CN112201315A - Method and device for analyzing natural frequency of composite material undercarriage structure - Google Patents

Method and device for analyzing natural frequency of composite material undercarriage structure Download PDF

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CN112201315A
CN112201315A CN202010916722.7A CN202010916722A CN112201315A CN 112201315 A CN112201315 A CN 112201315A CN 202010916722 A CN202010916722 A CN 202010916722A CN 112201315 A CN112201315 A CN 112201315A
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陈潇
张鑫
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Beijing Institute of Specialized Machinery
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Abstract

The application discloses a natural frequency analysis method of a composite landing gear structure, which can be used for carrying out preset treatment on a composite single-layer plate to obtain mechanical property parameters of the composite single-layer plate; according to the mechanical property parameters, determining uncertain distribution characteristic parameters of the composite single-layer plate and a maximum difference curve under any polar coordinate; determining the pole of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate; determining the corresponding natural frequency of each pole of the convex polyhedral model; and comparing the corresponding natural frequencies at the poles to determine the maximum and minimum values of the natural frequencies of the composite landing gear structure. Therefore, the distribution range of the natural frequency of the undercarriage can be rapidly and accurately obtained, and the influence of the composite material undercarriage structure on the structure safety situation can be more accurately evaluated.

Description

Method and device for analyzing natural frequency of composite material undercarriage structure
Technical Field
The application relates to the field of composite landing gear structure analysis, in particular to a natural frequency analysis method, a system and a device for a composite landing gear structure.
Background
The fiber reinforced composite material laminated plate has the advantages of light weight, high specific strength, high specific stiffness, good designability and the like, is widely applied to the field of aerospace, and gradually advances towards the structural design direction of the undercarriage. The landing gear generally accounts for 6% -8% of the weight of the structure, so that the application of the advanced composite material to the landing gear structure design has important significance. Furthermore, during the structural design process, the landing gear must not only meet certain static strength design criteria and requirements, but more importantly must also meet a range of dynamic requirements such as take-off, landing, running, etc. In particular, under the action of the dynamic loads which change periodically, the main components of the landing gear can generate strong resonance due to unreasonable structural design or insufficient rigidity or the coupling of the natural frequency of the system and the shimmy frequency, and the reliability and the stability of the landing gear operation are seriously influenced. Therefore, in the dynamic design process of the undercarriage structure, as a key parameter of the structure vibration performance, the accurate prediction of the characteristic value or the natural frequency, the modal shape and the like of the undercarriage structure has very obvious engineering significance.
However, it is clear that the macroscopic mechanical properties of the composite structure are often closely related to the inherent dispersibility of the component materials, the complex processing and production processes, and the like; in each link of preparation and service, uncertain factors are widely existed and can not be avoided, so that the structure has various uncertain sources and the parameter dispersion effect is obvious. Furthermore, the structural design and the structural response performance evaluation of the composite material are greatly influenced. Therefore, how to reasonably recognize and effectively measure the uncertain mechanical performance parameters and the dispersity of the strength parameters so as to evaluate the influence on the structural safety situation, and developing an efficient and accurate structural performance prediction theory and method are necessary conditions for guiding the structural analysis, design and manufacture of the composite material, and are also important challenges to be urgently broken through in the field of current aerospace.
Disclosure of Invention
The application provides a natural frequency analysis method and device of a composite landing gear structure, so that the distribution range of the natural frequency of the landing gear can be rapidly and accurately obtained, certain theoretical data support can be provided for further structural optimization design, vibration analysis and the like, and further the influence of the composite landing gear structure on the structure safety situation can be more accurately evaluated.
In a first aspect, the present application provides a method of natural frequency analysis of a composite landing gear structure comprising a single ply of composite material, the method comprising:
presetting a composite material single-layer plate to obtain mechanical property parameters of the composite material single-layer plate;
according to the mechanical property parameters, determining uncertain distribution characteristic parameters of the composite single-layer plate and a maximum difference curve under any polar coordinate;
determining the poles of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate;
determining the natural frequency corresponding to each pole of the convex polyhedral model; the calculation method of the corresponding natural frequency at each pole point is as follows: for each pole, determining the natural frequency corresponding to the pole by using the rigidity matrix and the mass matrix of the composite landing gear structure;
and determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency of each pole.
Optionally, the preset processing includes: longitudinal tensile test treatment, transverse tensile test treatment and in-plane shear test treatment; the mechanical property parameters of the composite material single-layer plate comprise: longitudinal tensile modulus, transverse tensile modulus, poisson's ratio, and in-plane shear modulus.
Optionally, the determining, according to the mechanical property parameter, an uncertain distribution characteristic parameter of the composite single-layer plate and a maximum difference curve under any polar coordinate includes:
evaluating and analyzing the mechanical property parameters by using a non-statistical measuring method gray scale theory or an information entropy theory to obtain uncertain distribution characteristic parameters of the composite material single-layer plate; the uncertain distribution characteristic parameters comprise a mean value, an interval radius, an upper bound and a lower bound of the mechanical property parameters;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the accumulated sequence and the mean accumulated sequence of the mechanical property parameters under any polar coordinate in different quantization directions.
