A method for analyzing the aeroelastic stability and dynamic response of rigid-elastic coupling aircraft

Abstract

The present invention relates to the field of aeroelastic mechanics analysis, and in particular to a method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling of an aircraft. The method comprises the following steps: determining the inherent shape parameters of the aircraft, dividing the mid-camber surface of the aircraft wing into a plurality of quadrilateral aerodynamic grids along the chord direction and the span direction; establishing a vortex grid method state-space equation based on the aerodynamic grid; establishing a flight dynamics model and a finite element structural model of the aircraft wing, and then establishing a rigid-elastic coupling dynamic equation; utilizing a three-dimensional spline interpolation method to obtain a rigid body motion-structure-aerodynamic coupling relationship, and determining the state-space equation of a generalized external force and a rigid-elastic coupling aeroelastic system based on the rigid body motion-structure-aerodynamic coupling relationship and the rigid-elastic coupling dynamic equation; and determining analysis results of elastic stability and dynamic response from the state-space equation. The present invention can realize efficient and accurate rigid-elastic coupling calculation and analysis.

Description

Technical Field

[0001] The present invention relates to the field of aeroelastic mechanics analysis, and in particular to a method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft. Background Art

[0002] Aeroelasticity, a branch of applied mechanics, primarily studies the coupling between aerodynamic forces, elastic forces, and inertial forces. Aerodynamic forces cause elastic structures to vibrate and deform. This elastic motion, in turn, causes changes in the magnitude and distribution of aerodynamic forces. This interaction leads to a variety of aeroelastic phenomena, including aeroelastic deformation, flutter, and gust response. Aeroelasticity affects aircraft safety and flight performance and is a core issue in aircraft design.

[0003] Another important research direction closely related to geometrically nonlinear aeroelasticity is its coupling with flight dynamics, also known as rigid-elastic coupling. This focuses on the coupling between the elastic vibrations of free-free aircraft and the rigid-body motions involved in flight dynamics. For conventional aircraft, elastic and rigid-body motions are typically modeled separately, corresponding to the aeroelastic and flight dynamics problems, respectively. For modern, highly flexible aircraft, the rigid-body motion can significantly couple with the elastic motion, significantly reducing the instability velocity and increasing the response amplitude. Rigid-elastic coupling analysis, commonly used in traditional engineering, is typically performed using a combination of the finite element method and the dipole grid method. The finite element method is well-suited for complex engineering models, but the dipole grid method, as a frequency-domain aerodynamic model, requires rational function fitting to convert it into a time-domain aerodynamic state-space equation. This manipulation inevitably introduces fitting errors. Furthermore, the rational function fitting requires the prior setting of aerodynamic hysteresis roots, and the selection of these hysteresis roots is highly empirical and subjective, which can also affect analysis accuracy. This characteristic of the aerodynamic model leads to a loss of accuracy in the rigid-elastic coupling analysis of aircraft, and the operation is cumbersome, which is not conducive to the mastery of engineers.

[0004] The state-space vortex lattice method offers advantages over the dipole grid method. As a three-dimensional aerodynamic analysis method in the time domain, it does not require the assumption of simple harmonic oscillations and can directly calculate unsteady aerodynamic forces under arbitrary motion. Its inherent state-space form allows it to be directly coupled with the elastic and rigid degrees of freedom of the finite element model to form state-space equations without loss of accuracy. In Chinese Invention Patent Publication No. CN113128085B, "A Gust Mitigation Analysis Method Based on a State-Space Vortex Grid Method," the applicant established a wing aeroelastic coupling equation based on the state-space vortex lattice method. In Chinese Invention Patent Publication No. CN113536457B, "A Method for Aerodynamic Force Reduction Based on a State-Space Vortex Grid Method," the applicant established a low-order aerodynamic analysis model for a wing based on the state-space vortex lattice method. Neither the aforementioned patents nor domestic and international research have reported methods or processes for applying the state-space vortex lattice method to aircraft rigid-elastic coupling analysis. When applied to rigid-elastic coupling analysis, the analysis process and technical steps differ significantly from traditional aeroelastic analysis. Summary of the Invention

[0005] In view of the above problems, the present invention provides a method for analyzing the aeroelastic stability and dynamic response of an aircraft rigid-elastic coupling, which solves the technical problems in the prior art of incomplete consideration of the flight mechanical degrees of freedom and the elastic motion degrees of freedom, the need for rational function fitting in the dipole grid method-rational function fitting method resulting in decreased accuracy, and cumbersome steps.

[0006] The present invention provides a method for analyzing the aeroelastic stability and dynamic response of an aircraft rigid-elastic coupling, comprising the following steps:

[0007] Step S1, determining the inherent shape parameters of the aircraft, and based on the inherent shape parameters, dividing the mid-camber surface of the aircraft wing into a plurality of quadrilateral aerodynamic grids along the chord direction and the span direction, wherein the aerodynamic grid includes an attached vortex grid on the wing surface and a trailing vortex grid dragged along the incoming flow direction; the inherent shape parameters include wing span, average aerodynamic chord length, fuselage width, total aircraft mass, and wing airfoil;

[0008] Step S2: establishing a vortex lattice method state space equation based on the aerodynamic grid, wherein the vortex lattice method state space equation is used to calculate an aerodynamic force vector based on the induced velocity on the wing surface;

[0009] Step S3: establishing a flight dynamics model and a finite element structural model of the aircraft wing, and establishing a linearized rigid-elastic coupling dynamics equation representing the rigid body motion and elastic deformation of the aircraft wing based on the flight dynamics model and the finite element structural model;

