are given in Fig. 3
It compares, the spatial distribution for the annular spread dynamic loading that identification obtains and the comparing result being really distributed is given in Fig. 4.Thus may be used
Know, the recognition methods in the present invention can accurately identify annular spread dynamic loading using the acceleration responsive data at limited measure node
With space distribution and change with time, suitable for the dynamic loading with abrupt local distribution characteristics.Meanwhile with based on just
Polynomial Dynamic Load Identification method is handed over to compare, when being identified for the annular spread dynamic loading with periodic feature, this
The method that invention proposes can guarantee the head and the tail continuity of dynamic loading spatial distribution recognition result, also can guarantee dynamic load distribution function
The continuity of derivative.In conclusion method proposed by the present invention has certain advance.
Claims (4)
1. a kind of annular spread Dynamic Load Identification method based on B-spline function, which is characterized in that this method includes following step
It is rapid:
S1, acceleration responsive of the ring section structure under the excitation of practical basis acceleration is obtained；
S2, the finite element model for establishing ring section structure；
S3, it determines B-spline basic function expression formula, applies the distribution pulse excitation of basic function form respectively to model, obtain and accelerate
Degree response measuring point unit impulse response function simultaneously establishes transfer function matrix；
S4, distribution dynamic loading is solved using actual measureed value of acceleration response and transfer function matrix.
2. a kind of annular distribution Dynamic Load Identification method based on B-spline function according to claim 1, feature exist
In establishing the finite element model of ring section structure described in step S2, the specific method is as follows:
S21: the initial finite element model of practical ring section structure is established；
S22: the modal data of practical structures is obtained based on modal test；
S23: Modifying model is carried out to initial finite element model based on the modal data of modal test, obtains revised finite element
Model.
3. a kind of annular distribution Dynamic Load Identification method based on B-spline function according to claim 1 or 2, feature
It is, determination B-spline basic function expression formula described in step S3, the distribution pulse for applying basic function form respectively to model swashs
It encourages, obtain acceleration responsive measuring point unit impulse response function and establishes transfer function matrix the specific method is as follows:
S31: determining B-spline basic function number and control point number and position, considers the periodic boundary item of annular distribution load
Part, in section [x0,xn) on obtain k B-spline basic function expression formula, x0It is section starting point, xnIt is section terminal, it can be with table
It is shown as:
Ni+1,p(x)=Ni,p(x+Δx) (3)
In formula, p is the number of B-spline basic function, Ni,pIt (x) is i-th p times B-spline basic function, xiFor i-th control point
Abscissa, it is contemplated that periodic boundary condition, xn+i=xi, Δ x is the distance between control point, and Δ x is arranged and immobilizes；
S32: finite element method is utilized, panel load is converted by the distribution pulse excitation of each B-spline basic function form and is applied to
On finite element model, the impulse response function g of acceleration responsive measuring point is calculated using finite element softwarek,i(t), specific step
It is rapid as follows:
The distribution pulse excitation N of B-spline basic function formi(x, t) may be expressed as:
Ni(x, t)=Ni,p(x)·s0(t) (4)
In formula, Ni(x, t) is i-th of distribution pulse excitation；s0(t) be unit pulse excitation, i.e., zero moment amplitude be 1, remaining when
The transient state that amplitude is 0 is carved to motivate；
Using finite element method, pulse excitation N will be distributedi(x, t) is converted into the panel load of structure, cell node load Fe(t)
It can be integrated and be obtained by shape function:
In formula, l is element length, NeIt (x) is unit shape function；
S33: by the impulse response function g of acceleration responsive measuring pointk,i(t) it is assembled into transfer function matrix G, and establishes structure and rings
It should can be indicated with the calculated relationship of excitation are as follows:
In formula, ymIt indicates to respond y at m-th of measuring pointmIn the column vector that the value at each time point forms；sn(t) n-th of control is indicated
S is motivated at pointn(t) column vector composed by the value at each time point；Gm,nIt is structure in n-th p times B-spline basic function Nn,pShape
Under the pulse excitation effect of formula, the impulse response function g that is obtained at m-th of measuring pointm,n(t) impulse response matrix composed by, Bn
It is the coefficient for representing n-th of B-spline basic function.
4. a kind of annular distribution Dynamic Load Identification method based on B-spline function according to claim 3, feature exist
In, in step S4, the specific method packet that distribution dynamic loading is solved using actual measureed value of acceleration response and transfer function matrix
It includes:
S41: utilizing least square method and regularization method, solves B-spline basic function coefficient BiWith multiplying for basic excitation time-histories s (t)
Product, the specific steps are as follows:
Formula (6) is turned to:
{ Bs (t) }=(GTG)-1GT{Y} (7)
In formula, Y is the acceleration responsive y of m measuring pointkThe column vector of composition；G is the transfer matrix that impulse response matrix is assembled into；
Bs (t) is B-spline basic function coefficient BiWith excitation each time point value si(t) column vector of product composition；
S42: according to the following formula, by B-spline basic function coefficient BiIt is cyclic annular with product vector Bs (t) inverting of basic excitation time-histories s (t)
It is distributed dynamic loading q (x, t):
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