Optionally, the determining a maximum difference curve of the composite single-layer plate in any polar coordinate according to the accumulated sequence and the mean accumulated sequence of the mechanical property parameters in any polar coordinate in different quantization directions includes:
randomly selecting two groups of mechanical property parameters from the mechanical property parameters;
determining a combination sequence under any polar coordinates in different quantization directions based on the two sets of mechanical property parameters;
determining the difference value between the accumulation sequence corresponding to the combination sequence under each polar coordinate and the mean accumulation sequence;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the combined sequence with the maximum difference between the accumulation sequence and the mean accumulation sequence.
Optionally, the determining the pole of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate includes:
determining a convex polyhedron model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinates;
based on the convex polyhedral model, poles of the convex polyhedral model are determined.
Optionally, for each pole, determining the natural frequency corresponding to the pole by using the stiffness matrix and the mass matrix of the composite landing gear structure includes:
for each pole, determining a characteristic value of the natural frequency corresponding to the pole by using the stiffness matrix and the mass matrix of the composite landing gear structure;
and determining the natural frequency corresponding to the pole according to the characteristic value of the natural frequency corresponding to the pole.
Optionally, the determining a maximum value and a minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency at each pole includes:
and determining the pole with the maximum or minimum characteristic value of the natural frequency in all the poles, and taking the maximum value and the minimum value of the natural frequency corresponding to the pole as the maximum value and the minimum value of the natural frequency of the composite landing gear structure.
In a second aspect, an apparatus for natural frequency analysis of a composite landing gear structure, the composite landing gear structure comprising a single sheet of composite material, the apparatus comprising:
the device comprises a first determining unit, a second determining unit and a control unit, wherein the first determining unit is used for carrying out preset processing on a composite material single-layer plate to obtain mechanical property parameters of the composite material single-layer plate;
the second determining unit is used for determining the uncertain distribution characteristic parameters of the composite material single-layer plate and the maximum difference curve under any polar coordinate according to the mechanical property parameters;
the third determining unit is used for determining the pole of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate;
a fourth determining unit, configured to determine natural frequencies corresponding to the poles of the convex polyhedral model; the calculation method of the corresponding natural frequency at each pole point is as follows: for each pole, determining the natural frequency corresponding to the pole by using the rigidity matrix and the mass matrix of the composite landing gear structure;
and the fifth determining unit is used for determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency of each pole.
Optionally, the preset processing includes: longitudinal tensile test treatment, transverse tensile test treatment and in-plane shear test treatment; the mechanical property parameters of the composite material single-layer plate comprise: longitudinal tensile modulus, transverse tensile modulus, poisson's ratio, and in-plane shear modulus.
Optionally, the second determining unit is configured to:
evaluating and analyzing the mechanical property parameters by using a non-statistical measuring method gray scale theory or an information entropy theory to obtain uncertain distribution characteristic parameters of the composite material single-layer plate; the uncertain distribution characteristic parameters comprise a mean value, an interval radius, an upper bound and a lower bound of the mechanical property parameters;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the accumulated sequence and the mean accumulated sequence of the mechanical property parameters under any polar coordinate in different quantization directions.
Optionally, the second determining unit is specifically configured to:
randomly selecting two groups of mechanical property parameters from the mechanical property parameters;
determining a combination sequence under any polar coordinates in different quantization directions based on the two sets of mechanical property parameters;
determining the difference value between the accumulation sequence corresponding to the combination sequence under each polar coordinate and the mean accumulation sequence;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the combined sequence with the maximum difference between the accumulation sequence and the mean accumulation sequence.
Optionally, the third determining unit is configured to:
determining a convex polyhedron model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinates;
based on the convex polyhedral model, poles of the convex polyhedral model are determined.
Optionally, the fourth determining unit is configured to:
for each pole, determining a characteristic value of the natural frequency corresponding to the pole by using the stiffness matrix and the mass matrix of the composite landing gear structure;
and determining the natural frequency corresponding to the pole according to the characteristic value of the natural frequency corresponding to the pole.
Optionally, the fourth determining unit is specifically configured to:
and determining the pole with the maximum or minimum characteristic value of the natural frequency in all the poles, and taking the maximum value and the minimum value of the natural frequency corresponding to the pole as the maximum value and the minimum value of the natural frequency of the composite landing gear structure.
In a third aspect, the present application provides a readable medium comprising executable instructions, which when executed by a processor of an electronic device, perform the method according to any of the first aspect.
In a fourth aspect, the present application provides an electronic device comprising a processor and a memory storing execution instructions, wherein when the processor executes the execution instructions stored in the memory, the processor performs the method according to any one of the first aspect.
