Resonance interaction analysis method of aircraft fluid delivery pipe under forced vibration

Abstract

The invention discloses a resonance interaction analysis method of an aircraft fluid conveying pipe under forced vibration, and belongs to the technical field of aircraft fluid conveying pipe structure dynamics. The method comprises the following steps of: firstly, establishing an aircraft fluid conveying pipe structure model which comprises a displacement field model and a nonlinear geometrical relationship model; then establishing a resonance dynamic model of the aircraft fluid conveying pipe under forced vibration, wherein the resonance dynamic model is represented by generalized displacement; based on a secondary perturbation method, a resonance behavior approximate solution of the aircraft fluid conveying pipe under forced vibration is developed; and finally, carrying out influence analysis on combined resonance interaction, and establishing a resonance characteristic database of the aircraft fluid conveying pipe, so that the resonance characteristics of the aircraft fluid conveying pipe are comprehensively evaluated and effectively utilized. The analysis method provided by the invention can be applied to resonance interaction analysis of the flow conveying pipe of the aircraft under various types of forced vibration, and has important significance for reasonably designing a flow conveying pipe system of the aircraft needing to be kept in a stable state.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft fluid delivery pipe structural dynamics, and in particular relates to a resonance interaction analysis method of an aircraft fluid delivery pipe under forced vibration. Background Art

[0002] In the field of modern aerospace, the performance and safety of aircraft have always been of vital concern. The fluid pipe system in aircraft is widely present, such as fuel delivery pipelines, hydraulic system pipelines, etc. These fluid pipes are often affected by various external excitations and internal fluid flow during operation, resulting in vibration. When the fluid pipe is subjected to external forced vibration, resonance may occur. Resonance can cause the vibration amplitude of the fluid pipe to increase sharply, posing a serious threat to the structural integrity and normal operation of the aircraft. Nonlinear large-scale vibration may cause pipeline rupture, loose connection parts, and even affect the control performance and flight safety of the aircraft. On the other hand, under the interaction of multi-source excitation, there may be multiple stable solutions for the aircraft fluid pipe. In past studies, the analysis methods for the resonant interaction of aircraft fluid pipes under forced vibration have certain limitations. Traditional analysis methods simplify the physical model of the fluid pipe and do not fully consider the complex interaction between the fluid and the pipe structure, as well as the various influencing factors in the actual working environment.

[0003] Therefore, there is an urgent need for a more accurate and comprehensive analysis method to deeply study the resonant interaction of aircraft fluid delivery pipes under forced vibration and analyze the interaction between forced resonance and parametric resonance in order to improve the reliability and safety of aircraft. Summary of the invention

[0004] The present invention discloses a method for analyzing the resonant interaction of an aircraft fluid delivery pipe under forced vibration. The proposed analysis method fully considers the nonlinear effects caused by curvature and boundary tension, and establishes a comprehensive nonlinear structural model of the aircraft fluid delivery pipe, thereby effectively solving at least one technical problem involved in the background technology.

[0005] To achieve the above object, the technical solution of the present invention is:

[0006] A resonance interaction analysis method for an aircraft fluid delivery pipe under forced vibration comprises the following steps:

[0007] Step S1, establishing a structure model of the aircraft fluid delivery pipe;

[0008] Step S2, establishing a resonant dynamic model of the aircraft fluid delivery pipe under forced vibration represented by generalized displacement;

[0009] Step S3, developing an approximate solution for the resonant behavior of the aircraft fluid delivery pipe under forced vibration;

[0010] Step S4, conducting an impact analysis of the combined resonance interaction and establishing a resonance characteristic database of the aircraft fluid delivery pipe.

