A rapid calculation method for carrier-based aircraft dynamics

Abstract

The application discloses a kind of shipboard aircraft dynamics fast calculation method.Method includes following process: establishing shipboard aircraft catapult take-off multi-flexible body system dynamics model, establishes shipboard aircraft catapult take-off multi-flexible body system topology, utilize finite element method to establish main tire refinement finite element model, then tire flexible body dynamics characteristic parameter is exported and deduces the dynamics equation of tire flexible element, based on multi-body system transfer matrix method (MSTMM) and finite element modal synthesis method deduce shipboard aircraft catapult take-off multi-flexible body system total transfer equation and total transfer matrix, solve the inherent frequency of shipboard aircraft multi-flexible body system considering inflatable flexible tire and the dynamic response of catapult take-off;The method proposed in the application overcomes the defects of high matrix order and large amount of calculation of traditional methods when dealing with complex coupling system of shipboard aircraft containing inflatable flexible tire, has the advantages of fast calculation speed, high degree of programming and strong universality, provides an efficient calculation method for the dynamic analysis of complex shipboard aircraft multi-flexible body system.

Description

Technical Field

[0001] This invention belongs to the field of shipborne aircraft dynamics calculation technology, and in particular, a rapid calculation method for shipborne aircraft dynamics. Background Technology

[0002] Catapult launch of carrier-based aircraft is a complex rigid-flexible coupled dynamic process involving large-scale fuselage motion, strong impact constraints from the catapult device, and flexible deformation of the tires. The dynamic characteristics of the carrier-based aircraft system are highly correlated with the dynamic responses of its various components, and accurate assessment of its dynamic characteristics is crucial for improving takeoff safety and structural reliability. However, existing technologies face severe computational bottlenecks when performing dynamic modeling and simulation of carrier-based aircraft systems. Traditional multibody dynamics methods require establishing global dynamic equations based on the entire aircraft system. With the increasing sophistication of carrier-based aircraft, especially after the introduction of inflatable flexible tire models, the system's degrees of freedom have increased dramatically, leading to difficulties in calculating the matrix order of the overall dynamic equations and low simulation efficiency. High-precision modeling of its flight dynamics faces a bottleneck where computational efficiency and model accuracy are difficult to balance, making it difficult to meet the real-time analysis requirements in engineering design. Furthermore, during the catapult launch transient process, the interaction between the tires and the deck of carrier-based aircraft exhibits strong nonlinearity. Traditional modeling frameworks, when dealing with such high-dimensional flexible coupling problems, often sacrifice model accuracy for computational speed, or prioritize accuracy at the expense of excessively long simulation cycles. This fails to meet the engineering requirements for real-time evaluation of carrier-based aircraft dynamics and rapid scheme verification. Therefore, there is an urgent need to develop a rapid computational method that can significantly reduce the order of the system matrix and overcome the limitations of solving high-dimensional carrier-based aircraft dynamics. Summary of the Invention

[0003] The purpose of this invention is to overcome the problems of low computational efficiency and high matrix order in existing technologies, and to provide a rapid calculation method for the catapult launch dynamics of carrier-based aircraft based on the finite element modal synthesis (MEMT) multibody system transfer matrix method. This invention organically combines the MEMT multibody system transfer matrix method (MSTMM) with the finite element method (FEM) to construct a dynamic model of a multibody system for carrier-based aircraft catapult launch. Based on the characteristics of system components, this method divides the subsystems into M-type subsystems suitable for the MEMT and F-type subsystems suitable for finite element modeling. While achieving refined modeling of individual components, it simplifies the overall matrix operation process of the system by utilizing the characteristics of the transfer matrix method, significantly improving the efficiency of dynamic simulation. This invention, while maintaining high accuracy, significantly reduces computation time compared to traditional multibody dynamics methods, providing economical and efficient computational support for the optimized design of carrier-based aircraft catapult launch systems, and offering a new approach to solving the problem of real-time dynamic analysis of complex carrier-based aircraft systems.

[0004] The technical solution to achieve the objective of this invention is: a method for rapid calculation of shipborne aircraft dynamics, the method comprising the following steps:

[0005] Step 1: Based on the structural form of each component of the carrier-based aircraft catapult launch multi-soft-body system, the carrier-based aircraft catapult launch multi-soft-body system is divided into components containing rigid body elements and the main tire is regarded as a soft body element. Each component is numbered, the input and output state vectors of each component are determined, and the dynamic topology diagram of the carrier-based aircraft catapult launch multi-soft-body system is established according to the connection method between each component.

[0006] Step 2: Divide the components of the carrier-based aircraft catapult launch multi-soft-body system into two types of subsystems: M-type subsystems processed using the multi-body system transfer matrix method, and F-type subsystems processed using the finite element method.

[0007] Step 3: For the M-type subsystem, construct the transfer equations relating the input and output state vectors of each component within the subsystem. Sweep through the entire system along the transfer path, recursively deriving from the input point to the output point to obtain the main transfer equation of the subsystem. For the F-type subsystem, construct the finite element model of the subsystem components and obtain the reduced tire mass matrix and stiffness matrix using the Craig-Bampton modal reduction method. Construct the overall transfer equation and overall transfer matrix of the carrier-based aircraft catapult takeoff multi-flexible body system. Solve for the root state vectors of the carrier-based aircraft multi-flexible body system based on the system boundary conditions. Then, recursively derive all the state vectors from the system output point to the input point to obtain the dynamic response of the entire carrier-based aircraft multi-flexible body system. Substitute the dynamic response calculation results at the end of the current stage into the initial conditions of the next stage until the dynamic response calculation is completed.

[0008] Step 4: Conduct simulation tests of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires, and solve for the natural frequency and dynamic response of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires during the initial stage of catapult takeoff.

[0009] Further, step 1 specifically includes dividing the carrier-based aircraft catapult launch multi-flexible body system into body elements and hinge elements, and numbering them sequentially according to the recursive direction to establish a dynamic topology diagram of the carrier-based aircraft catapult launch multi-flexible body system;

[0010] The fuselage, nose landing gear strut, nose landing gear outer cylinder, nose landing gear piston rod, upper front torsion arm, lower front torsion arm, traction rod, ejection rod, ejection tractor, left landing gear outer cylinder, left landing gear piston rod, left rear wheel, right landing gear outer cylinder, right landing gear piston rod, right rear wheel, left front wheel rim, and right front wheel rim are considered as rigid bodies in spatial motion. The fuselage, nose landing gear outer cylinder, nose landing gear piston rod, upper front torsion arm, lower front torsion arm, traction rod, left front wheel rim, and right front wheel rim are rigid bodies in spatial motion with multiple inputs and one output. The remaining components are rigid bodies with single inputs and single outputs. The left front tire and right front tire are considered as flexible bodies in spatial motion with multiple inputs and single outputs.