According to the technical scheme, the composite single-layer plate can be subjected to preset treatment to obtain the mechanical property parameters of the composite single-layer plate; then, according to the mechanical property parameters, determining uncertain distribution characteristic parameters of the composite material single-layer plate and a maximum difference curve under any polar coordinate; secondly, determining the poles of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate; then, determining the maximum value and the minimum value of the natural frequency respectively corresponding to each pole of the convex polyhedral model; and finally, determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency at each polar point. Therefore, in order to quickly and accurately predict the natural frequency performance response of the composite material undercarriage structure and simultaneously consider the influence of uncertain mechanical parameters of the composite material, the uncertain mechanical parameters are mathematically characterized into a convex polyhedral model described by a series of linear inequality constraint equations by a non-probability statistic measurement method, and then the pole of the convex polyhedral model is used for solving, so that the distribution range of the undercarriage natural frequency can be quickly and accurately obtained, the influence of the composite material undercarriage structure on the structure safety situation can be more accurately evaluated, data support is provided for effectively avoiding the undercarriage structure natural frequency from falling into a resonance and shimmy frequency domain area in the undercarriage structure optimization design, technical guarantee is provided for the rationality of the structure design, and the reliability and stability of the structure are improved; in addition, the method for analyzing and calculating the natural frequency of the composite landing gear structure not only ensures the effectiveness and rationality of the calculation of the natural frequency, but also considers the influence of uncertain mechanical parameters on the structure, so that the obtained natural frequency analysis result not only can reach certain precision and reliability, but also is convenient to calculate.
Further effects of the above-mentioned unconventional preferred modes will be described below in conjunction with specific embodiments.
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In order to more clearly illustrate the embodiments or prior art solutions of the present application, the drawings needed for describing the embodiments or prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present application, and that other drawings can be obtained by those skilled in the art without inventive exercise.
FIG. 1 is a schematic flow diagram of a method for natural frequency analysis of a composite landing gear structure according to the present application;
FIG. 2 is a schematic view of an uncertain region of mechanical property parameters of a composite single-layer board provided in an embodiment of the present application;
fig. 3 is a schematic diagram of a finite element model of a composite landing gear of an unmanned aerial vehicle according to an embodiment of the present application;
FIG. 4 is a schematic structural diagram of a natural frequency analysis device for a composite landing gear structure according to an embodiment of the present disclosure;
fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail and completely with reference to the following embodiments and accompanying drawings. It should be apparent that the described embodiments are only some of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
In order to quickly and accurately obtain the distribution range of the natural frequency of the undercarriage, certain theoretical data support can be provided for further structural optimization design, vibration analysis and the like, and further the influence of the composite undercarriage structure on the structural safety situation can be more accurately evaluated.
The application provides a natural frequency analysis method of a composite landing gear structure, which can be used for presetting a composite single-layer plate to obtain mechanical property parameters of the composite single-layer plate; then, according to the mechanical property parameters, determining uncertain distribution characteristic parameters of the composite material single-layer plate and a maximum difference curve under any polar coordinate; secondly, determining the poles of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate; then, determining the corresponding natural frequency of each pole of the convex polyhedral model; and finally, determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency at each polar point. Therefore, in order to quickly and accurately predict the natural frequency performance response of the composite material undercarriage structure and simultaneously consider the influence of uncertain mechanical parameters of the composite material, the uncertain mechanical parameters are mathematically characterized into a convex polyhedral model described by a series of linear inequality constraint equations by a non-probability statistic measurement method, and then the pole of the convex polyhedral model is used for solving, so that the distribution range of the undercarriage natural frequency can be quickly and accurately obtained, the influence of the composite material undercarriage structure on the structure safety situation can be more accurately evaluated, data support is provided for effectively avoiding the undercarriage structure natural frequency from falling into a resonance and shimmy frequency domain area in the undercarriage structure optimization design, technical guarantee is provided for the rationality of the structure design, and the reliability and stability of the structure are improved; in addition, the method for analyzing and calculating the natural frequency of the composite landing gear structure not only ensures the effectiveness and rationality of the calculation of the natural frequency, but also considers the influence of uncertain mechanical parameters on the structure, so that the obtained natural frequency analysis result not only can reach certain precision and reliability, but also is convenient to calculate.
Various non-limiting embodiments of the present application are described in detail below with reference to the accompanying drawings.
Referring to FIG. 1, a method of natural frequency analysis of a composite landing gear structure in an embodiment of the present application is shown. In this embodiment, the method may include, for example, the steps of:
s101: and carrying out preset treatment on the composite single-layer plate to obtain the mechanical property parameters of the composite single-layer plate.
After determining the composite landing gear structure needing to analyze the natural frequency, the composite single-layer plate in the composite landing gear structure can be subjected to preset processing, so that the mechanical property parameters of the composite single-layer plate can be obtained. Wherein the preset processing may include: longitudinal tensile test treatment, transverse tensile test treatment and in-plane shear test treatment; the longitudinal tensile modulus E of the composite single-layer board can be obtained by subjecting the composite single-layer board to a longitudinal tensile test treatment1And carrying out transverse tensile test treatment on the composite single-layer plate to obtain the transverse tensile modulus E of the composite single-layer plate2Carrying out in-plane shear test treatment on the composite material single-layer plate to obtain the Poisson ratio v of the composite material single-layer plate12And in-plane shear modulus G12That is, the mechanical property parameters of the composite single-layer board may include: longitudinal tensile modulus, transverse tensile modulus, Poisson's ratioAnd in-plane shear modulus. In one implementation, the composite monocoque panel may be a fiber-reinforced composite monocoque panel.