[0011] Optionally, in step S1, establishing a structure model of the aircraft fluid delivery pipe specifically includes:

[0012] Step S11, according to the nonlinear characteristics of the large deformation vibration of the aircraft fluid delivery pipe under two excitations, a displacement field is established; and the geometric relationship of the plane bending of the aircraft fluid delivery pipe is established in the von Kármán nonlinear framework; the displacement field is expressed by the following formula:

[0013]

[0014] Where x, y, z are the coordinates on the aircraft flow pipe; t is the vibration time; are the axial displacement and lateral displacement of any point on the aircraft fluid delivery pipe in the x-direction and z-direction respectively; u1 and u3 are the axial displacement and lateral displacement of the mid-plane of the aircraft pipe in the x-direction and z-direction respectively; is the cross-sectional rotation angle at the midplane; f and g are shape functions;

[0015] Step S12: Establishing a nonlinear geometric relationship of the plane bending of the aircraft fluid delivery pipe, wherein the nonlinear geometric relationship is expressed by the following formula:

[0016]

[0017] in, is the generalized in-plane normal strain, is the generalized shear strain, expressed as follows:

[0018]

[0019] in, and is the normal strain component in the x direction.

[0020] Optionally, in step S11, f and g are selected as follows:

[0021]

[0022] g=f+z

[0023] Among them, R o , R i , r are the outer radius, inner radius and radius of a certain position on the cross section of the aircraft flow pipe respectively;

[0024] The displacement field is established in a Cartesian coordinate system, including Zhang-Fu high-order shear beam theory and Reddy high-order shear beam theory.

[0025] Optionally, in step S2, a resonant dynamic model of the aircraft fluid delivery pipe under forced vibration represented by generalized displacement is established, specifically including:

[0026] The control equations of the aircraft fluid delivery pipe expressed in generalized displacement are obtained. The control equations are expressed as follows:

[0027]

[0028] Among them, ρ0, ρ1, ρ2, ρ3 are the generalized densities of the aircraft flow pipe; ζ i ,Υ i is the reduced stiffness coefficient; v s is the flow velocity of the fluid inside the flow pipe; L is the length of the aircraft flow pipe; m f k is the mass of fluid per unit length in the aircraft fluid delivery pipe; w and C d are the basic stiffness and viscous stiffness of the aircraft fluid delivery pipe respectively; q=Fδ(xL / 2) is the external excitation load.

[0029] Optionally, in step S3, developing an approximate solution for the resonant behavior of the aircraft fluid delivery pipe under forced vibration specifically includes:

[0030] Step S31, proposing a two-step perturbation format of generalized displacement and external load to discretize the resonant control equations of the aircraft fluid delivery pipe;

[0031] Step S32: Introduce the Galerkin method to solve the perturbation equations of each order to obtain the dynamic equations of the aircraft fluid delivery pipe in the time domain. The dynamic equations are expressed as follows:

[0032]

[0033] in, is the second-order kinetic coefficient, is the first-order kinetic coefficient, is the first-order kinetic coefficient, and is the cubic dynamic coefficient; ε is a small perturbation parameter without any physical meaning; Ω is the nonlinear frequency in adjacent states; τ is the dimensionless time; is the first-order amplitude of the lateral displacement; is the second-order amplitude of the lateral displacement; λ F is the dimensionless amplitude of the external load;

[0034] Step S33, combining the incremental harmonic balance method to obtain the incremental equation, and introducing the Galerkin method to obtain the numerical solution, the numerical solution is expressed as follows:

[0035]

[0036] Among them, Ω0 and U 30 are the nonlinear frequency and amplitude of the known vibration state at time τ0; ΔΩ and ΔU3 represent the increments of the nonlinear frequency and amplitude respectively; U3 is the amplitude of the adjacent state; Ω n is the dimensionless fundamental frequency.

[0037] Optionally, in step S31, the two-step perturbation format of the generalized displacement and external load is expressed as follows:

[0038]

[0039] in, U 3m ,U Θm are the perturbation expansion terms of external load, lateral displacement and section rotation respectively; m is the perturbation order m=1,2,3…n, n is the highest perturbation order; X is the dimensionless coordinate in the x direction.

[0040] Optionally, in step S32, the solution format of the Galerkin method is expressed as follows:

[0041]

[0042] in,

[0043] Optionally, in step S33, the solution format of the incremental harmonic balance method is expressed as follows:

[0044] Ω=Ω0+ΔΩ,U3=U 30 +ΔU3

[0045]

[0046] Optionally, in step S4, the core parameters of the aircraft fluid delivery pipe include amplitude ratio and pulsation amplitude; and the resonance characteristic database includes a stable boundary and an amplitude-frequency curve of parameter resonance.