[0010] Step S4: using a three-dimensional spline interpolation method, based on the vortex lattice state space equation and the rigid-elastic coupling dynamics equation, obtaining a rigid body motion-structure-aerodynamic coupling relationship, wherein the rigid body motion-structure-aerodynamic coupling relationship is specifically: a calculation expression for the induced velocity on the wing surface;

[0011] Step S5: determining the state space equation of the generalized external force and rigid-elastic coupled aeroelastic system based on the rigid-body motion-structure-aerodynamic coupling relationship and the rigid-elastic coupled dynamic equation;

[0012] Step S6, calculating a state matrix in a state space equation of the rigid-elastic coupled aeroelastic system, and determining a judgment result of the rigid-elastic coupled aeroelastic stability according to an eigenvalue of the state matrix;

[0013] After adding a disturbance force vector to the state space equation of the rigid-elastic coupled aeroelastic system, a time domain simulation is performed to obtain the instability velocity of the aircraft as a dynamic response analysis result.

[0014] Preferably, the step S2 specifically includes:

[0015] Step S2-1, arranging vortex segments at each 1 / 4 chord of the aerodynamic grid to form four vortex segments of equal strength, wherein the four vortex segments of equal strength are connected end to end to form a vortex ring; selecting the midpoint of the 1 / 4 chord as the aerodynamic force application point, and selecting the midpoint of the 3 / 4 chord as the aerodynamic force control point;

[0016] Step S2-2: Based on the action point and control point, establish the vortex lattice method state space equation, which is expressed as:

[0017]

[0018] y aero =C aero x aero +D aero u aero

[0019]

[0020] in, is the time derivative of the tail vortex strength vector, Γ w is the tail vortex strength vector, w is the induced velocity vector on the wing surface, A a is the state matrix, B a is the input matrix; F is the aerodynamic force vector, w is the normal velocity vector of the wing surface, is the derivative of the velocity vector with respect to time, B1, B2 are the direct transmission matrices, and B3 is the output matrix; x aero is the state variable, x aero =Γ w , is x aero The derivative with respect to time, u aero is the input quantity, y aero is the output, y aero =F,A aero ,B aero ,C aero ,D aero is the coefficient matrix of the state space equation, A aero =A a , B aero =[B a O],C aero =B3, D aero =[B1 B2], O is the zero matrix.

[0021] Preferably, the step S3 specifically includes:

[0022] Step S3-1, establishing a flight dynamics model, including: determining the aircraft position conversion relationship between the aircraft body coordinate system and the ground coordinate system, and determining the aircraft motion speed conversion relationship between the aircraft body coordinate system and the inertial coordinate system;

[0023] Step S3-2: Divide the aircraft wing into finite elements based on the inherent shape parameters of the aircraft, establish a finite element structural model, and determine the modal space structural dynamics equation of the finite element structural model;

[0024] Step S3-3: Based on the flight dynamics model and the finite element structural model, a linearized rigid-elastic coupling dynamic equation representing the rigid body motion and elastic deformation of the aircraft wing is established.

[0025] Preferably, the step S3-1 specifically includes:

[0026] Determine the body coordinate system, where the origin o of the body coordinate system is located at the center of mass of the undeformed aircraft, the ox axis is parallel to the fuselage axis in the aircraft symmetry plane and points to the tail of the aircraft, the oz axis is perpendicular to the ox axis in the symmetry plane and points to the top of the aircraft, and the oy axis is perpendicular to the symmetry plane and points to the right side of the aircraft;

[0027] The aircraft position transformation relationship between the body coordinate system and the ground coordinate system is determined as the transformation matrix L BE , the expression is:

[0028]

[0029] Among them, φ, θ, ψ are roll angle, pitch angle and yaw angle respectively, L x (φ),L y (θ),L z(ψ) are the rotation matrices for the rotation angle φ around the x-axis of the body coordinate system, the rotation matrices for the rotation angle θ around the y-axis of the body coordinate system, and the rotation matrices for the rotation angle ψ around the z-axis of the body coordinate system;

[0030] The velocity of the center of mass in the body coordinate system and the velocity of the center of mass in the inertial coordinate system have the following relationship:

[0031]

[0032] in, is the time derivative of the position vector in the earth coordinate system, and V0 is the velocity of the center of mass in the body coordinate system;

[0033] The position R of any mass element on an elastic aircraft in the inertial reference frame is expressed as:

[0034] R=R0+r=R0+r0+u

[0035] Where R0 represents the position vector of the origin o of the body coordinate system in the inertial system, r represents the position vector of the mass element on the elastic aircraft relative to the center of mass in the geodetic coordinate system, r0 is the undeformed position, and u is the elastic deformation;

[0036] The angular velocity ω can be expressed as the time rate of change of the Euler angle:

[0037]

[0038] Where ω = [pqr] T is the angular velocity of the body coordinate system relative to the earth system. After projecting to the body coordinate system, p, q, and r are the roll angular velocity, pitch angular velocity, and yaw angular velocity, respectively. BE is the transformation matrix, is the time rate of change of the Euler angle Θ.

[0039] Preferably, the step S3-2 specifically includes:

[0040] The structural model is established using the finite element method, and the structural dynamics equation in modal coordinates is obtained:

[0041]

[0042] Among them, M e ,B e ,K e are the generalized mass matrix, generalized damping matrix and generalized stiffness matrix respectively, q e are generalized modal coordinates, are generalized acceleration and generalized velocity, respectively, F e is the generalized force; the generalized modal coordinate q e With physical coordinate ue The relational expression is:

[0043] u e =Φ e q e

[0044] where Φ e is the modal matrix.