In one implementation, the mechanical property parameters of the composite material single-layer board may be stored in a form of a data matrix, for example, the data matrix formed by the mechanical property parameters of each composite material single-layer board may be:
Figure BDA0002665275640000091
wherein x1(1),x2(1),…,xmAnd (p) is a mechanical property parameter, m is the number of the mechanical property parameters of the single-layer plate, and p is the number of sample data of each mechanical property parameter.
For example, a composite landing gear may be comprised primarily of fuselage mounting plates, composite bumper beams, wheel forks, axles, wheels, and tires. The landing gear composite material bumper beam structure is a sandwich carbon fiber reinforced composite material structure. The core body material is of a foam structure, carbon fiber layering reinforcement is carried out on the upper surface and the lower surface of the core body, and finally solidification molding is carried out. The composite material is a T300/QY8911 carbon fiber unidirectional tape with the density of 1.62g/cm 3. The composite material layering information is [45/-45/0/0]2SAnd 16 layers in total, and the thickness of a single layer is 0.125 mm. The rest parts are 7050 aluminum alloy. The test data points of the composite material T300/QY8911 carbon fiber unidirectional tape elastic mechanical parameters (namely mechanical property parameters) are shown in Table 1.
TABLE 1T 300/QY8911 elastomechanical parameter test data points
Figure BDA0002665275640000092
S102: and according to the mechanical property parameters, determining uncertain distribution characteristic parameters of the composite material single-layer plate and a maximum difference curve under any polar coordinate.
In this embodiment, the uncertain distribution characteristic parameter of the composite material single-layer board may be determined according to the mechanical property parameter. As an example, a non-statistical measurement method gray scale theory or an information entropy theory may be utilized to perform evaluation analysis on the mechanical property parameters to obtain uncertain distribution characteristic parameters of the composite material single-layer plate; the uncertain distribution characteristic parameters can comprise a mean value, an interval radius, an upper bound and a lower bound of the mechanical property parameters.
Specifically, the uncertain distribution characteristic parameters of the mechanical property parameters X including the mean value X of the mechanical property parameters are obtained by evaluating and analyzing the test data by using a non-statistical measurement method gray scale theory or an information entropy theorycInterval radius XrUpper bound, lower bound
Figure BDA0002665275640000101
And lower boundXI.e. by
Figure BDA0002665275640000102
Wherein x ═ x1 x2 … xm]T，
Figure BDA0002665275640000103
AndX＝[x 1 x 2 … x m]T(ii) a Where x is1,x2,…,xmIs the mechanical property parameter of the single-layer board of the composite material. Wherein the gray scale theory is that a certain mechanical property parameter x is usedjArranging effective test data point sequences including longitudinal tensile modulus, transverse tensile modulus, Poisson's ratio and in-plane shear modulus from small to large to form a new sequence
Figure BDA0002665275640000104
And accumulating once to generate new sequence
Figure BDA0002665275640000105
Wherein the content of the first and second substances,
Figure BDA0002665275640000106
wherein max represents a maximum operation; sjIs based on grey evaluationObtaining an estimated value of the uncertain quantity of the mechanical property parameters; has an average value
Figure BDA0002665275640000107
Then the interval
Figure BDA0002665275640000108
Is the uncertain estimation interval of the mechanical property parameters, 3sjAre the corresponding interval radii. Repeating the operation to obtain the uncertain estimation interval of the mechanical property parameter x of the single-layer plate
Figure BDA0002665275640000109
And mean value XcAnd interval radius XrRespectively is as follows:
Figure BDA00026652756400001010
Xr＝[3s1 3s2 … 3sm]T，
Figure BDA00026652756400001011
Figure BDA0002665275640000111
in this embodiment, the maximum difference curve of the composite single-layer board in any polar coordinate may be determined according to the mechanical property parameter. As an example, the maximum difference curve of the composite single-layer board in any polar coordinate may be determined according to the accumulated sequence and the mean accumulated sequence of the mechanical property parameters in any polar coordinate in different quantization directions. In one implementation, two sets of mechanical property parameters can be selected from the mechanical property parameters at will; then, a combination sequence under any polar coordinate in different quantization directions can be determined based on the two sets of mechanical property parameters; then, the difference between the accumulated sequence and the mean accumulated sequence corresponding to the combined sequence in each polar coordinate can be determined, so that the difference between the accumulated sequence and the mean accumulated sequence corresponding to the combined sequences in a plurality of polar coordinates can be obtained; next, a maximum difference curve of the composite single-layer board at any polar coordinate may be determined according to a combination sequence with the maximum difference between the accumulation sequence and the mean accumulation sequence, that is, a combination sequence with the maximum difference between the accumulation sequence and the mean accumulation sequence may be determined from differences between the accumulation sequence and the mean accumulation sequence corresponding to the combination sequences at a plurality of polar coordinates, and the maximum difference curve of the composite single-layer board at any polar coordinate may be determined according to a combination sequence with the maximum difference between the accumulation sequence and the mean accumulation sequence.