[0047] The beneficial effects of the present invention are as follows:

[0048] 1. The analysis method proposed in the present invention fully considers the nonlinear effects caused by curvature and boundary tension, and establishes a comprehensive nonlinear structural model of the aircraft fluid delivery pipe.

[0049] 2. The two-step perturbation-increment harmonic balance method proposed in the present invention has strong applicability and high calculation accuracy, and is suitable for analyzing the interaction between two excitations in a strongly nonlinear system with an amplitude-frequency bifurcation response.

[0050] 3. Based on the core parameters and resonance characteristics database of the aircraft fluid delivery pipe, the present invention can select appropriate design parameters according to actual engineering design requirements, which is of great significance for the design of aircraft fluid delivery pipes that need to maintain a stable state. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0052] Figure 1 A flow chart of a method for analyzing resonance interaction of an aircraft fluid delivery pipe under forced vibration provided by the present invention;

[0053] Figure 2 A schematic diagram of the structure of a fluid delivery pipe for an aircraft under forced vibration provided by the present invention;

[0054] Figure 3 (a) and Figure 3 (b) Bifurcation diagram corresponding to different non-local stress parameters and strain gradient parameters provided by the present invention. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0057] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0058] In the present invention, unless otherwise clearly defined and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0059] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0060] See also Figure 1 As shown, an embodiment of the present invention provides a method for analyzing resonance interaction of an aircraft fluid delivery pipe under forced vibration, comprising the following steps:

[0061] Step S1, establishing a structure model of the aircraft fluid delivery pipe;

[0062] Recombination Figure 2 As shown, the aircraft fluid delivery pipe is assembled on a viscoelastic basis and has a length of L. The outer diameter and inner diameter are R o , R i . The viscoelastic foundation is obtained by k w ,C d In modeling, both ends of the aircraft fluid delivery pipe are assumed to be immovable simply supported boundaries, which are subjected to the combined action of the combined excitation, which is the forced excitation and the pulsating flow excitation.

[0063] In step S1, a structure model of the aircraft fluid delivery pipe is established, which specifically includes:

[0064] Step S11, establishing a displacement field according to the nonlinear characteristics of the large deformation vibration of the aircraft fluid delivery pipe under two excitations; and establishing the geometric relationship of the plane bending of the aircraft fluid delivery pipe in the von Kármán nonlinear framework.

[0065] In a specific embodiment, the displacement field established in the Cartesian coordinate system is the Zhang-Fu high-order shear beam theory considering nonlinear curvature, which is expressed by the following formula:

[0066]

[0067] Where x, y, z are the coordinates on the aircraft flow pipe; t is the vibration time; are the axial displacement and lateral displacement of any point on the aircraft fluid delivery pipe in the x-direction and z-direction respectively; u1 and u3 are the axial displacement and lateral displacement of the mid-plane of the aircraft pipe in the x-direction and z-direction respectively; is the cross-sectional rotation angle at the midplane; in addition, f and g are shape functions, and f and g are selected as follows:

[0068]

[0069] g=f+z

[0070] Among them, R o , R i , r are the outer radius, inner radius and radius of a certain position on the cross section of the aircraft fluid delivery pipe respectively.

[0071] Step S12, establishing a nonlinear geometric relationship of the plane bending of the aircraft fluid delivery pipe, wherein the nonlinear geometric relationship is expressed by the following formula:

[0072]

[0073] in, is the generalized in-plane normal strain; is the generalized shear strain, expressed as follows:

[0074]

[0075] in, and is the normal strain component in the x direction.