[0045] Preferably, the step S3-3 specifically includes:

[0046] Combining the flight dynamics model and the finite element structural model, based on the Lagrange equation, the linearized aircraft rigid-elastic coupling dynamics equation is obtained, which is expressed as follows:

[0047]

[0048] Among them, (·) represents the time derivative of the variable, (~) represents the expansion of a three-dimensional vector into its corresponding antisymmetric matrix form, () T Indicates the transposition of a matrix. M is the total mass of the aircraft, is the acceleration disturbance of the center of mass of the aircraft, ΔV0 is the velocity disturbance of the center of mass of the aircraft; is the disturbance of the aircraft’s angular acceleration, and Δω is the antisymmetric matrix of the disturbance of the aircraft’s angular velocity. ref is the total aircraft inertia matrix in the trim configuration, dm is a certain mass element on the aircraft, r ref is the position vector of the mass element relative to the center of mass of the aircraft. G ,ΔM G is the gravitational disturbance and gravitational moment disturbance, ΔF A ,ΔM A is the aerodynamic disturbance and aerodynamic moment disturbance, ΔF T ,ΔM T Δf is the thrust disturbance and thrust moment. G is the generalized gravitational perturbation, Δf A is the generalized aerodynamic disturbance, Δf T is the generalized thrust disturbance.

[0049] Preferably, the step S4 specifically includes:

[0050] Determine the aerodynamic surface displacement W A and structural displacement W S Relationship:

[0051] W A =EW S

[0052] Where E is the displacement interpolation matrix;

[0053] Determine the aerodynamic surface velocity V A and structural velocity V S Relationship:

[0054] V A =EV S

[0055] The relationship between the normal vector n after deformation and the generalized degree of freedom in the modal space is:

[0056] n=n0+Δn=n0+E N q e

[0057] Where n0 is the normal vector at the control point in the undeformed state, Δn is the normal vector increment caused by structural deformation, and E N is the interpolation matrix from the structural modal coordinates to the aerodynamic element normal vector increment;

[0058] After the rigid body's freedom of motion and structural deformation, the reference inflow velocity v0 in the trim state and the small perturbation inflow velocity v near the equilibrium solution are obtained. d :

[0059] v0=-(V0+ω×r ref )

[0060]

[0061] Among them, V0,ω,ΔV0,Δω represent the velocity, angular velocity, velocity disturbance and angular velocity disturbance at a certain point on the aircraft, r ref is the position vector of the point relative to the center of mass, u d is the structural elastic displacement generated at this point, is the elastic deformation velocity.

[0062] Determine the wash velocity w at the aerodynamic grid control point i i :

[0063]

[0064] Among them, v 0i is the reference incoming flow velocity at the i-th aerodynamic grid control point, Δn i is the normal vector increment of the i-th aerodynamic network, v di is the disturbance velocity at the i-th aerodynamic grid control point, n refi is the normal vector of the ith aerodynamic grid in the trimmed configuration, r refi is the position vector of the i-th aerodynamic grid control point in the trim configuration, u di is the elastic displacement at the i-th aerodynamic grid control point, is the elastic deformation velocity at the i-th aerodynamic grid control point. For the trim state of fixed straight and level flight, we simplify it, that is, get:

[0065]

[0066] Where G is the structural elastic deformation velocity interpolation matrix from the structure to the aerodynamic grid control point, Φ e is the linear elastic modal matrix of the structure.

[0067] Finally, the calculation expression of the wing surface normal wash velocity and its derivative is obtained:

[0068]

[0069] Among them, each item in the formula is based on the state quantity After sorting, the coefficient matrix of each item is simply written as

[0070]

[0071]

[0072] Preferably, the step S5 specifically includes:

[0073] Based on the rigid body motion-structure-aerodynamic coupling relationship and the rigid-elastic coupling dynamic equation, the generalized external force expression is determined as:

[0074]

[0075] Among them E F is the force interpolation matrix;

[0076] The state space equation of the rigid-elastic coupled aeroelastic system is expressed as:

[0077]

[0078] Among them, A fl&ae is the state matrix of the state space model, x fl&ae is the state quantity of the state space equation of the rigid-elastic coupled aeroelastic system, is x fl&ae Derivative with respect to time.

[0079] Preferably, in step S6, determining the judgment result of the rigid-elastic coupling aeroelastic stability based on the eigenvalue of the state matrix specifically includes:

[0080] Obtain the state matrix A in the state space equation of the rigid-elastic coupled aeroelastic system fl&ae , if A fl&aeIf the real parts of all eigenvalues ​​are negative, the system is considered stable; otherwise, the system is considered unstable.

[0081] Compared with the prior art, the present invention has at least the following beneficial effects:

[0082] (1) The present invention provides a state-space vortex lattice method for analyzing rigid-elastic coupling of aircraft, which avoids the need for rational function fitting in traditional methods, directly establishes the control equation, and improves the accuracy of the calculation.

[0083] (2) The present invention aims at the rigid-elastic coupling analysis of aircraft and establishes a structural model by combining the finite element method, which can better adapt to the actual shape and structural characteristics of complex aircraft and enhance the applicability of the model.

[0084] (3) The present invention provides the coupling relationship between the rigid body motion freedom, the structural dynamics equation and the aerodynamic control equation in the rigid-elastic coupling analysis of the aircraft, and applies the state space equation of the rigid-elastic coupling system to the stability analysis and dynamic response analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The drawings are only for purposes of illustrating particular embodiments and are not to be considered limiting of the invention.

[0086] Figure 1 This is a schematic diagram of the steps of the aircraft rigid-elastic coupled aeroelastic stability and dynamic response analysis method provided by the present invention.

[0087] Figure 2 This is a flow chart of the aircraft rigid-bullet coupled aeroelastic stability and dynamic response analysis method provided by the present invention.

[0088] Figure 3 This is a schematic diagram of an example flying wing full aircraft model provided by the present invention.