[0011] Based on the interrelationships between the components of the carrier-based aircraft catapult launch multi-flexible-body system, including: the fuselage and the nose landing gear strut are connected via elastic hinges; the nose landing gear strut and the landing gear outer cylinder are connected via elastic hinges; the fuselage and the landing gear outer cylinder are connected via elastic hinges; the landing gear outer cylinder and the nose landing gear piston rod are connected via sliding connection; the left front tire and the left front wheel rim are connected via sliding hinges; the right front tire and the right front wheel rim are connected via sliding hinges; the nose landing gear piston rod and the upper front torque arm are connected via elastic hinges; the upper and lower front torque arms and the restraint are connected via column hinges; the nose landing gear piston and the lower front torque arm are connected via elastic connection; the restraint and the deck are connected via elastic hinges; the nose landing gear piston rod and the catapult rod are connected via elastic hinges; the catapult rod and the catapult traction are connected via elastic hinges. The connections are as follows: the catapult tractor is connected to the ship's deck via a flexible hinge; the fuselage is connected to the left landing gear outer cylinder via a flexible hinge; the left landing gear outer cylinder is connected to the left landing gear piston rod via a sliding hinge; the left landing gear piston rod is connected to the left rear wheel via a column; the left rear wheel is connected to the ship via a flexible hinge; the fuselage is connected to the right landing gear outer cylinder via a flexible hinge; the right landing gear outer cylinder is connected to the right landing gear piston rod via a sliding hinge; the right landing gear piston rod is connected to the right rear wheel via a column; the right rear wheel is connected to the ship's deck via a flexible hinge; the right rear wheel is connected to the ship's deck via a flexible hinge; the left front wheel is connected to the ship's deck via a flexible hinge; the left front tire is connected to the ship's deck via a flexible hinge; the front landing gear piston rod is connected to the left front wheel rim via a column hinge; the front landing gear piston rod is connected to the right front wheel rim via a column hinge.

[0012] Furthermore, the connection points between the various subsystems in step 2 satisfy the geometric relationship that the displacement and angular displacement are equal, so as to realize the coupling between the M-type and F-type subsystems.

[0013] Furthermore, in step 2, the two nose wheels of the carrier-based aircraft are each designated as a separate F-type subsystem, while the rest of the carrier-based aircraft is designated as a separate M-type subsystem.

[0014] Furthermore, step 3 involves constructing the finite element model of the F-type subsystem components, including constructing the finite element model of the main tire of the F-type subsystem, specifically including:

[0015] (1) First, establish a finite element model of the tire with a degrees of freedom. Derive its a-order mass matrix M and stiffness matrix K. Use the Craig-Bampton modal reduction method to take two input ends. , With an output terminal Based on the degrees of freedom and the first few fixed interface modes, the a-order mass matrix and stiffness matrix are reduced to b-order and orthogonalized to obtain the reduced-order matrix. Tire mass array after order reduction With stiffness matrix The dynamic equations of the F-type subsystem are expressed as follows:

[0016]

[0017] in, Let b be the reduced-order coordinates of the flexible structure in the F subsystem. Let b be the reduced-order coordinates. , , These are the two input terminals of the F subsystem. , With an output terminal The state vector, , , , These are the coefficient matrices for the first input terminal, the second input terminal, and the output terminal, respectively. It is a b×3 zero matrix. , , These are the displacement reduction matrices for the first input terminal, the second input terminal, and the output terminal, respectively. , , These are the angle reduction matrices for the first input terminal, the second input terminal, and the output terminal, respectively.

[0018] (2) The connection points between the various subsystems satisfy the geometric relationship that the displacement and angular displacement are equal, as follows:

[0019]

[0020] In the formula, , , These are the reduced-order matrices for the output, the first input, and the second input, respectively. It is a coefficient matrix.

[0021] Furthermore, step 3 involves constructing the master transfer equations for the M-type subsystem, including:

[0022] Step 3-1: Construct the transfer equations for the rigid body elements of the M-class subsystem, specifically including:

[0023] (1) Rigid body processing of spatial motion is performed as single-ended input, single-ended output or multi-ended input, single-ended output components:

[0024]

[0025] In the formula, and These are the output terminal O of component j and the input terminal r, respectively. The state vector, For the r-th input terminal of component j The corresponding transfer matrix, where N represents the total number of inputs;

[0026] The motion of the spatial vibrating rigid body element j, which has an N-terminal input and a single-terminal output, is transmitted through the first input terminal. Linear displacements x, y, z and angular displacements , , Describe the local coordinate system that describes the relative positions of the input ends, center of mass, and output ends of the rigid body. The origin is located at the initial position of the first input point of the element, and the three coordinate axes are parallel to the coordinate axes of the global inertial system Oxyz. The transfer matrix of the spatial vibrating rigid body is:

[0027]

[0028] In the formula, It is a 3×3 identity matrix. It is a 3×3 zero matrix, where m is the mass of the rigid body element. Let ω be the angular velocity of the rigid body element. Let be the moment of inertia matrix of the rigid body element relative to the first input end. , , These are the cross product matrices of the coordinates of the output terminal relative to the first input terminal, the centroid of the component, and the position vector of the r-th input terminal, respectively. Let be the cross product matrix of the component's centroid relative to the position vector of the first input terminal. This indicates that the rigid body element is a single-input element. This indicates that the rigid body element has multiple inputs;

[0029] (2) For multi-terminal input body components, the component transfer equation only includes the geometric relationship between the output point and the first input point. It is necessary to add the geometric relationship between the r-th input terminal of the multi-terminal input body component j and the first input terminal:

[0030]

[0031] In the formula, The matrix describing the geometric relationships between the input terminals of a multi-input element j is called the element geometry matrix. and These represent the first input terminal and the r-th input terminal of component j, respectively. Let be the cross product matrix of the coordinates of the r-th input terminal of element j relative to the first input terminal;

[0032] Step 3-2, construct the transfer equations for the hinge elements of the M-type subsystem, specifically including:

[0033] (1) The spatial elastic hinge j has a coordinate system along its local coordinate system The springs and torsion springs on the three coordinate axes are single-ended input and single-ended output elements, and their transfer matrix... In the local coordinate system, it is represented as:

[0034]

[0035] In the formula, , and respectively spring edge , and Shaft stiffness, , and They are torsion springs , and Torsional stiffness of the shaft;

[0036] Step 3-3, closed-loop structure processing of subsystem M, specifically includes:

[0037] (1) Based on the multibody system transfer matrix method for processing closed-loop topology multibody systems, the closed loop is "cut off" at point P in the topology diagram of the carrier-based aircraft multi-flexible body system dynamics model. At each "cut-off" point, two new state vectors will be generated, and the two state vectors satisfy the following condition:

[0038]

[0039] In the formula, and For input boundaries, It is a coefficient matrix.

[0040] Furthermore, in step 3-2, if the spatial elastic hinge rotates in only one direction, it degenerates into a cylindrical hinge or pin, and its transfer matrix is ​​represented in the local coordinate system as follows:

[0041]

[0042] In the formula, This indicates that the spatial elastic hinge has only one direction. The transfer matrix corresponding to the rotation of the axis;

[0043] If a spatial elastic hinge has displacement in only one direction, it degenerates into a sliding hinge or sleeve, and its transfer matrix is ​​represented in the local coordinate system as follows:

[0044]

[0045] In the formula, This indicates that the spatial elastic hinge has only one direction. The transfer matrix corresponding to the rotation of the axis.

