Nonlinear kinetic analysis method for aircraft fluid delivery pipe

Abstract

The invention discloses a nonlinear dynamic analysis method for an aircraft fluid conveying pipe, and belongs to the technical field of aircraft fluid conveying pipe dynamics. According to the method, a control equation of stability and a nonlinear kinetic model is derived according to the Hamiltonian variation principle, a quadratic perturbation method is popularized to nonlinear analysis of the aircraft fluid conveying pipe, a perturbation scheme is provided, and the initial deflection of the aircraft fluid conveying pipe is calculated by solving the nonlinear kinetic model, so that the nonlinear analysis of the aircraft fluid conveying pipe is realized. And based on the obtained initial deflection-flow velocity relationship of the aircraft fluid delivery pipe, calculating an approximate solution of the inherent frequency and nonlinear frequency amplitude relationship of the aircraft fluid delivery pipe, finally carrying out stability and nonlinear dynamic analysis of the aircraft fluid delivery pipe, and establishing a nonlinear dynamic response database of the aircraft fluid delivery pipe. The analysis method provided by the invention is high in calculation precision, comprehensively considers the nonlinear effect of the aircraft fluid conveying pipe, and has important significance in nonlinear dynamic analysis of the aircraft fluid conveying pipe.

Description

Technical Field

[0001] The present application belongs to the technical field of aircraft fluid delivery pipe dynamics, and specifically relates to a nonlinear dynamic analysis method for aircraft fluid delivery pipes. Background Art

[0002] In the field of modern aviation, the fluid pipe system of aircraft plays a vital role. These carefully designed aircraft fluid pipes undertake the important task of transmitting various critical fluids, including fuel, hydraulic oil, coolant and other key fluids, and are the core elements to ensure the normal operation of various subsystems of the aircraft. With the continuous development of aviation technology, the performance requirements of aircraft are increasing day by day. In the process of pursuing higher speed, stronger maneuverability and lower energy consumption for the new generation of aircraft, the aircraft fluid pipe system has become more complex and sophisticated. However, in actual operation, the aircraft fluid pipe faces a variety of complex mechanical environments and working conditions. Factors such as strong airflow impact, huge inertial force generated by the aircraft when performing difficult maneuvers, and drastic fluctuations in temperature and pressure have brought severe tests to the normal operation of the aircraft fluid pipe.

[0003] Traditional linear dynamic analysis methods have certain limitations when dealing with aircraft fluid pipe problems. Linear models usually describe the behavior of the system based on a series of simplified assumptions and linear relationships, and often cannot accurately describe the dynamic behavior of aircraft fluid pipes under complex conditions such as large deformation, strong nonlinear vibration, and fluid-structure coupling. When nonlinear vibration occurs in aircraft fluid pipes, linear analysis methods may not be able to predict key parameters such as vibration amplitude, frequency, and mode, thus affecting the assessment of the reliability and safety of aircraft fluid pipe structures.

[0004] Based on this, it is necessary to provide a nonlinear dynamic analysis method for aircraft fluid delivery pipes to provide technical support for accurately analyzing the dynamic characteristics of aircraft fluid delivery pipes and ensuring the safe and reliable operation of aircraft. Summary of the invention

[0005] The present invention provides a nonlinear dynamic analysis method for an aircraft fluid delivery pipe, which can determine the flow velocity-initial deflection relationship and provide an initial research configuration for the nonlinear dynamic analysis of the aircraft fluid delivery pipe. On this basis, the velocity-natural frequency curve and the nonlinear amplitude-frequency curve are determined, laying a foundation for the structural design of the aircraft fluid delivery pipe, thereby solving at least one technical problem involved in the background technology.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] A nonlinear dynamic analysis method for an aircraft fluid delivery pipe comprises the following steps:

[0008] Step S1, constructing a structural model based on structural parameters of the aircraft fluid delivery pipe, performing endogenous excitation and external load analysis on the structural model, and constructing a displacement field model, a geometric relationship model, and a constitutive relationship model of the aircraft fluid delivery pipe;

[0009] Step S2, constructing a relationship between strain energy, kinetic energy and external work of the aircraft fluid delivery pipe based on the Hamiltonian variational principle, substituting the displacement field model, constitutive model and nonlinear geometric relationship model constructed in step S1 into the expression to obtain a nonlinear dynamic model of the aircraft fluid delivery pipe transmitting supercritical high-speed pulsating flow represented by generalized displacement;

[0010] Step S3, using a quadratic perturbation method to solve the nonlinear dynamic model, obtaining a quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid delivery pipe, and using the quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid delivery pipe to perform a discrete solution to the nonlinear stability model, and obtaining a relationship between the flow velocity and the initial deflection of the aircraft fluid delivery pipe;