[0089] Figure 4 This is a schematic diagram of the finite element model of an example flying wing provided by the present invention.

[0090] Figure 5 This is a schematic diagram of the finite element model of the wing and fuselage after splitting the example provided by the present invention. DETAILED DESCRIPTION

[0091] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited by the specific embodiments disclosed below.

[0092] The present invention establishes an aerodynamic grid based on a given model, establishes the relationship between the model's attached vortex strength, the tail vortex strength and the induced velocity on the aircraft's lift surface according to the state-space form vortex grid method, and forms a rigid-elastic coupled aeroelastic dynamics equation after interpolating the relationship between the finite element mode and the rigid body motion mode. The coupling equation is also in the state-space form. The stability problem can be analyzed by analyzing the eigenvalues ​​of the state matrix, and dynamic response analysis can be performed under given external excitation conditions.

[0093] In order to illustrate the effectiveness of the method proposed by the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment. Figure 1 As shown, a method for analyzing the aeroelastic stability and dynamic response of an aircraft rigid-elastic coupling is disclosed, and the specific implementation steps are as follows:

[0094] Step 1: Calculation initialization.

[0095] An aerodynamic model is established, and the mid-camber surface of the aircraft lifting surface (mainly the wing) is divided into multiple quadrilateral aerodynamic grids along the chord direction and the span direction. The aerodynamic grid includes the attached vortex grid on the lifting surface and the trailing vortex grid dragged along the incoming flow direction.

[0096] Step 2: Establish aerodynamic equations in state space form for the aerodynamic grid.

[0097] This step specifically includes:

[0098] (1) arranging vortex segments at each 1 / 4 chord of the aerodynamic grid to form four vortex segments of equal strength, which are connected end to end to form a vortex ring; selecting the midpoint of the 1 / 4 chord as the aerodynamic force action point, and selecting the midpoint of the 3 / 4 chord as the control point;

[0099] (2) Based on the existing state space vortex lattice method theory, the state space equation expression of the vortex lattice method is obtained as follows:

[0100]

[0101] in, is the time derivative of the tail vortex strength vector, Γ w is the tail vortex strength vector, w is the normal velocity vector of the wing surface, A a is the state matrix, B a is the input matrix, which is determined by the geometry of the aerodynamic surface and the division of the trailing vortex.

[0102] The aerodynamic force vector F, the output equation, is expressed as:

[0103]

[0104] in, is the derivative of the velocity vector with respect to time, B1 and B2 are the forward matrices, and B3 is the output matrix.

[0105] (3) The state space equation of the vortex-lattice method can be fully expressed as:

[0106]

[0107] Among them, x aero is the state variable, x aero =Γ w , is x aero The derivative with respect to time, u aero is the input quantity, y aero is the output, y aero =F,A aero ,B aero ,C aero ,D aero is the coefficient matrix of the state space equation, A aero =A a , B aero =[B a O],C aero =B3, D aero =[B1 B2], O is the zero matrix.

[0108] The vortex-lattice method state-space equation is also the aerodynamic equation in state-space form, which establishes the relationship between the wake vortex intensity, the wash velocity and the aerodynamic force vector.

[0109] The third step is to establish a flight kinematic model.

[0110] The flight dynamics model is defined in the body coordinate system, where the origin o is located at the center of mass of the undeformed aircraft. The ox axis is parallel to the fuselage axis within the aircraft's symmetry plane and points from the nose to the tail. The oz axis is perpendicular to the ox axis within the symmetry plane and points upward. The oy axis follows the right-hand rule and is perpendicular to the symmetry plane and points to the right of the aircraft. The ground coordinate system is a coordinate system with its origin on the ground. The orientation of the body coordinate system relative to the ground coordinate system represents the aircraft's attitude in the air, expressed as the Euler angles Θ = [φθψ] T Represented by , where φ, θ, and ψ are the angles of rotation around the x-axis, y-axis, and z-axis of the body coordinate system, respectively. Their projections onto the body coordinate system can be related to the roll angle, pitch angle, and yaw angle in flight dynamics. The transformation relationship from the earth coordinate system to the body coordinate system is represented by the Euler angle Θ, and the transformation matrix L from the earth coordinate system to the body coordinate system is obtained. BE :

[0111]

[0112] Among them, L x (φ),L y (θ),L z (ψ) are the rotation matrices for the rotation angle φ around the x-axis of the body coordinate system, the rotation matrix for the rotation angle θ around the y-axis of the body coordinate system, and the rotation matrix for the rotation angle ψ around the z-axis of the body coordinate system.

[0113] That is, the velocity of the center of mass in the body coordinate system and the velocity of the center of mass in the inertial coordinate system have the following relationship:

[0114]

[0115] in, is the time derivative of the position vector in the earth coordinate system, and V0 is the velocity of the center of mass in the body coordinate system.

[0116] The position R of any mass element on the elastic aircraft in the inertial reference frame can be expressed as:

[0117] R=R0+r=R0+r0+u(6)

[0118] Among them, R0 represents the position vector of the origin o of the body coordinate system in the inertial system, r represents the expression of the position vector of the mass element on the elastic aircraft relative to the center of mass in the geodetic coordinate system, r0 is the undeformed position, and u is the elastic deformation.

[0119] ω=[pqr] T is the angular velocity of the body coordinate system relative to the earth system. After projecting to the body coordinate system, p, q, and r are the roll angular velocity, pitch angular velocity, and yaw angular velocity, respectively.

[0120] The angular velocity ω can be expressed as the time rate of change of the Euler angle express:

[0121]

[0122]

[0123] Among them, D BE is the transformation matrix, is the time rate of change of the Euler angle vector Θ.