[0046] Furthermore, the overall transfer equation for the carrier-based aircraft multi-flexible body system in step 3 is:

[0047]

[0048] In the formula, For the overall transfer matrix of the carrier-based aircraft multi-flexible body system, This is the overall state vector of the carrier-based aircraft's multi-flexible-body system.

[0049] Furthermore, step 4 specifically includes:

[0050] Step 4-1, the body dynamics equations of the carrier-based aircraft's multi-flexible-body system are written as follows:

[0051]

[0052] In the formula, the mass matrix Damping array Stiffness matrix For augmentation operators of carrier-based aircraft multi-soft-body systems, , , These are the displacement, velocity, and acceleration coordinate arrays in the physical coordinates of the carrier-based aircraft's multi-soft-body system. For the external force array of the carrier-based aircraft multi-flexible body system, the subscript is the body element number, and n is the total number of body elements;

[0053] Step 4-2: Applying modal analysis, the displacement matrix in physical coordinates of the dynamic response of the carrier-based aircraft's multi-flexible-body system is expanded into a superposition of modal coordinates, i.e.:

[0054]

[0055] In the formula, Let be the displacement matrix of the carrier-based aircraft's multi-flexible-body system at any time t. Let be the k-th generalized coordinate, where k is the modal order; Let k be the augmented eigenvector of order k, whose elements are derived from the k-th natural frequencies of the system. The modal coordinates corresponding to the displacements and rotations at the input ends of all discrete body elements and the corresponding mode shapes of each continuous body element;

[0056] Step 4-3, based on the orthogonality of the augmented eigenvectors, that is:

[0057]

[0058] Inner product of the volume dynamics equations of a carrier-based aircraft multi-flexible body system To decouple them, we obtain the dynamic equations of the multi-flexible body system of each order that are independent under the generalized coordinate system:

[0059]

[0060] In the formula, The symbol for Kronecker. For the p-th modal mass of the carrier-based aircraft multi-flexible body system, For the p-th modal stiffness of the carrier-based aircraft multi-flexible body system, For the P-th order augmented eigenvector, It is the p-th natural frequency; Let be the generalized coordinates at any time t. For the damping ratio, The resultant external force on the multi-flexible body system of carrier-based aircraft; , They are respectively The first and second derivatives.

[0061] Step 4-4: Based on the initial conditions of the carrier-based aircraft multi-soft-body system, the generalized coordinates of the carrier-based aircraft multi-soft-body system at any time t are obtained using the numerical integration method. Thus, the displacement coordinate array of the first input terminals of each body element in the multi-flexible body system of the carrier-based aircraft is obtained. , which is the dynamic response of the carrier-based aircraft's multi-flexible-body system at any time t.

[0062] Furthermore, for the F-type subsystem, its augmented eigenvector and mode shape are:

[0063]

[0064] In the formula, This is the reduced-order matrix of the Craig-Bampton mode reduction. For the augmented feature vector of the F-class subsystem, Let a be the a-order displacement and rotation array of all nodes in the F-type subsystem, which is the mode shape of the left and right tires;

[0065] Substitute these steps 4-1 to 4-4 into the equation to obtain the dynamic response of the flexible tire.

[0066] Compared with the prior art, the significant advantages of this invention are:

[0067] (1) The total transfer equations of five rigid subsystems are automatically derived using the multibody system transfer matrix method. At the same time, the mass, stiffness and reduced-order matrix of the flexible tire subsystem under the inflated prestress state are extracted by combining the finite element method and the Craig-Bampton modal reduction technique. This method significantly reduces the order of the system matrix while maintaining the modeling accuracy, and the calculation time is only 27.8s. It provides an efficient technical approach for the rapid prediction and real-time performance analysis of the dynamic response of shipborne aircraft under complex working conditions.

[0068] (2) Based on the shape and material properties of the components, this invention divides the carrier-based aircraft catapult takeoff multi-flexible body system into two types of subsystems: the M-type subsystem processed by the multibody system transfer matrix method and the F-type subsystem processed by the finite element method. The M-type subsystem is analyzed by the multibody system transfer matrix method, deriving the component transfer equations and transfer matrices based on the transfer relationships between state vectors, and deriving the overall transfer equations and overall transfer matrix of the subsystem based on the automatic derivation theorem. The F-type subsystem has its dynamic equations written according to the finite element method, and the model is reduced using the Craig-Bampton order reduction method. This invention leverages the advantages of the high computational efficiency of the transfer matrix method and the high descriptive accuracy of the finite element method, achieving a balance between computational speed and model accuracy at the system level.

[0069] (3) This invention applies the finite element modal synthesis multibody system transfer matrix method to the catapult takeoff dynamics analysis of carrier-based aircraft. By establishing a system dynamics topology diagram, dividing and processing M-type (transfer matrix method) and F-type (finite element combined with modal reduction method) subsystems respectively, and finally integrating and establishing the overall system transfer equation and recursively solving it, modular and high-precision modeling of the entire multibody system containing complex flexible tires is achieved. This method combines the efficiency of the transfer matrix method with the accurate description capability of the finite element method for complex flexible bodies, thus enabling rapid solution of the dynamic response of the system under catapult takeoff conditions. The complete analysis takes only 27.8 seconds, providing an efficient and practical calculation method for the dynamics analysis of multi-flexible body systems under complex conditions such as catapult takeoff of carrier-based aircraft.

[0070] (4) This invention constructs a dynamic model of a carrier-based aircraft catapult takeoff multi-flexible body system by organically combining the Multibody System Transfer Matrix Method (MSTMM) with the Finite Element Method (FEM). Based on the characteristics of the system components, this method divides the subsystem into M-type subsystems applicable to the Multibody System Transfer Matrix Method and F-type subsystems applicable to the Finite Element Method. While achieving refined modeling of individual components, it simplifies the overall matrix operation process of the system by utilizing the characteristics of the transfer matrix method, significantly improving the efficiency of dynamic simulation.

[0071] (5) While maintaining high accuracy, this invention significantly reduces the computation time compared with traditional multibody dynamics methods, providing economical and efficient computational support for the optimized design of carrier-based aircraft catapult takeoff systems, and providing a new approach to solving the problem of real-time dynamic analysis of complex carrier-based aircraft systems.

[0072] (6) Based on the component composition of the carrier-based aircraft catapult takeoff system and the connection relationship between the components, the present invention establishes a dynamic model of the carrier-based aircraft catapult takeoff multi-soft-body system, realizes the automatic derivation of the overall transfer equation of the carrier-based aircraft catapult takeoff multi-soft-body system, eliminates the need for the overall dynamic equation of the carrier-based aircraft catapult takeoff multi-soft-body system, avoids the tedious derivation and solution process, involves a low matrix order, and has high computational efficiency.

[0073] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0074] Figure 1 This is a flowchart illustrating the main idea of ​​a rapid calculation method for carrier-based aircraft dynamics in one embodiment.

[0075] Figure 2 This is a topology diagram of the dynamic model of a carrier-based aircraft multi-flexible body system in one embodiment.