[0011] Step S4, using a quadratic perturbation method to propose a quadratic perturbation format of an external load and a generalized displacement of an aircraft fluid delivery pipe under the external load, discretizing a nonlinear dynamic model of the aircraft fluid delivery pipe, and discretely solving the nonlinear dynamic model using the quadratic perturbation format of an external load and a generalized displacement of the aircraft fluid delivery pipe under the external load to obtain an expression of a relationship between the load and the displacement of the aircraft fluid delivery pipe, and then further solving the nonlinear dynamic model using a harmonic balance method to obtain an approximate solution of a natural frequency and a nonlinear frequency;

[0012] Step S5, conducting stability and nonlinear dynamic analysis of the aircraft fluid delivery pipe, and establishing a nonlinear dynamic response database of the aircraft fluid delivery pipe.

[0013] As a preferred improvement, the structural parameters of the aircraft fluid delivery pipe include: inner diameter, outer diameter and length; in the structural model, both ends of the aircraft fluid delivery pipe are modeled as simple support states, and the interior is hollow for conveying fluid.

[0014] As a preferred improvement, the displacement field model is used to describe the bending deformation of the aircraft fluid delivery pipe, and is selected from one of the Euler-Bernoulli beam theory, Timoshenko first-order shear beam theory, and Zhang-Fu deformation beam theory; the geometric relationship model is based on the nonlinear strain-displacement relationship of the initial deflection under the assumption of large deformation and small strain.

[0015] As a preferred improvement, the displacement field model is selected as the Zhang-Fu deformation beam theory, which is expressed as:

[0016]

[0017] In the formula, and represent the displacement of the aircraft fluid delivery pipe in the x and z directions, respectively, where the x and z directions represent the directions indicated by the x-axis and z-axis in a Cartesian coordinate system with the center of the cross section of the aircraft fluid delivery pipe as the coordinate origin, the axis of the aircraft fluid delivery pipe as the x-axis, the axis perpendicular to the ground as the z-axis, and the axis perpendicular to both the x-axis and the z-axis as the y-axis; u x0 and u z0 represents the displacement of each point on the midplane (z=0 plane) of the aircraft fluid delivery pipe in the x-direction and the z-direction; θ0 represents the rotation angle of the midplane, which is represented by the angle between the tangent line of the curved section of the aircraft fluid delivery pipe in the midplane and the positive z-axis; f and g represent high-order shape functions; represents partial derivative calculation;

[0018] in:

[0019] u x0 =u x * +u x ;u z0 =u z * +u z ; and θ0 = θ * +θ;

[0020] In the formula, u x * 、u z * and θ * Both represent the initial deflection caused by the initial flow; u x and u z They represent the displacement of a point on the aircraft flow pipe in the x and z directions under vibration, respectively; θ represents the rotation angle of the midplane under vibration;

[0021]

[0022] In the formula, R0, R i They represent the outer diameter and inner diameter of the aircraft fluid delivery pipe respectively; r represents the pipe radius at the coordinate point (x, y, z) on the aircraft fluid delivery pipe,

[0023] The geometric relationship model is expressed as:

[0024]

[0025] In the formula, ε xx represents the generalized plane normal strain; γ xy and γ zx They are expressed as the shear strain in the xy plane and the shear strain in the xz plane, respectively;

[0026] The constitutive relationship model is expressed as:

[0027]

[0028]

[0029] In the formula, σ xx , τ xy , τ zx They represent the normal stress in the x direction, the shear stress in the xy direction and the shear stress in the xz direction respectively; E and ν represent the elastic modulus and Poisson's ratio of the aircraft fluid delivery pipe respectively.

[0030] As a preferred improvement, the Hamiltonian variation principle is expressed as follows:

[0031]

[0032] Where t1 and t2 represent the upper and lower limits of the integral in the time domain t, respectively; δ represents the variational calculation; δK P and K P They represent the virtual kinetic energy and kinetic energy of the aircraft flow pipe respectively; δK f and K f They represent the virtual kinetic energy and kinetic energy of the fluid in the aircraft fluid pipe, respectively; δU and U represent the virtual strain energy and strain energy of the aircraft fluid pipe, respectively; δW and W represent the virtual work and work of the external force, respectively, where:

[0033]

[0034] Where Ω represents the area of ​​the aircraft flow pipe; ρ and ρ f are the density of the aircraft fluid delivery pipe and the density of the fluid in the aircraft fluid delivery pipe respectively; v f represents the flow rate of the fluid in the aircraft fluid delivery pipe; A represents the cross-sectional area of ​​the aircraft fluid delivery pipe; A f represents the cross-sectional area of ​​the fluid in the aircraft fluid delivery pipe; q represents the external load, when the external load does not exist, q = 0; L represents the length of the aircraft fluid delivery pipe;