[0124] Through the above flight kinematic model, the present invention constructs the conversion relationship between the derivatives of the position vector and angle in the earth coordinate system and the velocity and angular velocity in the body coordinate system when the aircraft moves.

[0125] Step 4: Establish a finite element structural model

[0126] The structural model is established using the finite element method. Based on the modal superposition method under the assumption of linear elastic deformation of the structure, the structural dynamic equation in modal coordinates is given:

[0127]

[0128] Among them, M e ,B e ,K e are the generalized mass matrix, generalized damping matrix and generalized stiffness matrix respectively, q e are generalized modal coordinates, are generalized acceleration and generalized velocity, F e is the generalized force. The generalized modal coordinate q e With physical coordinate u e The relationship is:

[0129] u e =Φ e q e (9)

[0130] where Φ e is the modal matrix.

[0131] In this step, the present invention utilizes the finite element method to establish a dynamic model of the structure so as to perform subsequent dynamic analysis of the structure.

[0132] The fifth step is to establish the linearized rigid-elastic coupling dynamic equation.

[0133] Combining the aforementioned flight kinematic model with the finite element structural model, the kinetic energy and potential energy of the aircraft can be expressed. Based on the Lagrange equation, the linearized aircraft rigid-elastic coupled dynamic perturbation equation can be obtained:

[0134]

[0135] Where, represents the time derivative of the variable, (~) represents the expansion of a three-dimensional vector into its corresponding antisymmetric matrix form, () T Indicates transposing a matrix.

[0136] The first two equations constitute the translational and rotational equations of flight dynamics. The left side of the equation group, M, is the total mass of the aircraft. is the acceleration disturbance of the center of mass of the aircraft, ΔV0 is the velocity disturbance of the center of mass of the aircraft; is the disturbance of the aircraft’s angular acceleration, and Δω is the antisymmetric matrix of the disturbance of the aircraft’s angular velocity. ref is the total aircraft inertia matrix in the trim configuration, dm is a certain mass element on the aircraft, r ref is the position vector of the mass element relative to the center of mass of the aircraft.G ,ΔM G is the gravitational disturbance and gravitational moment disturbance, ΔF A ,ΔM A is the aerodynamic disturbance and aerodynamic moment disturbance, ΔF T ,ΔM T are the thrust disturbance and thrust torque.

[0137] The third equation is the structural dynamics equation. The specific meaning of each term on the left side is exactly the same as that on the left side of equation (8). The right side Δf G is the generalized gravitational perturbation, Δf A is the generalized aerodynamic disturbance, Δf T is the generalized thrust disturbance.

[0138] Step 6: Use three-dimensional spline interpolation to obtain the rigid body motion-structure-aerodynamic coupling relationship.

[0139] In the above steps, the second step yields the aerodynamic equations, and the fifth step yields the rigid-elastic coupling dynamic equations. Rigid-elastic coupling aeroelastic calculations require coupling aerodynamics with rigid-body degrees of freedom and structural calculations. This paper utilizes spline interpolation theory to couple rigid-body motion degrees of freedom, finite element modal generalized degrees of freedom, and the normal vector variations of aerodynamic surface control points, thereby characterizing the coupling relationship between the aerodynamic equations and the structural dynamic equations.

[0140] Aerodynamic surface displacement W A and structural displacement W S The relationship is:

[0141] W A =EW S (11)

[0142] Where E is the displacement interpolation matrix. Similarly, the aerodynamic surface deformation velocity V A Interpolation can be obtained by the structural deformation velocity V S Solve with mapping relationship:

[0143] V A =EV S (12)

[0144] The relationship between the normal vector n after deformation and the generalized degree of freedom in the modal space is:

[0145] n=n0+Δn=n0+E N q e (13)

[0146] Among them, n0 is the normal vector of each pneumatic unit in the undeformed state, Δn is the normal vector increment caused by structural deformation, E N is the interpolation matrix from the structural modal coordinates to the aerodynamic element normal vector increment.

[0147] After the rigid body's freedom of motion and structural deformation, v0 is the reference flow velocity in the trim state, v d The small perturbation incoming flow velocity near the equilibrium solution is expressed as follows:

[0148] v0=-(V0+ω×r ref )(14)

[0149]

[0150] Among them, the meanings of V0,ω,ΔV0,Δω are consistent with those in formula (10), representing the velocity, angular velocity, velocity disturbance and angular velocity disturbance at a certain point on the aircraft, r ref is the position vector of the point relative to the center of mass, u d is the structural elastic displacement generated at this point, is the elastic deformation velocity.

[0151] The wash velocity w at the i-th aerodynamic grid control point i for:

[0152]

[0153] Among them, v 0i is the reference incoming flow velocity at the i-th aerodynamic grid control point, Δn i is the normal vector increment of the i-th aerodynamic network, v di is the disturbance velocity at the i-th aerodynamic grid control point, n refi is the normal vector of the ith aerodynamic grid in the trimmed configuration, r refi is the position vector of the i-th aerodynamic grid control point in the trim configuration, u di is the elastic displacement at the i-th aerodynamic grid control point, is the elastic deformation velocity at the ith aerodynamic grid control point.

[0154] According to formula (9), the elastic deformation is expressed as a structural mode, and the velocity column vector of the aerodynamic grid control point small perturbation method can be associated with the generalized modal coordinates of the structure;

[0155] For the trim state of fixed straight and level flight, simplify Therefore, the wash velocity and wash velocity derivative of the i-th aerodynamic grid can be simplified as:

[0156]

[0157] Among them, E Ni is the normal vector increment interpolation matrix at the i-th aerodynamic grid control point, G is the structural elastic deformation velocity interpolation matrix from the structure to the aerodynamic grid control point, Φe is the linear elastic modal matrix of the structure.