Specifically, aiming at the test data matrix corresponding to the mechanical property parameters
Figure BDA0002665275640000112
Taking any two mechanical property parameter test data to form a new data sequence
Figure BDA0002665275640000113
Taking any polar coordinate theta in different quantization directionslForming a combined sequence as follows: e (theta)l)＝{e(k,θl) K ═ 1,2, …, p }; wherein e (k, theta)l)＝xi(k)cosθl+xj(k)sinθl. Then, each polar coordinate θlThe following combined sequences can be arranged in ascending order, and the ascending sequence can be obtained as follows: e.g. of the type(0)(θl)＝{e(0)(k,θl) K is 1,2, …, p, and the accumulated sequence is e(1)(θl)＝{e(1)(k,θl) K is 1,2, …, p, wherein,
Figure BDA0002665275640000114
the difference between the accumulated sequence and the mean accumulated sequence is obtained
Figure BDA0002665275640000121
Then arbitrary polar coordinate θlThe following maximum difference curve is calculated as shown in the following formula：
Δij max(θl)＝max(Δmax(k,θl),k＝1,2,…,p)。
After obtaining the maximum difference curves in all polar coordinates, the maximum difference curve Δ can be usedij max(θl) To estimate the dispersion of two uncertain mechanical property parameters.
Next, the explanation is continued by taking the example corresponding to table 1 as an example. The interval model and the convex polyhedron model of the composite material with uncertain mechanical property parameters can be obtained by a non-probability analysis method, which are respectively shown in (a) and (b) in fig. 2, and the characteristic parameters of the uncertain mechanical parameters are shown in table 2. The hollow points are test data sample points, and the solid points are uncertain mechanical parameter nominal values. The area enveloped by the straight line A is an uncertain interval model of elastic mechanical parameters, and the area enveloped by the curve B is an uncertain convex polyhedral model of the elastic mechanical parameters.
TABLE 2 uncertain mechanical parameters characteristic parameters
Figure BDA0002665275640000122
S103: and determining the pole of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate.
After the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate are determined, the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate can be utilized to characterize the mechanical property parameters into a convex polyhedral model described by a linear constraint inequality equation. Then, the linear constraint inequality can be solved to obtain the pole of the convex polyhedral model corresponding to the mechanical property parameters.
As an example, the obtained uncertain distribution characteristic parameters of the mechanical property parameters and the maximum difference curve under any polar coordinate can be used to mathematically characterize the mechanical property parameters x of the composite material single-layer plate as a series of linear inequality constraint equations as follows:
Figure BDA0002665275640000131
the method can be simplified as follows:
Ax≤b
A∈RM×m,x∈Rm,b∈RM
wherein A ═ aij)M×mIs an M × M dimensional coefficient matrix, M is the number of linear inequality constraints, and then a feasible domain S (a closed and bounded convex polyhedron model) of mechanical property parameters can be expressed as:
S＝{x∈Rm|Ax≤b}。
after the convex polyhedral model corresponding to the mechanical property parameters is determined, the linear inequality equation corresponding to the convex polyhedral model corresponding to the mechanical property parameters can be solved, and the pole of the convex polyhedral model can be obtained. The poles of the convex polyhedral model are determined in the following manner: according to the Krein-Milman theory of quantitation, each point x in the convex polyhedral model can be expressed as
Figure BDA0002665275640000132
Wherein y isiIs the poles of the convex polyhedral model, L is the number of all poles, alphaiA coefficient of 0 or more; and solving to obtain the pole of the convex polyhedron model.
S104: determining a corresponding natural frequency at each pole of the convex polyhedral model.
After the poles of the convex polyhedral model are determined, the corresponding natural frequencies at each pole can be determined. The calculation method of the natural frequency corresponding to each pole is as follows: and for each pole, determining the natural frequency corresponding to the pole by using the rigidity matrix and the mass matrix of the composite landing gear structure. Specifically, the characteristic value corresponding to the natural frequency of the pole may be determined by using a stiffness matrix and a mass matrix of the composite landing gear structure, where the characteristic value corresponding to the natural frequency is a square of the natural frequency.