[0035] Substituting the constitutive relationship model and nonlinear geometric relationship of the aircraft fluid delivery pipe into the above formula, the nonlinear dynamic model of the aircraft fluid delivery pipe is obtained, which is expressed as:

[0036]

[0037] In the formula, m f Indicates the mass of fluid per unit length; P i represents the stiffness coefficient; ρ i represents the generalized density of the aircraft fluid delivery pipe, i = 0, 1, 2, 3, 4; where:

[0038]

[0039] As a preferred improvement, the quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid delivery pipe is:

[0040]

[0041]

[0042] In the formula, represents the small perturbation parameter; k represents the perturbation order; (v f 2 ) (k) , denote the k-th order perturbation velocity, mid-plane displacement and plane rotation angle respectively;

[0043] In order to meet the requirements of simply supported boundaries, the deflection of the aircraft fluid delivery pipe after first-order buckling is and the corresponding rotation angle θ1 * It is expressed as:

[0044]

[0045] In the formula, represents the mid-plane displacement amplitude, represents the mid-plane rotation angle amplitude;

[0046] The asymptotic solution of the initial deflection of the aircraft fluid delivery pipe is expressed as:

[0047]

[0048] In the formula, O(ε 4 ) represents the fourth-order truncation, and the velocity-initial deflection relationship of the aircraft flow pipe is expressed as:

[0049]

[0050] Among them, v f Indicates the flow velocity of the fluid in the aircraft fluid delivery pipe; v f (0) It represents the critical flow velocity of the fluid in the aircraft fluid delivery pipe; Indicates the maximum initial deflection of the aircraft fluid delivery pipe; m f Indicates the mass of fluid per unit length of the tube ρ f represents the density of the fluid in the tube, A f represents the fluid area in the tube;

[0051] in:

[0052]

[0053] As a preferred improvement, the quadratic perturbation format q of the external load is expressed as:

[0054]

[0055] In the formula, represents the dynamic term used to delay the higher-order equation; q (k) represents the k-th order perturbation load;

[0056] The generalized displacement of the aircraft fluid delivery pipe under the action of external load is expressed as:

[0057]

[0058]

[0059] In the formula, u z represents the displacement of the aircraft fluid delivery pipe under the external load; θ represents the rotation angle of the aircraft fluid delivery pipe under the external load; u zk and θ k They represent the displacement and rotation angle of the aircraft fluid delivery pipe under the k-order perturbation load respectively;

[0060] u z The first-order form of and θ is as follows:

[0061] u z1 =A 10 sin(πx / L);

[0062] θ1=B 10 cos(πx / L);

[0063] In the formula, A 10 and B 10 u z1 and the amplitude of θ1;

[0064] Substituting the quadratic perturbation format of the external load and the generalized displacement of the aircraft fluid delivery pipe under the external load into the nonlinear dynamic model to obtain an approximate solution of the load of the aircraft fluid delivery pipe;

[0065] The approximate solution of the load on the aircraft fluid delivery pipe is expressed by the relationship between load and displacement, as shown below:

[0066]

[0067] Let the external load be: q =0, then the nonlinear dynamic time domain equation of the aircraft fluid delivery pipe is expressed as follows:

[0068]

[0069] In the formula,i Represents the kinetic coefficients of each order, i = 0, 1, 2, 3; u zm It represents the lateral displacement amplitude of the aircraft fluid delivery pipe;

[0070] The approximate solution of the nonlinear frequency is expressed by the relationship between the nonlinear frequency and the amplitude, which is expressed as follows:

[0071]

[0072] Then the natural frequency of the aircraft flow pipe is expressed as:

[0073]

[0074] As a preferred improvement, step S5 specifically includes the following process:

[0075] Step S51, numerically calculating the relationship between the initial deflection of the aircraft fluid delivery pipe and the flow velocity of the fluid in the aircraft fluid delivery pipe;

[0076] Step S52, numerically calculating the relationship between the natural frequency and the flow velocity of the aircraft fluid delivery pipe; the analysis range of the relationship between the natural frequency and the flow velocity is from the pre-buckling state-critical buckling state-post-buckling state;

[0077] Step S53, numerically calculating the relationship between the nonlinear frequency and amplitude of the aircraft fluid delivery pipe;

[0078] Step S54, establishing a database of core variables and stability and nonlinear dynamic response of the aircraft fluid pipe, wherein the core variables of the aircraft fluid pipe include material parameters, dimensional parameters and boundary conditions of the aircraft fluid pipe; the stability and nonlinear dynamic response of the aircraft fluid pipe include the critical flow velocity of the fluid in the aircraft fluid pipe, the relationship between the natural frequency of the aircraft fluid pipe and the flow velocity of the fluid in the aircraft fluid pipe, and the nonlinear frequency-amplitude relationship of the aircraft fluid pipe.