[0158] The Fasching velocity w at each aerodynamic grid control point is assembled into a column vector w, and the Fasching velocity derivative is also assembled. The Fasching velocity of the entire aerodynamic surface can be expressed as:

[0159]

[0160] Each item in the formula is in accordance with the state quantity After sorting, the coefficient matrix of each item is simply written as

[0161]

[0162] Step 7: Establish the state space equation of the rigid-elastic coupled aeroelastic system.

[0163] Substitute the rigid body motion-structure-aerodynamic coupling relationship obtained in the sixth step into the aerodynamic equation given in the second step, and then substitute the aerodynamic equation into the linearized rigid-elastic coupling dynamic equation obtained in the fifth step to obtain the state space equation of the rigid-elastic coupling aeroelastic system.

[0164] For the aerodynamic equation (2) in the second step, combined with equation (9), the generalized aerodynamic force F on the structure is S The expression is:

[0165]

[0166] Among them E F is the force interpolation matrix.

[0167] Combining equations (10)(19)(20)(25) we can obtain the state space equations of the rigid-elastic coupled aeroelastic system:

[0168]

[0169] Among them, A fl&ae is the state matrix of the state space model, x fl&ae is the state quantity of the state space equation of the rigid-elastic coupled aeroelastic system, is x fl&ae Derivative with respect to time.

[0170] Step 8: Analyze stability and response issues.

[0171] Analyze the state matrix A in the state space equation of the rigid-elastic coupled aeroelastic system fl&aeStability analysis can be performed. If the real parts of all eigenvalues ​​are negative, the system is stable; otherwise, the system is unstable. By adding disturbance inputs to the state-space model and performing time-domain simulation, time-domain dynamic response analysis can be performed.

[0172] The following describes in detail the specific implementation of the aircraft rigid-elastic coupled aeroelastic stability and dynamic response analysis method provided by the present invention through a specific embodiment.

[0173] This example uses a large-aspect-chord flying-wing UAV model. This flying-wing UAV has a wingspan of 4 meters, an aspect ratio of 14, and a total flight weight of 5.7 kg. It consists of a central wing-body fusion structure (fuselage), two wings, and wingtip vertical tails. The fuselage is 0.74 meters long and 0.37 meters wide, exhibiting high strength and rigidity. Some model parameters are shown in Table 1.

[0174] Table 1

[0175] Parameter name Parameter value Wingspan / m 4.07 Average aerodynamic chord length / m 0.3 Fuselage width / m 0.37 Aspect ratio 14 Total machine mass / kg 5.7 Wing airfoil Supercritical airfoil

[0176] Step 1: Calculation initialization.

[0177] An aerodynamic model was established, with the mid-camber surface of the wing divided into 15 grids along the chord direction and 45 grids along the span direction. The trailing vortex grid was divided into 150 grids along the chord direction and 45 grids along the span direction.

[0178] Step 2: Establish the aerodynamic equations in state space form for the aerodynamic grid obtained in step 1.

[0179] The vortex-lattice state space equation can be fully expressed as:

[0180]

[0181] State variable x aero =Γ w , input Output y aero =F;A aero =A a , B aero =[B a O],C aero =B3, D aero =[B1 B2].

[0182] Step 3: Define the flight dynamics model.

[0183] The flight dynamics model is defined in the body coordinate system, where the origin o of the body coordinate system is located at the center of mass of the undeformed aircraft, the ox axis is parallel to the fuselage axis in the aircraft symmetry plane and points to the tail of the aircraft, the oz axis is perpendicular to the ox axis in the symmetry plane and points to the top of the aircraft, and the oy axis is perpendicular to the symmetry plane and points to the right side of the aircraft.

[0184] Step 4: Establish finite element structural model.

[0185] The structural model is established using the finite element method. The finite element model is as follows: Figure 4 The finite element model was established in MSC.Nastran software. The first five modes were used in the calculation to give the modal space structural dynamic equation. The modal information is shown in Table 2:

[0186] Table 2

[0187]

[0188] Step 5: Establish linearized rigid-elastic coupling dynamic equations.

[0189] Combining the above flight dynamics model and finite element model, based on the Lagrange equation, the linearized aircraft rigid-elastic coupling dynamics equation can be obtained:

[0190]

[0191] Step 6: Use three-dimensional spline interpolation theory to give the rigid body motion-structure-aerodynamic coupling relationship.

[0192] Characterizing the coupling relationship between the aerodynamic equations and the structural dynamics equations, the integrated induced velocity can be expressed as:

[0193]

[0194] Step 7: Give the state space equation of the rigid-elastic coupled aeroelastic system.

[0195] The state space equations of the rigid-elastic coupled aeroelastic system can be assembled by coupling the aerodynamic equations given in step 2 with the structure-aerodynamic coupling relationship given in step 6:

[0196]

[0197] Among them A fl&ae is the state space model coefficient matrix,

[0198] Step 8: Analyze stability and response issues.

[0199] Analyze the state matrix A in the state space equation of the rigid-elastic coupled aeroelastic system fl&ae Stability analysis can be performed. If the real parts of all eigenvalues ​​are negative, the system is stable; otherwise, the system is unstable. Supplementing the state-space model with a disturbance force vector for time-domain simulation allows for time-domain dynamic response analysis. The stability analysis of the embodiment was implemented in Matlab software. Figure 5The characteristic root analysis results show that the instability velocity is 19.8 m / s, which fully demonstrates that the method provided by the present invention is effective.

[0200] The present invention provides an aeroelastic-rigid-elastic coupling stability and dynamic response analysis method based on the state-space formal vortex lattice method, which is of great significance in practical aircraft design applications.