[0076] In step S2, a resonant dynamic model of the aircraft fluid delivery pipe under forced vibration represented by generalized displacement is established, which specifically includes:

[0077] Step S21, obtaining a control equation group of the aircraft fluid delivery pipe expressed in generalized displacement;

[0078] Based on the Hamiltonian variation principle, a dynamic model of the aircraft fluid delivery pipe is established. The Hamiltonian variation principle is as follows:

[0079]

[0080] Among them, δU, δK N,δK F ,δW are the virtual strain energy, the virtual kinetic energy of the aircraft flow pipe and fluid, and the virtual work of the external force; q=Fδ(xL / 2),ρ,ρ f represents the mass density of the aircraft flow pipe and flow rate; nt represents the aircraft flow pipe; V nt is the volume of the aircraft fluid delivery pipe; ν s is the fluid velocity inside the flow pipe; by substituting and introducing the constitutive equation, we can obtain the control equation group expressed in generalized displacement, as follows:

[0081]

[0082] Among them, ρ0, ρ1, ρ2, ρ3 are generalized densities, which are specifically expressed as:

[0083] (ρ0,ρ1,ρ2,ρ3)=∫∫ A ρ(1,f 2 ,fg,g 2 )dA

[0084] Wherein, A represents the cross-sectional area of ​​the aircraft fluid delivery pipe.

[0085] The reduced stiffness coefficient is expressed as:

[0086]

[0087] Step S3, developing an approximate solution for the resonant behavior of the aircraft fluid delivery pipe under forced vibration, specifically includes:

[0088] Step S31, proposing a two-step perturbation format of generalized displacement and external load to discretize the resonant control equations of the aircraft fluid delivery pipe;

[0089] The two-step perturbation format of generalized displacement and external load is as follows:

[0090]

[0091] Among them, ε is a small perturbation parameter without any physical meaning; U 3m ,U Θm are the perturbation expansion terms of external load, lateral displacement and section rotation respectively; m is the perturbation order m=1,2,3…n; n is the highest perturbation order, and X is the dimensionless coordinate in the x direction.

[0092] Step S32, introducing the Galerkin method to solve the perturbation equations of each order, and obtaining the dynamic equations of the aircraft fluid delivery pipe in the time domain;

[0093] The Galerkin method solution format is as follows:

[0094]

[0095] in,

[0096] The kinetic equations are as follows:

[0097]

[0098] in, is the second-order kinetic coefficient; is the first-order kinetic coefficient; is the first-order kinetic coefficient; and is the cubic dynamic coefficient; ε is a small perturbation parameter without any physical meaning; Ω is the nonlinear frequency in adjacent states; τ is the dimensionless time; is the first-order amplitude of the lateral displacement; is the second-order amplitude of the lateral displacement; λ F is the dimensionless external load amplitude.

[0099] Step S33, combining the incremental harmonic balance method to obtain the incremental equation, and introducing the Galerkin method to obtain the numerical solution;

[0100] Among them, Replaced by the midpoint displacement U 3m , as shown below:

[0101]

[0102] By introducing τ0=Ωτ, the above control equations can be rewritten as:

[0103]

[0104] Among them, Ω n is the dimensionless fundamental frequency, defined as follows:

[0105]

[0106] The kinetic coefficient is defined as:

[0107]

[0108] Then, define Ω0,U 30 The nonlinear frequency and amplitude of the known vibration state at time τ0; Ω, U3 represent the nonlinear frequency and amplitude of the adjacent state; ΔΩ and ΔU3 represent the increments of the nonlinear frequency and amplitude respectively; Ω, U3 of the adjacent state can be expressed in the following incremental form:

[0109] Ω=Ω0+ΔΩ,U 3m =U 30+ΔU3

[0110] Substituting the above formula into the control equations, the control equations in incremental form are as follows:

[0111]

[0112] Where R = 0, Ω0, U 30 is the exact solution.

[0113] Finally, the incremental harmonic balance method is used to calculate ΔU3(τ0), ΔU3(τ0) with a period of 2π and U 30 (τ0) is expanded as follows:

[0114]

[0115] Substituting it into the control equations in incremental form, the numerical solution is as follows:

[0116]