[0076] Figure 3 This is a schematic diagram of the subsystem division of a carrier-based aircraft multibody system in one embodiment.

[0077] Figure 4 (a) in the figure is a finite element model of the tire subsystem and a schematic diagram of the inner wall air pressure setting. Figure 4 (b) in the diagram is a schematic diagram of the input and output points of the tire subsystem. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0079] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0080] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0081] The purpose of this invention is to overcome the problems of low computational efficiency and high matrix order in existing technologies, and to provide a rapid calculation method for the catapult launch dynamics of carrier-based aircraft based on the finite element modal synthesis multibody system transfer matrix method. The aim is to establish a dynamic model of a carrier-based aircraft multibody system considering inflatable flexible tires and to simulate its dynamic response. This invention organically combines the multibody system transfer matrix method (MSTMM) with the finite element method (FEM) to construct a dynamic model of a carrier-based aircraft catapult launch multibody system. Based on the characteristics of system components, this method divides the subsystems into M-type subsystems suitable for the MTMM and F-type subsystems suitable for finite element modeling. While achieving refined modeling of individual components, it simplifies the overall matrix operation process of the system by utilizing the characteristics of the transfer matrix method, significantly improving the efficiency of dynamic simulation. While maintaining high accuracy, this invention significantly reduces computation time compared to traditional multibody dynamics methods, providing economical and efficient computational support for the optimized design of carrier-based aircraft catapult launch systems, and offering a new approach to solving the problem of real-time dynamic analysis of complex carrier-based aircraft systems.

[0082] In one embodiment, combined Figure 1 A method for rapid calculation of shipborne aircraft dynamics is provided, the method comprising the following steps:

[0083] Step 1: Based on the structural form of each component of the carrier-based aircraft catapult launch multi-soft-body system, the carrier-based aircraft catapult launch multi-soft-body system is divided into components containing rigid body elements and the main tire is regarded as a soft body element. Each component is numbered, the input and output state vectors of each component are determined, and the dynamic topology diagram of the carrier-based aircraft catapult launch multi-soft-body system is established according to the connection method between each component.

[0084] Step 2: Divide the components of the carrier-based aircraft catapult launch multi-soft-body system into two types of subsystems: M-type subsystems processed using the multi-body system transfer matrix method, and F-type subsystems processed using the finite element method.

[0085] Step 3: For the M-type subsystem, construct the transfer equations relating the input and output state vectors of each component within the subsystem. Sweep through the entire system along the transfer path, recursively deriving from the input point to the output point to obtain the main transfer equation of the subsystem. For the F-type subsystem, construct the finite element model of the subsystem components and obtain the reduced tire mass matrix and stiffness matrix using the Craig-Bampton modal reduction method. Construct the overall transfer equation and overall transfer matrix of the carrier-based aircraft catapult takeoff multi-flexible body system. Solve for the root state vectors of the carrier-based aircraft multi-flexible body system based on the system boundary conditions. Then, recursively derive all the state vectors from the system output point to the input point to obtain the dynamic response of the entire carrier-based aircraft multi-flexible body system. Substitute the dynamic response calculation results at the end of the current stage into the initial conditions of the next stage until the dynamic response calculation is completed.

[0086] Step 4: Conduct simulation tests of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires, and solve for the natural frequency and dynamic response of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires during the initial stage of catapult takeoff.

[0087] Furthermore, in one embodiment, step 1 specifically includes dividing the carrier-based aircraft catapult launch multi-flexible body system into body elements and hinge elements, and numbering them sequentially according to the recursive direction to establish a dynamic topology diagram of the carrier-based aircraft catapult launch multi-flexible body system, as shown below. Figure 2 As shown;

[0088] The fuselage (including wings, tail, ammunition, etc.), nose landing gear strut, nose landing gear outer cylinder, nose landing gear piston rod, upper front torque arm, lower front torque arm, traction rod, ejection rod, ejection tractor, left landing gear outer cylinder, left landing gear piston rod, left rear wheel (including rim), right landing gear outer cylinder, right landing gear piston rod, right rear wheel (including rim), left front wheel rim, and right front wheel rim are considered as rigid bodies in spatial motion. The fuselage, nose landing gear outer cylinder, nose landing gear piston rod, upper front torque arm, lower front torque arm, traction rod, left front wheel rim, and right front wheel rim are rigid bodies in spatial motion with multiple inputs and one output. The remaining components are rigid bodies with one input and one output. The left front tire and right front tire are considered as flexible bodies in spatial motion with multiple inputs and one output.

[0089] Based on the interrelationships between the components of the carrier-based aircraft catapult launch multi-flexible-body system, including: the fuselage and the nose landing gear strut are connected via elastic hinges; the nose landing gear strut and the landing gear outer cylinder are connected via elastic hinges; the fuselage and the landing gear outer cylinder are connected via elastic hinges; the landing gear outer cylinder and the nose landing gear piston rod are connected via sliding connection; the left front tire and the left front wheel rim are connected via sliding hinges; the right front tire and the right front wheel rim are connected via sliding hinges; the nose landing gear piston rod and the upper front torque arm are connected via elastic hinges; the upper and lower front torque arms and the restraint are connected via column hinges; the nose landing gear piston and the lower front torque arm are connected via elastic connection; the restraint and the deck are connected via elastic hinges; the nose landing gear piston rod and the catapult rod are connected via elastic hinges; the catapult rod and the catapult traction are connected via elastic hinges. The connections are as follows: the catapult tractor is connected to the ship's deck via a flexible hinge; the fuselage is connected to the left landing gear outer cylinder via a flexible hinge; the left landing gear outer cylinder is connected to the left landing gear piston rod via a sliding hinge; the left landing gear piston rod is connected to the left rear wheel via a column; the left rear wheel is connected to the ship via a flexible hinge; the fuselage is connected to the right landing gear outer cylinder via a flexible hinge; the right landing gear outer cylinder is connected to the right landing gear piston rod via a sliding hinge; the right landing gear piston rod is connected to the right rear wheel via a column; the right rear wheel is connected to the ship's deck via a flexible hinge; the right rear wheel is connected to the ship's deck via a flexible hinge; the left front wheel is connected to the ship's deck via a flexible hinge; the left front tire is connected to the ship's deck via a flexible hinge; the front landing gear piston rod is connected to the left front wheel rim via a column hinge; the front landing gear piston rod is connected to the right front wheel rim via a column hinge.

[0090] Furthermore, in one embodiment, step 2 specifically includes: dividing the components of the carrier-based aircraft catapult launch multi-soft-body system into two types of subsystems, namely, the M-type subsystem processed using the multi-body system transfer matrix method and the F-type subsystem processed using the finite element method, such as... Figure 3 As shown; the connection points between the various subsystems satisfy the geometric relationship that the displacement and angular displacement are equal, so as to realize the coupling between the M-type and F-type subsystems.

[0091] Preferably, in some embodiments, in step 2, the present invention focuses on the dynamic behavior of the flexible nose wheel of the carrier-based aircraft during catapult launch, and regards the two nose wheels of the carrier-based aircraft as two F-type subsystems, while regards the other parts of the carrier-based aircraft as five M-type subsystems.