[0201] Although the specific embodiments of the present invention have been described in a particular order, it should be understood that such actions or steps are required to be performed in the particular order shown or in a sequential order, or that all illustrated actions or steps are required to be performed to obtain the desired result. Under certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although some specific implementation details have been included in the above discussion, these should not be construed as limiting the scope of the present disclosure. Some features described in the context of a separate embodiment can also be implemented in a single implementation in combination. On the contrary, the various features described in the context of a single implementation can also be implemented in multiple implementations individually or in any suitable sub-combination.

[0202] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for analyzing the aeroelastic stability and dynamic response of an aircraft rigid-elastic coupling, characterized in that: The following steps are involved: Step S1, determining the inherent shape parameters of the aircraft, and based on the inherent shape parameters, dividing the mid-camber surface of the aircraft wing into a plurality of quadrilateral aerodynamic grids along the chord direction and the span direction, wherein the aerodynamic grid includes an attached vortex grid on the wing surface and a trailing vortex grid dragged along the incoming flow direction; the inherent shape parameters include wing span, average aerodynamic chord length, fuselage width, total aircraft mass, and wing airfoil; Step S2: establishing a vortex lattice method state space equation based on the aerodynamic grid, wherein the vortex lattice method state space equation is used to calculate an aerodynamic force vector based on the induced velocity on the wing surface; Step S3: establishing a flight dynamics model and a finite element structural model of the aircraft wing, and establishing a linearized rigid-elastic coupling dynamics equation representing the rigid body motion and elastic deformation of the aircraft wing based on the flight dynamics model and the finite element structural model; Step S4: using a three-dimensional spline interpolation method, based on the vortex lattice state space equation and the rigid-elastic coupling dynamics equation, obtaining a rigid body motion-structure-aerodynamic coupling relationship, wherein the rigid body motion-structure-aerodynamic coupling relationship is specifically: a calculation expression for the induced velocity on the wing surface; Step S5: determining the state space equation of the generalized external force and rigid-elastic coupled aeroelastic system based on the rigid-body motion-structure-aerodynamic coupling relationship and the rigid-elastic coupled dynamic equation; Step S6, calculating a state matrix in a state space equation of the rigid-elastic coupled aeroelastic system, and determining a judgment result of the rigid-elastic coupled aeroelastic stability according to an eigenvalue of the state matrix; After adding a disturbance force vector to the state space equation of the rigid-elastic coupled aeroelastic system, a time domain simulation is performed to obtain the instability velocity of the aircraft as a dynamic response analysis result.

2. The method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft according to claim 1, characterized in that: The step S2 specifically includes: Step S2-1, arranging vortex segments at each 1 / 4 chord of the aerodynamic grid to form four vortex segments of equal strength, wherein the four vortex segments of equal strength are connected end to end to form a vortex ring; selecting the midpoint of the 1 / 4 chord as the aerodynamic force application point, and selecting the midpoint of the 3 / 4 chord as the aerodynamic force control point; Step S2-2: Based on the action point and control point, establish the vortex lattice method state space equation, which is expressed as: y aero =C aero x aero +D aero u aero in, is the time derivative of the tail vortex strength vector, Γ w is the tail vortex strength vector, w is the induced velocity vector on the wing surface, A a is the state matrix, B a is the input matrix; F is the aerodynamic force vector, w is the normal velocity vector of the wing surface, is the derivative of the velocity vector with respect to time, B1, B2 are the direct transmission matrices, and B3 is the output matrix; x aero is the state variable, x aero =Γ w , is x aero The derivative with respect to time, u aero is the input quantity, y aero is the output, y aero =F,A aero ,B aero ,C aero ,D aero is the coefficient matrix of the state space equation, A aero =A a , B aero =[B a O],C aero =B3, D aero =[B1B2], O is a zero matrix.

3. The method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft according to claim 2, characterized in that: The step S3 specifically includes: Step S3-1, establishing a flight dynamics model, including: determining the aircraft position conversion relationship between the aircraft body coordinate system and the ground coordinate system, and determining the aircraft motion speed conversion relationship between the aircraft body coordinate system and the inertial coordinate system; Step S3-2: Divide the aircraft wing into finite elements based on the inherent shape parameters of the aircraft, establish a finite element structural model, and determine the modal space structural dynamics equation of the finite element structural model; Step S3-3: Based on the flight dynamics model and the finite element structural model, a linearized rigid-elastic coupling dynamic equation representing the rigid body motion and elastic deformation of the aircraft wing is established.

4. The method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft according to claim 3, characterized in that: The step S3-1 specifically includes: Determine the body coordinate system, where the origin o of the body coordinate system is located at the center of mass of the undeformed aircraft, the ox axis is parallel to the fuselage axis in the aircraft symmetry plane and points to the tail of the aircraft, the oz axis is perpendicular to the ox axis in the symmetry plane and points to the top of the aircraft, and the oy axis is perpendicular to the symmetry plane and points to the right side of the aircraft; The aircraft position transformation relationship between the body coordinate system and the ground coordinate system is determined as the transformation matrix L BE , the expression is: Among them, φ, θ, ψ are roll angle, pitch angle and yaw angle respectively, L x (φ),L y (θ),L z (ψ) are the rotation matrices for the rotation angle φ around the x-axis of the body coordinate system, the rotation matrices for the rotation angle θ around the y-axis of the body coordinate system, and the rotation matrices for the rotation angle ψ around the z-axis of the body coordinate system; The velocity of the center of mass in the body coordinate system and the velocity of the center of mass in the inertial coordinate system have the following relationship: in, is the time derivative of the position vector in the earth coordinate system, and V0 is the velocity of the center of mass in the body coordinate system; The position R of any mass element on an elastic aircraft in the inertial reference frame is expressed as: R=R0+r=R0+r0+u Where R0 represents the position vector of the origin o of the body coordinate system in the inertial system, r represents the position vector of the mass element on the elastic aircraft relative to the center of mass in the geodetic coordinate system, r0 is the undeformed position, and u is the elastic deformation; The angular velocity ω can be expressed as the time rate of change of the Euler angle: Where ω = [pqr] T is the angular velocity of the body coordinate system relative to the earth system. After projecting to the body coordinate system, p, q, and r are the roll angular velocity, pitch angular velocity, and yaw angular velocity respectively; D BE is the transformation matrix, is the time rate of change of the Euler angle Θ.