[0079] Compared with the related art, the beneficial effects of the present invention are:

[0080] (1) The method proposed in the present invention can accurately carry out nonlinear dynamics and stability modeling of aircraft fluid delivery pipes, taking into account both calculation accuracy and solution efficiency;

[0081] (2) The method proposed in the present invention has strong applicability and can accurately obtain the natural frequency and nonlinear frequency-amplitude relationship from the pre-buckling state to the critical buckling state to the post-buckling state, meeting the requirements of engineering applications;

[0082] (3) The present invention establishes a database of core variables and stability and nonlinear dynamic response through core variable analysis, and can select appropriate design parameters according to actual engineering design requirements. It can be widely promoted in the fields of aircraft fluid delivery pipe dynamics and so on. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 A schematic diagram of the structure of an aircraft fluid delivery pipe provided by an embodiment of the present invention;

[0084] Figure 2 is a curve showing the relationship between the initial deflection and flow velocity of the aircraft fluid delivery pipe in Example 1;

[0085] Figure 3 is the natural frequency curve of the aircraft fluid delivery pipe in Example 1;

[0086] Figure 4 This is a nonlinear amplitude-frequency relationship diagram of the aircraft fluid delivery pipe in Example 1. DETAILED DESCRIPTION

[0087] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are 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.

[0088] Please refer to Figure 1-Figure 4 The present invention provides a nonlinear dynamic analysis method for an aircraft fluid delivery pipe, comprising the following steps:

[0089] Step S1, constructing a structural model based on the structural parameters of the aircraft fluid delivery pipe, performing a stress analysis on the structural model, and constructing a displacement field model, a geometric relationship model, and a constitutive relationship model of the aircraft fluid delivery pipe.

[0090] The structural parameters of the aircraft fluid delivery pipe include: inner diameter, outer diameter and length.

[0091] In the structural model, both ends of the aircraft fluid delivery pipe are modeled as simple support states, and the interior is hollow for conveying fluid.

[0092] The displacement field model is used to describe the bending deformation of the aircraft fluid delivery pipe, and is selected from one of the Euler-Bernoulli beam theory, the Timoshenko first-order shear beam theory, and the Zhang-Fu deformable beam theory. In this embodiment, the Zhang-Fu deformable beam theory is specifically selected, and the specific displacement field model is as follows:

[0093]

[0094] In the formula, and represent the displacement of the aircraft fluid delivery pipe in the x and z directions, respectively, where the x and z directions represent the directions indicated by the x-axis and z-axis in a Cartesian coordinate system with the center of the cross section of the aircraft fluid delivery pipe as the coordinate origin, the axis of the aircraft fluid delivery pipe as the x-axis, the axis perpendicular to the ground as the z-axis, and the axis perpendicular to both the x-axis and the z-axis as the y-axis; u x0 and u z0 represents the displacement of each point on the midplane (z=0 plane) of the aircraft fluid delivery pipe in the x-direction and the z-direction; θ0 represents the rotation angle of the midplane, which is represented by the angle between the tangent line of the curved section of the aircraft fluid delivery pipe in the midplane and the positive z-axis; f and g represent high-order shape functions; represents partial derivative calculation;

[0095] in:

[0096] u x0 =u x * +u x ;u z0 =u z * +u z ; and θ0 = θ * +θ;

[0097] In the formula, u x * 、u z * and θ * Both represent the initial deflection caused by the initial flow; u x and u z They represent the displacement of a point on the aircraft flow pipe in the x and z directions under vibration, respectively; θ represents the rotation angle of the midplane under vibration;

[0098]

[0099] In the formula, R0, R i They represent the outer diameter and inner diameter of the aircraft fluid delivery pipe respectively; r represents the pipe radius at the coordinate point (x, y, z) on the aircraft fluid delivery pipe,

[0100] The geometric relationship model is based on the assumption of large deformation and small strain, considering the nonlinear strain-displacement relationship of the initial deflection, which is specifically expressed as:

[0101]

[0102] In the formula, ε xx represents the generalized plane normal strain; γ xy and γzx They are expressed as the shear strain in the xy plane and the shear strain in the xz plane, respectively.

[0103] The constitutive relationship model is expressed as:

[0104]

[0105] In the formula, σ xx , τ xy , τ zx They represent the normal stress in the x direction, the shear stress in the xy direction and the shear stress in the xz direction respectively; E and ν represent the elastic modulus and Poisson's ratio of the aircraft fluid delivery pipe respectively.

[0106] Step S2, based on the Hamiltonian variational principle, construct the relationship between the strain energy, kinetic energy and external work of the aircraft fluid pipe, and substitute the displacement field model, constitutive model and nonlinear geometric relationship model constructed in step S1 into the expression to obtain a nonlinear dynamic model of the aircraft fluid pipe transmitting supercritical high-speed pulsating flow represented by generalized displacement.