[0092] Furthermore, in one embodiment, step 3, constructing the finite element model of the F-type subsystem component, includes constructing the finite element model of the main tire of the F-type subsystem, specifically including:

[0093] (1) First, a finite element model of the tire is established, which has a total of 4896 degrees of freedom, such as Figure 4As shown, its 4896th order mass matrix M and stiffness matrix K are derived using the Craig-Bampton modal reduction method with two input points ( , ) and an output point ( The degrees of freedom and the first few fixed interface modes are used to reduce the 4896-order mass matrix and stiffness matrix to 28-order, and then orthogonalize them to obtain the reduced-order matrix. Tire mass array after order reduction With stiffness matrix .

[0094] For the F-type subsystem, the dynamic equations are expressed as:

[0095]

[0096] In the formula, For the 28th order reduced coordinates of the flexible structure in the F subsystem,

[0097]

[0098] In the formula, , , These are the coefficient matrices for the first input point, the second input point, and the output point, respectively. It is a b×3 zero matrix. , , These are the displacement reduction matrices for the first and second input terminals and the output terminal, respectively. , , These are the angle reduction matrices for the first and second input terminals and the output terminal, respectively.

[0099] The connection points between the various subsystems satisfy the geometric relationship that displacement and angular displacement are equal, as follows:

[0100]

[0101] In the formula, It is a coefficient matrix.

[0102] The overall transfer equations for the carrier-based aircraft multi-flexible body system are obtained by refining the equations.

[0103]

[0104] In the formula, For the overall transfer matrix of the carrier-based aircraft multi-flexible body system, This refers to the overall state vector of the carrier-based aircraft's multi-flexible-body system.

[0105] In the formula,

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] Furthermore, in one embodiment, step 3, constructing the master transfer equations for the M-type subsystem, includes:

[0113] Step 3-1: Construct the transfer equations for the rigid body elements of the M-class subsystem, specifically including:

[0114] (1) Rigid body processing of spatial motion is performed as single-ended input, single-ended output or multi-ended input, single-ended output components:

[0115]

[0116] In the formula, and These are the output terminal O of component j and the input terminal r, respectively. The state vector, For the r-th input terminal of component j The corresponding transfer matrix, where N represents the total number of inputs;

[0117] The motion of the spatial vibrating rigid body element j, which has an N-terminal input and a single-terminal output, is transmitted through the first input terminal. Linear displacements x, y, z and angular displacements , , Describe the local coordinate system that describes the relative positions of the input ends, center of mass, and output ends of the rigid body. The origin is located at the initial position of the first input point of the element, and the three coordinate axes are parallel to the coordinate axes of the global inertial system Oxyz. The transfer matrix of the spatial vibrating rigid body is:

[0118]

[0119] In the formula, It is a 3×3 identity matrix. It is a 3×3 zero matrix, where m is the mass of the rigid body element. Let ω be the angular velocity of the rigid body element. Let be the moment of inertia matrix of the rigid body element relative to the first input end. , , These are the cross product matrices of the coordinates of the output terminal relative to the first input terminal, the centroid of the component, and the position vector of the r-th input terminal, respectively. Let be the cross product matrix of the component's centroid relative to the position vector of the first input terminal. This indicates that the rigid body element is a single-input element. This indicates that the rigid body element has multiple inputs;

[0120] (2) For multi-terminal input body components, the component transfer equation only includes the geometric relationship between the output point and the first input point. It is necessary to add the geometric relationship between the r-th input terminal of the multi-terminal input body component j and the first input terminal:

[0121]

[0122] In the formula, The matrix describing the geometric relationships between the input terminals of a multi-input element j is called the element geometry matrix. and These represent the first input terminal and the r-th input terminal of component j, respectively. Let be the cross product matrix of the coordinates of the r-th input terminal of element j relative to the first input terminal;

[0123] Step 3-2, construct the transfer equations for the hinge elements of the M-type subsystem, specifically including:

[0124] (1) The spatial elastic hinge j has a coordinate system along its local coordinate system The springs and torsion springs on the three coordinate axes are single-ended input and single-ended output elements, and their transfer matrix... In the local coordinate system, it is represented as:

[0125]

[0126] In the formula, , and respectively spring edge , and Shaft stiffness, , and They are torsion springs , and Torsional stiffness of the shaft;

[0127] Step 3-3, closed-loop structure processing of M1 type subsystem, specifically includes,

[0128] (1) Based on the multibody system transfer matrix method for processing closed-loop topology multibody systems, in the dynamic model topology of carrier-based aircraft multi-flexible body systems. Figure 2The closed loop will be "cut off" at midpoints P31, P35, P38, P41, and P42. At each "cut-off" point, two new state vectors will be generated, and the two state vectors satisfy the following condition:

[0129]

[0130] In the formula, , , , , , , and for Figure 3 Each input boundary state vector, It is a coefficient matrix.

[0131] Steps 3-4, the main transfer equations of the M1 class subsystem, specifically include:

[0132] Furthermore, for the tree-shaped M1 subsystem, by traversing each element in the reverse transmission direction from the "root" to the "tip" of the system, the main transfer equation of the subsystem can be obtained.

[0133]

[0134] In the formula, , , , , , , , , , and For each input boundary, there is a state vector;

[0135] In the formula,

[0136]

[0137] In the formula, , , , , , , , , , , , , Let M1 be the transfer matrix for each transfer path in subsystem M1. This is the transmission path from component i to component j in the M1 subsystem. Let U be the transfer path from the r-th input point of component i to component j in the M1 subsystem; the transfer matrix U of each component can be obtained from the geometric and mechanical parameters of that component. Subscript j is the component number. The transfer matrix of the solid component is shown in step 3-1 and the transfer matrix of the hinge component is shown in step 3-2.

[0138] Based on the multibody system transfer matrix method, the relationship between the non-first input point and the first input point of each multi-terminal input element is described, i.e., the consistency equation is:

[0139]

[0140] In the formula, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , These are the consistency equations for each multi-terminal input element. The propagation path and geometric matrix from the r-th input point of element i to element j in the M1 subsystem. Multiply, The transfer path and geometric matrix from element i to element j in the M1 subsystem Multiply;

[0141] in,

[0142]

[0143] In the formula, Let the geometric matrix be the input point r-th point of the solid element j;

[0144] Preferably, in some embodiments, in step 3-2, if the spatial elastic hinge rotates in only one direction, it degenerates into a cylindrical hinge or pin, and its transfer matrix is ​​represented in the local coordinate system as follows:

[0145]

[0146] In the formula, This indicates that the spatial elastic hinge has only one direction. The transfer matrix corresponding to the rotation of the axis;

[0147] If a spatial elastic hinge has displacement in only one direction, it degenerates into a sliding hinge or sleeve, and its transfer matrix is ​​represented in the local coordinate system as follows:

[0148]

[0149] In the formula, This indicates that the spatial elastic hinge has only one direction. The transfer matrix corresponding to the rotation of the axis.