5. The method for analyzing the aeroelastic stability and dynamic response of an aircraft rigid-elastic coupling according to claim 4 is characterized in that: The step S3-2 specifically includes: The structural model is established using the finite element method, and the structural dynamics equation in modal coordinates is obtained: Among them, M e ,B e ,K e are the generalized mass matrix, generalized damping matrix and generalized stiffness matrix respectively, q e are generalized modal coordinates, are generalized acceleration and generalized velocity, respectively, F e is the generalized force; the generalized modal coordinate q e With physical coordinate u e The relational expression is: you e =Φ e q e where Φ e is the modal matrix.

6. The method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft according to claim 5, characterized in that: The step S3-3 specifically includes: Combining the flight dynamics model and the finite element structural model, based on the Lagrange equation, the linearized aircraft rigid-elastic coupling dynamics equation is obtained, which is expressed as follows: Among them, (·) represents the time derivative of the variable, (~) represents the expansion of a three-dimensional vector into its corresponding antisymmetric matrix form, () T Indicates the transposition of a matrix; M is the total mass of the aircraft, is the acceleration disturbance of the center of mass of the aircraft, ΔV0 is the velocity disturbance of the center of mass of the aircraft; is the disturbance of the aircraft angular acceleration, Δω is the antisymmetric matrix of the disturbance of the aircraft angular velocity; J ref is the total aircraft inertia matrix in the trim configuration, dm is a certain mass element on the aircraft, r ref is the position vector of the mass element relative to the center of mass of the aircraft; ΔF G ,ΔM G is the gravitational disturbance and gravitational moment disturbance, ΔF A ,ΔM A is the aerodynamic disturbance and aerodynamic moment disturbance, ΔF T ,ΔM T is the thrust disturbance and thrust moment; Δf G is the generalized gravitational perturbation, Δf A is the generalized aerodynamic disturbance, Δf T is the generalized thrust disturbance.

7. The method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft according to claim 6, characterized in that: The step S4 specifically includes: Determine the aerodynamic surface displacement W A and structural displacement W S Relationship: W A =HE S Where E is the displacement interpolation matrix; Determine the aerodynamic surface velocity V A and structural velocity V S Relationship: V A =EV S The relationship between the normal vector n after deformation and the generalized degree of freedom in the modal space is: n=n0+Δn=n0+E N q e Where n0 is the normal vector at the control point in the undeformed state, Δn is the normal vector increment caused by structural deformation, and E N is the interpolation matrix from the structural modal coordinates to the aerodynamic element normal vector increment; After the rigid body's freedom of motion and structural deformation, the reference inflow velocity v0 in the trim state and the small perturbation inflow velocity v near the equilibrium solution are obtained. d : v0=-(V0+ω×r ref ) Among them, V0,ω,ΔV0,Δω represent the velocity, angular velocity, velocity disturbance and angular velocity disturbance at a certain point on the aircraft, r ref is the position vector of the point relative to the center of mass, u d is the structural elastic displacement generated at this point, is the elastic deformation velocity; Determine the wash velocity w at the aerodynamic grid control point i i : Among them, v 0i is the reference incoming flow velocity at the i-th aerodynamic grid control point, Δn i is the normal vector increment of the i-th aerodynamic network, v di is the disturbance velocity at the i-th aerodynamic grid control point, n refi is the normal vector of the ith aerodynamic grid in the trimmed configuration, r refi is the position vector of the i-th aerodynamic grid control point in the trim configuration, u di is the elastic displacement at the i-th aerodynamic grid control point, is the elastic deformation velocity at the i-th aerodynamic grid control point; For the trim state of fixed straight and level flight, simplify get: Where G is the structural elastic deformation velocity interpolation matrix from the structure to the aerodynamic grid control point, Φ e is the linear elastic modal matrix of the structure; Finally, the calculation expression of the wing surface normal wash velocity and its derivative is obtained: Among them, each term is based on the state quantity q e , ΔV0, Δω are sorted out, and the coefficient matrix of each item is simply written as R ω ; .

8. The method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft according to claim 7, characterized in that: The step S5 specifically includes: Based on the rigid body motion-structure-aerodynamic coupling relationship and the rigid-elastic coupling dynamic equation, the generalized external force expression is determined as: Among them E F is the force interpolation matrix; The state space equation of the rigid-elastic coupled aeroelastic system is expressed as: Among them, A fl&ae is the state matrix of the state space model, x fl&ae is the state quantity of the state space equation of the rigid-elastic coupled aeroelastic system, is x fl&ae Derivative with respect to time.

9. The method for analyzing the aeroelastic stability and dynamic response of a rigid-elastic coupling aircraft according to claim 8, characterized in that: In step S6, determining the result of the rigid-elastic coupled aeroelastic stability based on the eigenvalue of the state matrix specifically includes: Obtain the state matrix A in the state space equation of the rigid-elastic coupled aeroelastic system fl&ae , if A fl&ae If the real parts of all eigenvalues ​​are negative, the system is considered stable; otherwise, the system is considered unstable.

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