[0117] Among them, Ω n is the dimensionless fundamental frequency. As the first step of the iterative calculation, an initial value is determined based on the numerical simulation results (Runge-Kutta method). The other initial values ​​are obtained by solving R=0. The following process is numerically iterative. The unknowns are ΔA and ΔΩ, and there is one more unknown than the number of equations. Therefore, an increment must be selected as a valid increment (a value is preset), and then the other increments can be determined by the equations. In this case, ΔΩ is selected as the valid increment, and the remaining increment value ΔA can be solved by using the equation. Subsequently, the original value is replaced by the incremental value. This method continues to iterate until the state value obtained satisfies the unbalanced force R=0. Then, Ω0 is replaced by Ω0+ΔΩ, and the above process is repeated. In this way, the amplitude-frequency bifurcation diagram under a certain excitation amplitude can be obtained. Finally, the stability can be evaluated by Floquet theory. First, let U 30 is a provisional solution, and gives U 30 A small disturbance ΔU3, that is, U 3m =U 30 +ΔU 30 , and substitute it into the equation. Generate the perturbation equation and obtain its basic solution and period. According to Floquet theory, the stability of the solution is judged from the eigenvalues ​​of the matrix P. If all eigenvalues ​​are less than 1, the periodic solution is stable; if at least one eigenvalue is greater than 1, the periodic solution is unstable.

[0118] Step S4, conducting an impact analysis of the combined resonance interaction and establishing a resonance characteristic database of the aircraft fluid delivery pipe.

[0119] In step S4, the core parameters of the aircraft fluid delivery pipe include amplitude ratio and pulsation amplitude. The resonance characteristic database includes the stable boundary and amplitude-frequency curve of parameter resonance.

[0120] The following describes in detail a resonance interaction analysis method of an aircraft fluid delivery pipe under forced vibration provided by the present invention with reference to a first specific embodiment.

[0121] Embodiment 1

[0122] In this embodiment, the resonant interaction between the forced excitation of the aircraft fluid delivery pipe under fluid pulsation and the parametric excitation is considered. The geometric dimensions of the aircraft fluid delivery pipe are selected as follows: R i =9m, R0=h / 2=10m, L=100R0; the characteristic parameters of the fluid are as follows: v0=100m / s; the material characteristic parameters of the aircraft fluid delivery pipe are: k w =1×10 6 Pa c d =5×10 - 6 Ns / m 2 ,E=210GPa,μ=0.24,ρ=2331kg / m 3 .

[0123] Example 1 studied the strong and weak interactions of two excitations, such as Figure 3 As shown. Figure 3 From the unstable boundary in a and its correspondence with the parametric resonance bifurcation diagram, it can be found that when the parametric resonance is excited, it is precisely the bottom of the stable boundary that cannot lead to parametric resonance. The two cases of whether the two resonances are excited separately are defined as the strong interaction and weak interaction of the two excitations. In the case of strong interaction, Figure 3 The parameter resonance bifurcation diagram in b can be regarded as the spine line of the combined resonance, and dominates the inclination direction of the combined resonance bifurcation diagram. At the same time, multiple stable attractors will only appear when both excitations can produce resonance respectively. Under weak interaction, when parameter resonance cannot occur, the amplitude of the combined resonance is still much larger than the amplitude of a single forced vibration response. Therefore, it can be determined that the combined resonance is not just the superposition of two resonant responses. There is an interaction between the two excited states. It can be concluded that the analysis method of the present invention is effective for the resonant interaction of aircraft fluid pipes under forced vibration, and the resonant interaction database of aircraft fluid pipes under forced vibration provided by the present invention has reference value for the structural design of aircraft fluid pipes.

[0124] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A resonance interaction analysis method for aircraft fluid delivery pipes under forced vibration, characterized in that: The following steps are involved: Step S1, establishing a structure model of the aircraft fluid delivery pipe; Step S2, establishing a resonant dynamic model of the aircraft fluid delivery pipe under forced vibration represented by generalized displacement; Step S3, developing an approximate solution for the resonant behavior of the aircraft fluid delivery pipe under forced vibration; Step S4, conducting an impact analysis of the combined resonance interaction and establishing a resonance characteristic database of the aircraft fluid delivery pipe.