In particular, the characteristic values of the natural frequencies of the composite landing gear structure may be expressed in the form:
K(x)u＝λM(x)u；
wherein: k and M are the stiffness matrix and the mass matrix of the landing gear structure, respectively. Wherein the composite material structure rigidity matrix K is composed of a unit rigidity matrix KeAssembled to form a cell stiffness matrix KeAs shown below
Figure BDA0002665275640000141
Wherein l is the number of laminated structure layers of the composite material, [ B ]]And [ D ]]Respectively a geometric matrix and an elastic matrix. Wherein the elastic matrix [ D]Calculating the mechanical property parameter to obtain [ D]＝[T]-1[C][T]-T；[T]Is a conversion matrix, related to the fiber lay direction; [ C ]]For laminate stiffness, it can be determined by:
Figure BDA0002665275640000142
wherein, based on Maxwell's theorem, it can obtain
Figure BDA0002665275640000143
E2＝E3,G12＝G13
Figure BDA0002665275640000144
Where u is the structural vibration feature vector or mode shape and λ is the square of the corresponding eigenvalue or natural frequency, i.e., λ ═ ω2. According to the convex polyhedral model, the structural stiffness matrix k (x) and the mass matrix m (x) can be expressed in the following combination:
Figure BDA0002665275640000145
Figure BDA0002665275640000146
wherein, Ki,MiRespectively determining a pole matrix of a stiffness matrix and a pole matrix of a quality matrix in an uncertain domain; α ═ α (α)i) Are the corresponding combined coefficient vectors. The eigenvalues can be expressed as: k (α) u ═ λ M (α) u; when the structural rigidity matrix K and the mass matrix M change within an uncertain range, the structural characteristic value change domain can be expressed as: k (α) u ═ λ M (α) u | K, M ∈ Φ }; where Φ is a close-bounded convex polyhedral model, i.e.
Figure BDA0002665275640000151
Figure BDA0002665275640000152
Solving the characteristic value of the structural characteristic value variation domain to obtain the characteristic value of the natural frequency corresponding to the pole as
Figure BDA0002665275640000153
The maximum and minimum values, i.e., the upper and lower bounds, of the eigenvalues may be:
Figure BDA0002665275640000154
wherein λ isminAnd λmaxIs the minimum and maximum of the eigenvalues;
uTK(α)u＝uT(α1K1+α2K2+…+αLKL)u
＝α1uTK1u+α2uTK2u+…+αLuTKL
＝α1p1+α2p2+…+αLpL＝pTα
and
uTM(α)u＝uT(α1M1+α2M2+…+αLML)u
＝α1uTM1u+α2uTM2u+…+αLuTMLu
＝α1p1+α2p2+…+αLpL＝pTα
wherein the content of the first and second substances,
pi＝uTKiu,qi＝uTMiu；i＝1,2,…,L。
further, the maximum and minimum values of the natural frequency can be determined:
Figure BDA0002665275640000155
s105: and determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency of each pole.
As an example, in determining the corresponding natural frequency at each pole, the maximum or minimum of the natural frequencies of all the poles may be determined, and the corresponding natural frequencies at the poles may be taken as the maximum and minimum of the natural frequencies of the composite landing gear structure.
Specifically, in determining the natural frequency corresponding to each pole, the eigenvalues or natural frequencies under all the poles may be compared, the maximum or minimum of the natural frequencies among all the poles determined, and the natural frequency corresponding to the pole taken as the maximum and minimum of the natural frequency of the composite landing gear structure. The characteristic value boundary of the composite landing gear can be obtained as follows:
Figure BDA0002665275640000161
Figure BDA0002665275640000162
continuing with the example illustrated in correspondence with table 2, a finite element analysis model may be created using ANSYS finite element analysis software, as shown in fig. 3. The uncertainty regions (i.e., maximum (upper bound) and minimum (lower bound)) for the natural frequencies of the resulting composite landing gear structure are shown in table 3.
TABLE 3 composite landing gear natural frequency
Figure BDA0002665275640000163
This example utilizes the analytical calculation of the natural frequency of a composite landing gear structure with uncertain mechanical properties parameters by means of MATLAB and finite element analysis software ANSYS.
According to the technical scheme, the composite single-layer plate can be subjected to preset treatment to obtain the mechanical property parameters of the composite single-layer plate; then, according to the mechanical property parameters, determining uncertain distribution characteristic parameters of the composite material single-layer plate and a maximum difference curve under any polar coordinate; secondly, determining the poles of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate; then, determining the corresponding natural frequency of each pole of the convex polyhedral model; and finally, determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency at each polar point. Therefore, in order to quickly and accurately predict the natural frequency performance response of the composite material undercarriage structure and simultaneously consider the influence of uncertain mechanical parameters of the composite material, the uncertain mechanical parameters are mathematically characterized into a convex polyhedral model described by a series of linear inequality constraint equations by a non-probability statistic measurement method, and then the pole of the convex polyhedral model is used for solving, so that the distribution range of the undercarriage natural frequency can be quickly and accurately obtained, the influence of the composite material undercarriage structure on the structure safety situation can be more accurately evaluated, data support is provided for effectively avoiding the undercarriage structure natural frequency from falling into a resonance and shimmy frequency domain area in the undercarriage structure optimization design, technical guarantee is provided for the rationality of the structure design, and the reliability and stability of the structure are improved; in addition, the method for analyzing and calculating the natural frequency of the composite landing gear structure not only ensures the effectiveness and rationality of the calculation of the natural frequency, but also considers the influence of uncertain mechanical parameters on the structure, so that the obtained natural frequency analysis result not only can reach certain precision and reliability, but also is convenient to calculate.