[0150] Furthermore, in one embodiment, step 4 specifically includes:

[0151] Step 4-1: The system's body dynamics equations differ from its overall dynamics equations; they are merely a simple combination of the body dynamics equations of individual body components. The body dynamics equations of various body components, such as concentrated mass, rigid bodies, and elastic bodies, have a unified form. Without considering the constraint relationships between body components, the body dynamics equations of the shipborne aircraft multi-flexible body system are written as follows:

[0152]

[0153] In the formula, the mass matrix Damping array Stiffness matrix For augmentation operators of carrier-based aircraft multi-soft-body systems, , , These are the displacement, velocity, and acceleration coordinate arrays in the physical coordinates of the carrier-based aircraft's multi-soft-body system. For the external force array of the carrier-based aircraft multi-flexible body system, the subscript is the body element number, and n is the total number of body elements;

[0154] Step 4-2: Applying modal analysis, the displacement matrix in physical coordinates of the dynamic response of the carrier-based aircraft's multi-flexible-body system is expanded into a superposition of modal coordinates, i.e.:

[0155]

[0156] In the formula, Let be the displacement matrix of the carrier-based aircraft's multi-flexible-body system at any time t. Let be the k-th generalized coordinate, where k is the modal order; Let k be the augmented eigenvector of order k, whose elements are derived from the k-th natural frequencies of the system. The modal coordinates corresponding to the displacements and rotations at the input ends of all discrete body elements and the corresponding mode shapes of each continuous body element;

[0157] Step 4-3, based on the orthogonality of the augmented eigenvectors, that is:

[0158]

[0159] Inner product of the volume dynamics equations of a carrier-based aircraft multi-flexible body system To decouple them, we obtain the dynamic equations of the multi-flexible body system of each order that are independent under the generalized coordinate system:

[0160]

[0161] In the formula, The symbol for Kronecker. For the p-th modal mass of the carrier-based aircraft multi-flexible body system, For the p-th modal stiffness of the carrier-based aircraft multi-flexible body system, For the P-th order augmented eigenvector, It is the p-th natural frequency; Let be the generalized coordinates at any time t. For the damping ratio, The resultant external force on the multi-flexible body system of carrier-based aircraft; , They are respectively The first and second derivatives.

[0162] Step 4-4: Based on the initial conditions of the carrier-based aircraft multi-soft-body system, use numerical integration methods (such as the fourth-order Runge-Kutta method) to obtain the generalized coordinates of the carrier-based aircraft multi-soft-body system at any time t. Thus, the displacement coordinate array of the first input terminals of each body element in the multi-flexible body system of the carrier-based aircraft is obtained. , which is the dynamic response of the carrier-based aircraft's multi-flexible-body system at any time t.

[0163] It should be noted that for the F-type subsystem, its augmented eigenvector and mode shape are:

[0164]

[0165] In the formula, This is the reduced-order matrix of the Craig-Bampton mode reduction. For the augmented feature vector of the F-class subsystem, The 4896th order displacement and rotation array of all 816 nodes in the F-type subsystem represents the mode shapes of the left and right tires. Substituting these values ​​into the formulas in steps 4-1 to 4-4 yields the dynamic response of the flexible tire.

[0166] In one embodiment, a rapid calculation system for shipborne aircraft dynamics is provided, the system comprising:

[0167] The first module is used to break down the multi-flexible body system for catapult takeoff of carrier-based aircraft into components containing rigid body elements and the main tire as a flexible body element, based on the structural form between the components of the multi-flexible body system for catapult takeoff of carrier-based aircraft. It also numbers each component, determines the input and output state vectors of each component, and establishes the dynamic topology diagram of the multi-flexible body system for catapult takeoff of carrier-based aircraft based on the connection method between each component.

[0168] The second module is used to divide the components of the carrier-based aircraft catapult takeoff multi-soft-body system into two types of subsystems: M-type subsystems processed using the multi-body system transfer matrix method, and F-type subsystems processed using the finite element method.

[0169] The third module is used to construct the transfer equations between the input and output state vectors of each component in the M-type subsystem for the purpose of constructing the main transfer equations of the subsystem by sweeping the entire system along the transfer path and recursively deriving them from the input point to the output point. For the F-type subsystem, the module constructs the finite element model of the subsystem components and obtains the reduced tire mass matrix and stiffness matrix using the Craig-Bampton modal reduction method. The module constructs the overall transfer equations and overall transfer matrix of the carrier-based aircraft catapult takeoff multi-flexible body system, solves the root state vectors of the carrier-based aircraft multi-flexible body system according to the system boundary conditions, and then recursively derives all the state vectors from the system output point to the input point, thus obtaining the dynamic response of the entire carrier-based aircraft multi-flexible body system. The dynamic response calculation results at the end of the current stage are substituted into the next stage as the initial conditions until the dynamic response calculation is completed.

[0170] The fourth module is used to conduct simulation tests of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires, and to solve for the natural frequency and dynamic response of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires during the initial stage of catapult takeoff.

[0171] Specific limitations regarding the rapid calculation system for carrier-based aircraft dynamics can be found in the limitations of the rapid calculation method for carrier-based aircraft dynamics described above, and will not be repeated here. Each module in the aforementioned rapid calculation system for carrier-based aircraft dynamics can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in the computer device, or stored in the memory of the computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0172] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements:

[0173] Step 1: Based on the structural form of each component of the carrier-based aircraft catapult launch multi-soft-body system, the carrier-based aircraft catapult launch multi-soft-body system is divided into components containing rigid body elements and the main tire is regarded as a soft body element. Each component is numbered, the input and output state vectors of each component are determined, and the dynamic topology diagram of the carrier-based aircraft catapult launch multi-soft-body system is established according to the connection method between each component.

[0174] Step 2: Divide the components of the carrier-based aircraft catapult launch multi-soft-body system into two types of subsystems: M-type subsystems processed using the multi-body system transfer matrix method, and F-type subsystems processed using the finite element method.

[0175] Step 3: For the M-type subsystem, construct the transfer equations relating the input and output state vectors of each component within the subsystem. Sweep through the entire system along the transfer path, recursively deriving from the input point to the output point to obtain the main transfer equation of the subsystem. For the F-type subsystem, construct the finite element model of the subsystem components and obtain the reduced tire mass matrix and stiffness matrix using the Craig-Bampton modal reduction method. Construct the overall transfer equation and overall transfer matrix of the carrier-based aircraft catapult takeoff multi-flexible body system. Solve for the root state vectors of the carrier-based aircraft multi-flexible body system based on the system boundary conditions. Then, recursively derive all the state vectors from the system output point to the input point to obtain the dynamic response of the entire carrier-based aircraft multi-flexible body system. Substitute the dynamic response calculation results at the end of the current stage into the initial conditions of the next stage until the dynamic response calculation is completed.

[0176] Step 4: Conduct simulation tests of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires, and solve for the natural frequency and dynamic response of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires during the initial stage of catapult takeoff.

[0177] For specific limitations on each step, please refer to the limitations on the rapid calculation method for carrier-based aircraft dynamics mentioned above, which will not be repeated here.