2. The method according to claim 1, characterized in that In step S1, a structure model of the aircraft fluid delivery pipe is established, which specifically includes: Step S11, according to the nonlinear characteristics of the large deformation vibration of the aircraft fluid delivery pipe under two excitations, a displacement field is established; and the geometric relationship of the plane bending of the aircraft fluid delivery pipe is established in the von Kármán nonlinear framework; the displacement field is expressed by the following formula: Where x, y, z are the coordinates on the aircraft flow pipe; t is the vibration time; are the axial displacement and lateral displacement of any point on the aircraft fluid delivery pipe in the x-direction and z-direction respectively; u1 and u3 are the axial displacement and lateral displacement of the mid-plane of the aircraft pipe in the x-direction and z-direction respectively; u θ is the cross-sectional rotation angle at the midplane; f and g are shape functions; Step S12: Establishing a nonlinear geometric relationship of the plane bending of the aircraft fluid delivery pipe, wherein the nonlinear geometric relationship is expressed by the following formula: in, is the generalized in-plane normal strain, is the generalized shear strain, expressed as follows: in, and is the normal strain component in the x direction.

3. The method according to claim 2, characterized in that In step S11, f and g are selected as follows: g=f+z Among them, R o , R i , r are the outer radius, inner radius and radius of a certain position on the cross section of the aircraft flow pipe respectively; The displacement field is established in a Cartesian coordinate system, including Zhang-Fu high-order shear beam theory and Reddy high-order shear beam theory.

4. The method according to claim 1, characterized in that: In step S2, a resonant dynamic model of the aircraft fluid delivery pipe under forced vibration represented by generalized displacement is established, which specifically includes: The control equations of the aircraft fluid delivery pipe expressed in generalized displacement are obtained. The control equations are expressed as follows: Among them, ρ0, ρ1, ρ2, ρ3 are the generalized densities of the aircraft flow pipe; ζ i ,Υ i is the reduced stiffness coefficient; v s is the flow velocity of the fluid inside the flow pipe; L is the length of the aircraft flow pipe; m f k is the mass of fluid per unit length in the aircraft fluid delivery pipe; w and C d are the basic stiffness and viscous stiffness of the aircraft fluid delivery pipe respectively; q=Fδ(xL / 2) is the external excitation load.

5. The method according to claim 1, characterized in that In step S3, an approximate solution for the resonant behavior of the aircraft fluid delivery pipe under forced vibration is developed, specifically including: Step S31, proposing a two-step perturbation format of generalized displacement and external load to discretize the resonant control equations of the aircraft fluid delivery pipe; Step S32: Introduce the Galerkin method to solve the perturbation equations of each order to obtain the dynamic equations of the aircraft fluid delivery pipe in the time domain. The dynamic equations are expressed as follows: in, is the second-order kinetic coefficient, is the first-order kinetic coefficient, is the first-order kinetic coefficient, and is the cubic dynamic coefficient; ε is a small perturbation parameter without any physical meaning; Ω is the nonlinear frequency in adjacent states; τ is the dimensionless time; is the first-order amplitude of the lateral displacement; is the second-order amplitude of the lateral displacement; λ F is the dimensionless external load amplitude; Step S33, combining the incremental harmonic balance method to obtain the incremental equation, and introducing the Galerkin method to obtain the numerical solution, the numerical solution is expressed as follows: Among them, Ω0 and U 30 are the nonlinear frequency and amplitude of the known vibration state at time τ0; ΔΩ and ΔU3 represent the increments of the nonlinear frequency and amplitude respectively; U3 is the amplitude of the adjacent state; Ω n is the dimensionless fundamental frequency.

6. The method according to claim 5, characterized in that In step S31, the two-step perturbation format of the generalized displacement and external load is expressed as follows: in, U 3m ,U Θm are the perturbation expansion terms of external load, lateral displacement and section rotation respectively; m is the perturbation order m=1,2,3…n, n is the highest perturbation order; X is the dimensionless coordinate in the x direction.

7. The method according to claim 6, characterized in that In step S32, the solution format of the Galerkin method is expressed as follows: in, 8. The method according to claim 7, characterized in that In step S33, the solution format of the incremental harmonic balance method is expressed as follows: Ω=Ω0+ΔΩ,U3=U 30 +ΔU3 9. The method according to claim 1, characterized in that: In step S4, the core parameters of the aircraft fluid delivery pipe include amplitude ratio and pulsation amplitude; the resonance characteristic database includes the stable boundary and amplitude-frequency curve of parameter resonance.

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