Fig. 4 illustrates a specific embodiment of a natural frequency analysis device for a composite landing gear structure according to the present application. The apparatus of this embodiment is a physical apparatus for executing the method of the above embodiment. The technical solution is essentially the same as that in the above embodiment, and the corresponding description in the above embodiment is also applicable to this embodiment. The composite landing gear structure comprises a composite single-ply panel, the device in this embodiment comprising:
the first determining unit 401 is configured to perform preset processing on a composite single-layer board to obtain mechanical property parameters of the composite single-layer board;
a second determining unit 402, configured to determine, according to the mechanical property parameter, an uncertain distribution characteristic parameter of the composite single-layer plate and a maximum difference curve in any polar coordinate;
a third determining unit 403, configured to determine a pole of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and a maximum difference curve under any polar coordinate;
a fourth determining unit 404, configured to determine natural frequencies corresponding to the poles of the convex polyhedral model; the calculation method of the natural frequency corresponding to each pole is as follows: for each pole, determining the natural frequency corresponding to the pole by using the rigidity matrix and the mass matrix of the composite landing gear structure;
a fifth determining unit 405, configured to determine a maximum value and a minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency at each pole.
Optionally, the preset processing includes: longitudinal tensile test treatment, transverse tensile test treatment and in-plane shear test treatment; the mechanical property parameters of the composite material single-layer plate comprise: longitudinal tensile modulus, transverse tensile modulus, poisson's ratio, and in-plane shear modulus.
Optionally, the second determining unit 502 is configured to:
evaluating and analyzing the mechanical property parameters by using a non-statistical measuring method gray scale theory or an information entropy theory to obtain uncertain distribution characteristic parameters of the composite material single-layer plate; the uncertain distribution characteristic parameters comprise a mean value, an interval radius, an upper bound and a lower bound of the mechanical property parameters;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the accumulated sequence and the mean accumulated sequence of the mechanical property parameters under any polar coordinate in different quantization directions.
Optionally, the second determining unit 502 is specifically configured to:
randomly selecting two groups of mechanical property parameters from the mechanical property parameters;
determining a combination sequence under any polar coordinates in different quantization directions based on the two sets of mechanical property parameters;
determining the difference value between the accumulation sequence corresponding to the combination sequence under each polar coordinate and the mean accumulation sequence;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the combined sequence with the maximum difference between the accumulation sequence and the mean accumulation sequence.
Optionally, the third determining unit 503 is configured to:
determining a convex polyhedron model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinates;
based on the convex polyhedral model, poles of the convex polyhedral model are determined.
Optionally, the fourth determining unit 504 is configured to:
for each pole, determining a characteristic value of the natural frequency corresponding to the pole by using the stiffness matrix and the mass matrix of the composite landing gear structure;
and determining the natural frequency corresponding to the pole according to the characteristic value of the natural frequency corresponding to the pole.
Optionally, the fourth determining unit 504 is specifically configured to:
and determining the maximum or minimum pole of all the poles, and taking the natural frequency corresponding to the pole as the maximum value and the minimum value of the natural frequency of the composite landing gear structure.
Fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present application. On the hardware level, the electronic device comprises a processor and optionally an internal bus, a network interface and a memory. The Memory may include a Memory, such as a Random-Access Memory (RAM), and may further include a non-volatile Memory, such as at least 1 disk Memory. Of course, the electronic device may also include hardware required for other services.
The processor, the network interface, and the memory may be connected to each other via an internal bus, which may be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, an EISA (Extended Industry Standard Architecture) bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one double-headed arrow is shown in FIG. 5, but this does not indicate only one bus or one type of bus.
And the memory is used for storing the execution instruction. In particular, a computer program that can be executed by executing instructions. The memory may include both memory and non-volatile storage and provides execution instructions and data to the processor.
In a possible implementation mode, the processor reads corresponding execution instructions from the nonvolatile memory into the memory and then runs the corresponding execution instructions, and corresponding execution instructions can also be obtained from other equipment so as to form the natural frequency analysis device of the composite landing gear structure on a logic level. The processor executes the execution instructions stored in the memory to implement the natural frequency analysis method of the composite landing gear structure provided in any embodiment of the present application through the executed execution instructions.
The method performed by the natural frequency analysis device for the composite landing gear structure provided in the embodiment of fig. 1 of the present application may be applied to or implemented by a processor. The processor may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in a processor or instructions in the form of software. The Processor may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; but also Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components. The various methods, steps, and logic blocks disclosed in the embodiments of the present application may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The steps of the method disclosed in connection with the embodiments of the present application may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in a memory, and a processor reads information in the memory and completes the steps of the method in combination with hardware of the processor.
Embodiments of the present application also provide a readable storage medium storing executable instructions, which when executed by a processor of an electronic device, enable the electronic device to perform the method for natural frequency analysis of a composite landing gear structure provided in any of the embodiments of the present application, and in particular for performing the method for natural frequency analysis of a composite landing gear structure described above.
The electronic device described in the foregoing embodiments may be a computer.
It will be apparent to those skilled in the art that embodiments of the present application may be provided as a method or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects.