[0107] The Hamiltonian variational principle is expressed as follows:

[0108]

[0109] Where t1 and t2 represent the upper and lower limits of the integral in the time domain t, respectively; δ represents the variational calculation; δK P and K P They represent the virtual kinetic energy and kinetic energy of the aircraft flow pipe respectively; δK f and K f They represent the virtual kinetic energy and kinetic energy of the fluid in the aircraft fluid pipe, respectively; δU and U represent the virtual strain energy and strain energy of the aircraft fluid pipe, respectively; δW and W represent the virtual work and work of the external force, respectively, where:

[0110]

[0111] Where Ω represents the area of ​​the aircraft flow pipe; ρ and ρ f are the density of the aircraft fluid delivery pipe and the density of the fluid in the aircraft fluid delivery pipe respectively; v f represents the flow rate of the fluid in the aircraft fluid delivery pipe; A represents the cross-sectional area of ​​the aircraft fluid delivery pipe; A f represents the cross-sectional area of ​​the fluid in the aircraft fluid delivery pipe; q represents the external load, when the external load does not exist, q = 0; L represents the length of the aircraft fluid delivery pipe;

[0112] Substituting the constitutive relationship model and nonlinear geometric relationship of the aircraft fluid delivery pipe into the above formula, the nonlinear dynamic model of the aircraft fluid delivery pipe can be obtained, which is expressed as:

[0113]

[0114] In the formula, m f Indicates the mass of fluid per unit length; P i represents the stiffness coefficient; ρ i represents the generalized density of the aircraft fluid delivery pipe, i = 0, 1, 2, 3, 4; where:

[0115]

[0116] Step S3, using the quadratic perturbation method to solve the nonlinear dynamic model, obtaining the quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid delivery pipe, and discretely solving the nonlinear stability model with the quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid delivery pipe to obtain the relationship between the flow velocity and the initial deflection of the aircraft fluid delivery pipe.

[0117] The quadratic perturbation format for the generalized displacement and velocity is:

[0118]

[0119] In the formula, represents the small perturbation parameter; k represents the perturbation order; (v f 2 ) (k) , denote the k-th order perturbation velocity, mid-plane displacement and plane rotation angle respectively;

[0120] In order to meet the requirements of simply supported boundaries, the deflection of the aircraft fluid delivery pipe after first-order buckling is and the corresponding rotation angle θ1 * It is expressed as:

[0121]

[0122] In the formula, represents the mid-plane displacement amplitude, Indicates the mid-plane rotation angle

[0123] The asymptotic solution of the initial deflection of the aircraft fluid delivery pipe is expressed as:

[0124]

[0125] In the formula, O(ε 4 ) represents the fourth-order truncation, and the velocity-initial deflection relationship of the aircraft flow pipe is expressed as:

[0126]

[0127] Among them, v f Indicates the flow velocity of the fluid in the aircraft fluid delivery pipe; v f (0)It represents the critical flow velocity of the fluid in the aircraft fluid delivery pipe; Indicates the maximum initial deflection of the aircraft fluid delivery pipe; m f Indicates the mass of fluid per unit length of the tube ρ f represents the density of the fluid in the tube, A f Represents the fluid area inside the tube.

[0128] in:

[0129]

[0130] Step S4, using the quadratic perturbation method to propose the quadratic perturbation format of the external load and the generalized displacement of the aircraft fluid pipe under the external load, discretizing the nonlinear dynamic model of the aircraft fluid pipe, and discretely solving the nonlinear dynamic model using the quadratic perturbation format of the external load and the generalized displacement of the aircraft fluid pipe under the external load to obtain an expression for the relationship between the load and the displacement of the aircraft fluid pipe, and then further using the harmonic balance method to solve the nonlinear dynamic model to obtain an approximate solution of the natural frequency and the nonlinear frequency.

[0131] The quadratic perturbation format q of the external load is expressed as:

[0132]

[0133] In the formula, represents the dynamic term used to delay the higher-order equation; q (k) represents the k-th order perturbation load;

[0134] The generalized displacement of the aircraft fluid delivery pipe under the action of external load is expressed as:

[0135]

[0136] In the formula, u z represents the displacement of the aircraft fluid delivery pipe under the external load; θ represents the rotation angle of the aircraft fluid delivery pipe under the external load; u zk and θ k They represent the displacement and rotation angle of the aircraft fluid delivery pipe under the k-order perturbation load respectively;

[0137] u z The first-order form of and θ is as follows:

[0138] u z1 =A 10 sin(πx / L);

[0139] θ1=B 10 cos(πx / L);

[0140] In the formula, A 10 and B10 u z1 and the amplitude of θ1.