[0178] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being implemented when executed by a processor:

[0179] Step 1: Based on the structural form of each component of the carrier-based aircraft catapult launch multi-soft-body system, the carrier-based aircraft catapult launch multi-soft-body system is divided into components containing rigid body elements and the main tire is regarded as a soft body element. Each component is numbered, the input and output state vectors of each component are determined, and the dynamic topology diagram of the carrier-based aircraft catapult launch multi-soft-body system is established according to the connection method between each component.

[0180] Step 2: Divide the components of the carrier-based aircraft catapult launch multi-soft-body system into two types of subsystems: M-type subsystems processed using the multi-body system transfer matrix method, and F-type subsystems processed using the finite element method.

[0181] Step 3: For the M-type subsystem, construct the transfer equations relating the input and output state vectors of each component within the subsystem. Sweep through the entire system along the transfer path, recursively deriving from the input point to the output point to obtain the main transfer equation of the subsystem. For the F-type subsystem, construct the finite element model of the subsystem components and obtain the reduced tire mass matrix and stiffness matrix using the Craig-Bampton modal reduction method. Construct the overall transfer equation and overall transfer matrix of the carrier-based aircraft catapult takeoff multi-flexible body system. Solve for the root state vectors of the carrier-based aircraft multi-flexible body system based on the system boundary conditions. Then, recursively derive all the state vectors from the system output point to the input point to obtain the dynamic response of the entire carrier-based aircraft multi-flexible body system. Substitute the dynamic response calculation results at the end of the current stage into the initial conditions of the next stage until the dynamic response calculation is completed.

[0182] Step 4: Conduct simulation tests of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires, and solve for the natural frequency and dynamic response of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires during the initial stage of catapult takeoff.

[0183] For specific limitations on each step, please refer to the limitations on the rapid calculation method for carrier-based aircraft dynamics mentioned above, which will not be repeated here.

[0184] The method proposed in this invention overcomes the shortcomings of traditional methods, such as high matrix order and large computational load, when dealing with complex coupled systems of carrier-based aircraft containing pneumatic flexible tires. It has the advantages of fast calculation speed, high degree of programmability and strong versatility, and provides an efficient calculation means for the dynamic analysis of complex multi-flexible body systems of carrier-based aircraft.

[0185] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. A method for rapid calculation of shipborne aircraft dynamics, characterized in that, The method includes the following steps: Step 1: Based on the structural form of each component of the carrier-based aircraft catapult launch multi-soft-body system, the carrier-based aircraft catapult launch multi-soft-body system is divided into components containing rigid body elements and the main tire is regarded as a soft body element. Each component is numbered, the input and output state vectors of each component are determined, and the dynamic topology diagram of the carrier-based aircraft catapult launch multi-soft-body system is established according to the connection method between each component. Step 2: Divide the components of the carrier-based aircraft catapult launch multi-soft-body system into two types of subsystems: M-type subsystems processed using the multi-body system transfer matrix method, and F-type subsystems processed using the finite element method. Step 3: For the M-type subsystem, construct the transfer equations relating the input and output state vectors of each component within the subsystem. Sweep through the entire system along the transfer path, recursively deriving from the input point to the output point to obtain the main transfer equation of the subsystem. For the F-type subsystem, construct the finite element model of the subsystem components and obtain the reduced tire mass matrix and stiffness matrix using the Craig-Bampton modal reduction method. Construct the overall transfer equation and overall transfer matrix of the carrier-based aircraft catapult takeoff multi-flexible body system. Solve for the root state vectors of the carrier-based aircraft multi-flexible body system based on the system boundary conditions. Then, recursively derive all the state vectors from the system output point to the input point to obtain the dynamic response of the entire carrier-based aircraft multi-flexible body system. Substitute the dynamic response calculation results at the end of the current stage into the initial conditions of the next stage until the dynamic response calculation is completed. Step 4: Conduct simulation tests of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires, and solve for the natural frequency and dynamic response of the carrier-based aircraft multi-flexible body system considering pneumatic flexible tires during the initial stage of catapult takeoff.

2. The rapid calculation method for shipborne aircraft dynamics according to claim 1, characterized in that, Step 1 specifically includes dividing the carrier-based aircraft catapult launch multi-flexible body system into body elements and hinge elements, numbering them sequentially according to the recursive direction, and establishing a dynamic topology diagram of the carrier-based aircraft catapult launch multi-flexible body system. The fuselage, nose landing gear strut, nose landing gear outer cylinder, nose landing gear piston rod, upper front torsion arm, lower front torsion arm, restraint rod, ejection rod, ejection tractor, left landing gear outer cylinder, left landing gear piston rod, left rear wheel, right landing gear outer cylinder, right landing gear piston rod, right rear wheel, left front wheel rim, and right front wheel rim are considered as spatial motion rigid bodies. The fuselage, nose landing gear outer cylinder, nose landing gear piston rod, upper front torsion arm, lower front torsion arm, restraint rod, left front wheel rim, and right front wheel rim are spatial motion rigid bodies with multi-end input and one-end output, while the remaining components are rigid bodies with single-end input and single-end output. The left front tire and the right front tire are considered as flexible bodies of spatial motion, which are flexible bodies of spatial motion with multi-end input and single-end output. Based on the interrelationships between the components of the carrier-based aircraft catapult launch multi-flexible-body system, including: the fuselage and the nose landing gear strut are connected via elastic hinges; the nose landing gear strut and the landing gear outer cylinder are connected via elastic hinges; the fuselage and the landing gear outer cylinder are connected via elastic hinges; the landing gear outer cylinder and the nose landing gear piston rod are connected via sliding connection; the left front tire and the left front wheel rim are connected via sliding hinges; the right front tire and the right front wheel rim are connected via sliding hinges; the nose landing gear piston rod and the upper front torque arm are connected via elastic hinges; the upper and lower front torque arms and the restraint are connected via column hinges; the nose landing gear piston and the lower front torque arm are connected via elastic connection; the restraint and the deck are connected via elastic hinges; the nose landing gear piston rod and the catapult rod are connected via elastic hinges; the catapult rod and the catapult traction are connected via elastic hinges. The connections are as follows: the catapult tractor is connected to the ship's deck via a flexible hinge; the fuselage is connected to the left landing gear outer cylinder via a flexible hinge; the left landing gear outer cylinder is connected to the left landing gear piston rod via a sliding hinge; the left landing gear piston rod is connected to the left rear wheel via a column; the left rear wheel is connected to the ship via a flexible hinge; the fuselage is connected to the right landing gear outer cylinder via a flexible hinge; the right landing gear outer cylinder is connected to the right landing gear piston rod via a sliding hinge; the right landing gear piston rod is connected to the right rear wheel via a column; the right rear wheel is connected to the ship's deck via a flexible hinge; the right rear wheel is connected to the ship's deck via a flexible hinge; the left front wheel is connected to the ship's deck via a flexible hinge; the left front tire is connected to the ship's deck via a flexible hinge; the front landing gear piston rod is connected to the left front wheel rim via a column hinge; the front landing gear piston rod is connected to the right front wheel rim via a column hinge.