The embodiments in the present application are described in a progressive manner, and the same and similar parts among the embodiments can be referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, as for the apparatus embodiment, since it is substantially similar to the method embodiment, the description is relatively simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above description is only an example of the present application and is not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims (10)

1. A method of natural frequency analysis of a composite landing gear structure, wherein the composite landing gear structure comprises a composite single-ply panel, the method comprising:
presetting a composite material single-layer plate to obtain mechanical property parameters of the composite material single-layer plate;
according to the mechanical property parameters, determining uncertain distribution characteristic parameters of the composite single-layer plate and a maximum difference curve under any polar coordinate;
determining the poles of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate;
determining the natural frequency corresponding to each pole of the convex polyhedral model; the calculation method of the corresponding natural frequency at each pole point is as follows: for each pole, determining the natural frequency corresponding to the pole by using the rigidity matrix and the mass matrix of the composite landing gear structure;
and determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency of each pole.
2. The method according to claim 1, wherein the pre-setting process comprises: longitudinal tensile test treatment, transverse tensile test treatment and in-plane shear test treatment; the mechanical property parameters of the composite material single-layer plate comprise: longitudinal tensile modulus, transverse tensile modulus, poisson's ratio, and in-plane shear modulus.
3. The method according to claim 1, wherein the determining of the uncertain distribution characteristic parameter of the composite material single-layer plate and the maximum difference curve in any polar coordinate according to the mechanical property parameter comprises:
evaluating and analyzing the mechanical property parameters by using a non-statistical measuring method gray scale theory or an information entropy theory to obtain uncertain distribution characteristic parameters of the composite material single-layer plate; the uncertain distribution characteristic parameters comprise a mean value, an interval radius, an upper bound and a lower bound of the mechanical property parameters;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the accumulated sequence and the mean accumulated sequence of the mechanical property parameters under any polar coordinate in different quantization directions.
4. The method according to claim 3, wherein the determining the maximum difference curve of the composite single-layer board in any polar coordinate according to the accumulated sequence and the mean accumulated sequence of the mechanical property parameters in any polar coordinate in different quantification directions comprises:
randomly selecting two groups of mechanical property parameters from the mechanical property parameters;
determining a combination sequence under any polar coordinates in different quantization directions based on the two sets of mechanical property parameters;
determining the difference value between the accumulation sequence corresponding to the combination sequence under each polar coordinate and the mean accumulation sequence;
and determining a maximum difference curve of the composite material single-layer plate under any polar coordinate according to the combined sequence with the maximum difference between the accumulation sequence and the mean accumulation sequence.
5. The method of claim 1, wherein determining the poles of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate comprises the following steps:
determining a convex polyhedron model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinates;
based on the convex polyhedral model, poles of the convex polyhedral model are determined.
6. The method of claim 1, wherein determining, for each pole, a natural frequency for the pole using a stiffness matrix and a mass matrix of the composite landing gear structure comprises:
for each pole, determining a characteristic value of the natural frequency corresponding to the pole by using the stiffness matrix and the mass matrix of the composite landing gear structure;
and determining the natural frequency corresponding to the pole according to the characteristic value of the natural frequency corresponding to the pole.
7. The method of claim 6, wherein determining the maximum and minimum values of the natural frequency of the composite landing gear structure based on the corresponding natural frequencies at the respective poles comprises:
and determining the pole with the maximum or minimum characteristic value of the natural frequency in all the poles, and taking the maximum value and the minimum value of the natural frequency corresponding to the pole as the maximum value and the minimum value of the natural frequency of the composite landing gear structure.
8. An apparatus for natural frequency analysis of a composite landing gear structure, wherein the composite landing gear structure comprises a single ply of composite material, the apparatus comprising:
the device comprises a first determining unit, a second determining unit and a control unit, wherein the first determining unit is used for carrying out preset processing on a composite material single-layer plate to obtain mechanical property parameters of the composite material single-layer plate;
the second determining unit is used for determining the uncertain distribution characteristic parameters of the composite material single-layer plate and the maximum difference curve under any polar coordinate according to the mechanical property parameters;
the third determining unit is used for determining the pole of the convex polyhedral model according to the uncertain distribution characteristic parameters of the composite single-layer plate and the maximum difference curve under any polar coordinate;
a fourth determining unit, configured to determine natural frequencies corresponding to the poles of the convex polyhedral model; the calculation method of the corresponding natural frequency at each pole point is as follows: for each pole, determining the natural frequency corresponding to the pole by using the rigidity matrix and the mass matrix of the composite landing gear structure;
and the fifth determining unit is used for determining the maximum value and the minimum value of the natural frequency of the composite landing gear structure according to the corresponding natural frequency of each pole.
9. A readable medium, characterized in that the readable medium comprises executable instructions, which when executed by a processor of an electronic device, the electronic device performs the method of any of claims 1-7.
10. An electronic device comprising a processor and a memory storing execution instructions, wherein the processor performs the method of any one of claims 1-7 when the processor executes the execution instructions stored by the memory.
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