[0141] The quadratic perturbation format of the external load and the generalized displacement of the aircraft fluid delivery pipe under the external load is substituted into the nonlinear dynamic model to obtain an approximate solution of the load of the aircraft fluid delivery pipe.

[0142] The approximate solution of the load on the aircraft fluid delivery pipe is expressed by the relationship between load and displacement, as shown below:

[0143]

[0144] Let the external load be: q =0, then the nonlinear dynamic time domain equation of the aircraft fluid delivery pipe is expressed as follows:

[0145]

[0146] In the formula, i Represents the kinetic coefficients of each order, i = 0, 1, 2, 3; u zm Represents the lateral displacement amplitude of the aircraft fluid delivery pipe.

[0147] The approximate solution of the nonlinear frequency is expressed by the relationship between the nonlinear frequency and the amplitude, which is expressed as follows:

[0148]

[0149] Then the natural frequency of the aircraft flow pipe is expressed as:

[0150]

[0151] Step S5, conducting stability and nonlinear dynamic analysis of the aircraft fluid delivery pipe, and establishing a nonlinear dynamic response database of the aircraft fluid delivery pipe.

[0152] Step S5 specifically includes the following process:

[0153] Step S51, numerically calculating the relationship between the initial deflection of the aircraft fluid delivery pipe and the flow velocity of the fluid in the aircraft fluid delivery pipe;

[0154] Step S52, numerically calculating the relationship between the natural frequency and the flow velocity of the aircraft fluid delivery pipe; the analysis range of the relationship between the natural frequency and the flow velocity is from the pre-buckling state-critical buckling state-post-buckling state;

[0155] Step S53, numerically calculating the relationship between the nonlinear frequency and amplitude of the aircraft fluid delivery pipe;

[0156] Step S54, establishing a database of core variables and stability and nonlinear dynamic response of the aircraft fluid pipe, wherein the core variables of the aircraft fluid pipe include material parameters, dimensional parameters and boundary conditions of the aircraft fluid pipe; the stability and nonlinear dynamic response of the aircraft fluid pipe include the critical flow velocity of the fluid in the aircraft fluid pipe, the relationship between the natural frequency of the aircraft fluid pipe and the flow velocity of the fluid in the aircraft fluid pipe, and the nonlinear frequency-amplitude relationship of the aircraft fluid pipe.

[0157] Example 1

[0158] In this embodiment, the structural parameters of the aircraft fluid delivery pipe are as follows: inner diameter R i =0.09m, outer diameter R o =0.1m, length L=40Ro=4m. The nonlinear dynamic analysis method of the aircraft fluid delivery pipe provided by the present invention is used to analyze the post-buckling, natural frequency and amplitude-frequency relationship of the aircraft fluid delivery pipe.

[0159] The analysis results are as follows Figure 2-Figure 4 As shown, Figure 2 It represents the curve between the initial deflection and flow velocity of the aircraft fluid delivery pipe; Figure 3 is the natural frequency curve of the aircraft flow pipe; Figure 4 This is the nonlinear amplitude-frequency relationship diagram of the aircraft flow pipe. Figure 2 It can be seen that the aircraft fluid delivery pipe will experience bifurcation instability. Figure 3 It can be seen that with the increase of flow velocity, the natural frequency of the aircraft flow pipe first decreases and then increases. Since the vibration of the aircraft flow pipe (including linear and nonlinear vibration) is based on the initial flow-induced instability behavior, a two-step analysis is required. Figure 4 It can be seen that when the aircraft fluid delivery pipe is in a post-buckling state, the aircraft fluid delivery pipe will show a softening characteristic. Therefore, it can be concluded that opposite conclusions may be obtained for linear and nonlinear vibrations. It can be concluded that the analysis method of the present invention is effective for the nonlinear dynamics of the aircraft fluid delivery pipe in an unstable state, and the key parameters, stability and nonlinear dynamic response database of the aircraft fluid delivery pipe provided by the present invention are of reference value for the nonlinear dynamic design of the aircraft fluid delivery pipe.

[0160] 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 nonlinear dynamic analysis method for an aircraft fluid delivery pipe, characterized in that: The steps include: Step S1, constructing a structural model based on structural parameters of the aircraft fluid delivery pipe, performing endogenous excitation and external load analysis on the structural model, and constructing a displacement field model, a geometric relationship model, and a constitutive relationship model of the aircraft fluid delivery pipe; Step S2, constructing a relationship between strain energy, kinetic energy and external work of the aircraft fluid delivery pipe based on the Hamiltonian variational principle, substituting the displacement field model, constitutive model and nonlinear geometric relationship model constructed in step S1 into the expression to obtain a nonlinear dynamic model of the aircraft fluid delivery pipe transmitting supercritical high-speed pulsating flow represented by generalized displacement; Step S3, using a quadratic perturbation method to propose a quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid delivery pipe, and using the quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid delivery pipe to perform a discrete solution to the nonlinear stability model, and obtain a relationship between the flow velocity and the initial deflection of the aircraft fluid delivery pipe; Step S4, using a quadratic perturbation method to propose a quadratic perturbation format of the external load and the generalized displacement of the aircraft fluid delivery pipe under the external load, performing a discrete solution to the nonlinear dynamic model, obtaining an expression of the relationship between the load and the displacement of the aircraft fluid delivery pipe, and then further using a harmonic balance method to solve the nonlinear dynamic model to obtain an approximate solution of the natural frequency and the nonlinear frequency; Step S5, conducting stability and nonlinear dynamic analysis of the aircraft fluid delivery pipe, and establishing a nonlinear dynamic response database of the aircraft fluid delivery pipe.

2. The nonlinear dynamic analysis method of an aircraft fluid delivery pipe according to claim 1, characterized in that: The structural parameters of the aircraft fluid delivery pipe include: inner diameter, outer diameter and length; in the structural model, both ends of the aircraft fluid delivery pipe are modeled as simple support states, and the interior is hollow for conveying fluid.

3. The nonlinear dynamic analysis method of an aircraft fluid delivery pipe according to claim 1, characterized in that: The displacement field model is used to describe the bending deformation of the aircraft fluid delivery pipe, and is selected from one of the Euler-Bernoulli beam theory, Timoshenko first-order shear beam theory, and Zhang-Fu deformation beam theory; the geometric relationship model is a nonlinear strain-displacement relationship considering the initial deflection under the assumption of large deformation and small strain.

4. The nonlinear dynamic analysis method of an aircraft fluid delivery pipe according to claim 3, characterized in that: The displacement field model is selected as the Zhang-Fu deformable beam theory, which is expressed as: In the formula, and represent the displacement of the aircraft fluid delivery pipe in the x and z directions, respectively, where the x and z directions represent the directions indicated by the x-axis and z-axis in a Cartesian coordinate system with the center of the cross section of the aircraft fluid delivery pipe as the coordinate origin, the axis of the aircraft fluid delivery pipe as the x-axis, the axis perpendicular to the ground as the z-axis, and the axis perpendicular to both the x-axis and the z-axis as the y-axis; u x0 and u z0 represents the displacement of each point on the midplane of the aircraft fluid delivery pipe in the x-direction and the z-direction; θ0 represents the rotation angle of the midplane, which is expressed by the angle between the tangent line of the curved section of the aircraft fluid delivery pipe in the midplane and the positive z-axis; f and g represent high-order shape functions; represents partial derivative calculation; in: u x0 =u x * +u x ;u z0 =u z * +u z ; Sum θ0 = θ * +θ; In the formula, u x * 、u z * and θ * Both represent the initial deflection caused by the initial flow; u x and u z They represent the displacement of a point on the aircraft flow pipe in the x and z directions under vibration, respectively; θ represents the rotation angle of the midplane under vibration; In the formula, R0, R i They represent the outer diameter and inner diameter of the aircraft fluid delivery pipe respectively; r represents the pipe radius at the coordinate point (x, y, z) on the aircraft fluid delivery pipe, The geometric relationship model is expressed as: In the formula, ε xx represents the generalized plane normal strain; γ xy and γ zx They are expressed as the shear strain in the xy plane and the shear strain in the xz plane, respectively; The constitutive relationship model is expressed as: In the formula, σ xx , τ xy , τ zx They represent the normal stress in the x direction, the shear stress in the xy direction and the shear stress in the xz direction respectively; E and ν represent the elastic modulus and Poisson's ratio of the aircraft fluid delivery pipe respectively.

5. The nonlinear dynamic analysis method of an aircraft fluid delivery pipe according to claim 4, characterized in that: The Hamiltonian variational principle is expressed as follows: Where t1 and t2 represent the upper and lower limits of the integral in the time domain t, respectively; δ represents the variational calculation; δK P and K P They represent the virtual kinetic energy and kinetic energy of the aircraft flow pipe respectively; δK f and K f They represent the virtual kinetic energy and kinetic energy of the fluid in the aircraft fluid pipe, respectively; δU and U represent the virtual strain energy and strain energy of the aircraft fluid pipe, respectively; δW and W represent the virtual work and work of the external force, respectively, where: Where Ω represents the area of ​​the aircraft flow pipe; ρ and ρ f are the density of the aircraft fluid delivery pipe and the density of the fluid in the aircraft fluid delivery pipe respectively; v f represents the flow rate of the fluid in the aircraft fluid delivery pipe; A represents the cross-sectional area of ​​the aircraft fluid delivery pipe; A f represents the cross-sectional area of ​​the fluid in the aircraft fluid delivery pipe; q represents the external load, when the external load does not exist, q = 0; L represents the length of the aircraft fluid delivery pipe; Substituting the constitutive relationship model and nonlinear geometric relationship of the aircraft fluid delivery pipe into the above formula, the nonlinear dynamic model of the aircraft fluid delivery pipe is obtained, which is expressed as: In the formula, m f Indicates the mass of fluid per unit length; P i represents the stiffness coefficient; ρ i represents the generalized density of the aircraft fluid delivery pipe, i = 0, 1, 2, 3, 4; where:

6. The nonlinear dynamic analysis method of an aircraft fluid delivery pipe according to claim 5, characterized in that: The quadratic perturbation format of the generalized displacement and flow velocity of the aircraft fluid pipe is: In the formula, represents the small perturbation parameter; k represents the perturbation order; (v f 2 ) (k) , denote the k-th order perturbation velocity, mid-plane displacement and plane rotation angle respectively; In order to meet the requirements of simply supported boundaries, the deflection of the aircraft fluid delivery pipe after first-order buckling is and the corresponding turning angle It is expressed as: In the formula, represents the mid-plane displacement amplitude, represents the mid-plane rotation angle amplitude; The asymptotic solution of the initial deflection of the aircraft fluid delivery pipe is expressed as: In the formula, O(ε 4 ) represents the fourth-order truncation, and the velocity-initial deflection relationship of the aircraft flow pipe is expressed as: Among them, v f Indicates the flow velocity of the fluid in the aircraft fluid delivery pipe; v f (0) It represents the critical flow velocity of the fluid in the aircraft fluid delivery pipe; Indicates the maximum initial deflection of the aircraft fluid delivery pipe; m f Indicates the mass of fluid per unit length of the tube ρ f represents the density of the fluid in the tube, A f represents the fluid area in the tube; in:

7. The nonlinear dynamic analysis method of an aircraft fluid delivery pipe according to claim 6, characterized in that: The quadratic perturbation format q of the external load is expressed as: In the formula, represents the dynamic term used to delay the higher-order equation; q (k) represents the k-th order perturbation load; The generalized displacement of the aircraft fluid delivery pipe under the action of external load is expressed as: In the formula, u z represents the displacement of the aircraft fluid delivery pipe under the external load; θ represents the rotation angle of the aircraft fluid delivery pipe under the external load; u zk and θ k They represent the displacement and rotation angle of the aircraft fluid delivery pipe under the k-order perturbation load respectively; u z The first-order form of and θ is as follows: u z1 =A 10 sin(πx / L); θ1=B 10 cos(πx / L); In the formula, A 10 and B 10 u z1 and the amplitude of θ1; Substituting the quadratic perturbation format of the external load and the generalized displacement of the aircraft fluid delivery pipe under the external load into the nonlinear dynamic model to obtain an approximate solution of the load of the aircraft fluid delivery pipe; The approximate solution of the load on the aircraft fluid delivery pipe is expressed by the relationship between load and displacement, as shown below: Let the external load be: q =0, then the nonlinear dynamic time domain equation of the aircraft fluid delivery pipe is expressed as follows: In the formula, i Represents the kinetic coefficients of each order, i = 0, 1, 2, 3; u zm It represents the lateral displacement amplitude of the aircraft fluid delivery pipe; The approximate solution of the nonlinear frequency is expressed by the relationship between the nonlinear frequency and the amplitude, which is expressed as follows: Then the natural frequency of the aircraft flow pipe is expressed as:

8. The nonlinear dynamic analysis method of an aircraft fluid delivery pipe according to claim 7, characterized in that: Step S5 specifically includes the following process: Step S51, numerically calculating the relationship between the initial deflection of the aircraft fluid delivery pipe and the flow velocity of the fluid in the aircraft fluid delivery pipe; Step S52, numerically calculating the relationship between the natural frequency and the flow velocity of the aircraft fluid delivery pipe; the analysis range of the relationship between the natural frequency and the flow velocity is from the pre-buckling state-critical buckling state-post-buckling state; Step S53, numerically calculating the relationship between the nonlinear frequency and amplitude of the aircraft fluid delivery pipe; Step S54, establishing a database of core variables and stability and nonlinear dynamic response of the aircraft fluid pipe, wherein the core variables of the aircraft fluid pipe include material parameters, dimensional parameters and boundary conditions of the aircraft fluid pipe; the stability and nonlinear dynamic response of the aircraft fluid pipe include the critical flow velocity of the fluid in the aircraft fluid pipe, the relationship between the natural frequency of the aircraft fluid pipe and the flow velocity of the fluid in the aircraft fluid pipe, and the nonlinear frequency-amplitude relationship of the aircraft fluid pipe.

Images