3. The rapid calculation method for shipborne aircraft dynamics according to claim 1, characterized in that, In step 2, the connection points between the various subsystems satisfy the geometric relationship that the displacement and angular displacement are equal, so as to realize the coupling between the M-type and F-type subsystems.

4. The rapid calculation method for shipborne aircraft dynamics according to claim 1, characterized in that, In step 2, the two nose wheels of the carrier-based aircraft are each designated as a separate F-type subsystem, while the rest of the carrier-based aircraft is designated as a separate M-type subsystem.

5. The rapid calculation method for shipborne aircraft dynamics according to claim 1, characterized in that, Step 3 involves constructing the finite element model of the F-type subsystem components, including constructing the finite element model of the main tire of the F-type subsystem, specifically including: (1) First, establish a finite element model of the tire with a degrees of freedom. Derive its a-order mass matrix M and stiffness matrix K. Use the Craig-Bampton modal reduction method to take two input ends. , With an output terminal Based on the degrees of freedom and the first few fixed interface modes, the a-order mass matrix and stiffness matrix are reduced to b-order and orthogonalized to obtain the reduced-order matrix. Tire mass array after order reduction With stiffness matrix The dynamic equations of the F-type subsystem are expressed as follows: in, Let b be the reduced-order coordinates of the flexible structure in the F subsystem. Let b be the reduced-order coordinates. , , These are the two input terminals of the F subsystem. , With an output terminal The state vector, , , , These are the coefficient matrices for the first input terminal, the second input terminal, and the output terminal, respectively. It is a b×3 zero matrix. , , These are the displacement reduction matrices for the first input terminal, the second input terminal, and the output terminal, respectively. , , These are the angle reduction matrices for the first input terminal, the second input terminal, and the output terminal, respectively. (2) The connection points between the various subsystems satisfy the geometric relationship that the displacement and angular displacement are equal, as follows: In the formula, , , These are the reduced-order matrices for the output, the first input, and the second input, respectively. It is a coefficient matrix.

6. The rapid calculation method for shipborne aircraft dynamics according to claim 1, characterized in that, Step 3 involves constructing the master transfer equations for the M-type subsystem, including: Step 3-1: Construct the transfer equations for the rigid body elements of the M-class subsystem, specifically including: (1) Rigid body processing of spatial motion is performed as single-ended input, single-ended output or multi-ended input, single-ended output components: In the formula, and These are the output terminal O of component j and the input terminal r, respectively. The state vector, For the r-th input terminal of component j The corresponding transfer matrix, where N represents the total number of inputs; The motion of the spatial vibrating rigid body element j, which has an N-terminal input and a single-terminal output, is transmitted through the first input terminal. Linear displacements x, y, z and angular displacements , , Describe the local coordinate system that describes the relative positions of the input ends, center of mass, and output ends of the rigid body. The origin is located at the initial position of the first input point of the element, and the three coordinate axes are parallel to the coordinate axes of the global inertial system Oxyz. The transfer matrix of the spatial vibrating rigid body is: In the formula, It is a 3×3 identity matrix. It is a 3×3 zero matrix, where m is the mass of the rigid body element. Let ω be the angular velocity of the rigid body element. Let be the moment of inertia matrix of the rigid body element relative to the first input end. , , These are the cross product matrices of the coordinates of the output terminal relative to the first input terminal, the centroid of the component, and the position vector of the r-th input terminal, respectively. Let be the cross product matrix of the component's centroid relative to the position vector of the first input terminal. This indicates that the rigid body element is a single-input element. This indicates that the rigid body element has multiple inputs; (2) For multi-terminal input body components, the component transfer equation only includes the geometric relationship between the output point and the first input point. It is necessary to add the geometric relationship between the r-th input terminal of the multi-terminal input body component j and the first input terminal: In the formula, The matrix describing the geometric relationships between the input terminals of a multi-input element j is called the element geometry matrix. and These represent the first input terminal and the r-th input terminal of component j, respectively. Let be the cross product matrix of the coordinates of the r-th input terminal of element j relative to the first input terminal; Step 3-2, construct the transfer equations for the hinge elements of the M-type subsystem, specifically including: (1) The spatial elastic hinge j has a coordinate system along its local coordinate system The springs and torsion springs on the three coordinate axes are single-ended input and single-ended output elements, and their transfer matrix... In the local coordinate system, it is represented as: In the formula, , and respectively spring edge , and Shaft stiffness, , and They are torsion springs , and Torsional stiffness of the shaft; Step 3-3, closed-loop structure processing of subsystem M, specifically includes: (1) Based on the multibody system transfer matrix method for processing closed-loop topology multibody systems, the closed loop is "cut off" at point P in the topology diagram of the carrier-based aircraft multi-flexible body system dynamics model. At each "cut-off" point, two new state vectors will be generated, and the two state vectors satisfy the following condition: In the formula, and For input boundaries, It is a coefficient matrix.

7. The rapid calculation method for shipborne aircraft dynamics according to claim 6, characterized in that, In step 3-2, if the spatial elastic hinge rotates in only one direction, it degenerates into a cylindrical hinge or pin, and its transfer matrix is ​​represented in the local coordinate system as follows: In the formula, This indicates that the spatial elastic hinge has only one direction. The transfer matrix corresponding to the rotation of the axis; If a spatial elastic hinge has displacement in only one direction, it degenerates into a sliding hinge or sleeve, and its transfer matrix is ​​represented in the local coordinate system as follows: In the formula, This indicates that the spatial elastic hinge has only one direction. The transfer matrix corresponding to the rotation of the axis.

8. The rapid calculation method for shipborne aircraft dynamics according to claim 1, characterized in that, The overall transfer equation for the carrier-based aircraft multi-flexible body system in step 3 is: In the formula, For the overall transfer matrix of the carrier-based aircraft multi-flexible body system, This is the overall state vector of the carrier-based aircraft's multi-flexible-body system.

9. The rapid calculation method for shipborne aircraft dynamics according to claim 1, characterized in that, Step 4 specifically includes: Step 4-1, the body dynamics equations of the carrier-based aircraft's multi-flexible-body system are written as follows: In the formula, the mass matrix Damping array Stiffness matrix For augmentation operators of carrier-based aircraft multi-soft-body systems, , , These are the displacement, velocity, and acceleration coordinate arrays in the physical coordinates of the carrier-based aircraft's multi-soft-body system. For the external force array of the carrier-based aircraft multi-flexible body system, the subscript is the body element number, and n is the total number of body elements; Step 4-2: Applying modal analysis, the displacement matrix in physical coordinates of the dynamic response of the carrier-based aircraft's multi-flexible-body system is expanded into a superposition of modal coordinates, i.e.: In the formula, Let be the displacement matrix of the carrier-based aircraft's multi-flexible-body system at any time t. Let be the k-th generalized coordinate, where k is the modal order; Let k be the augmented eigenvector of order k, whose elements are derived from the k-th natural frequencies of the system. The modal coordinates corresponding to the displacements and rotations at the input ends of all discrete body elements and the corresponding mode shapes of each continuous body element; Step 4-3, based on the orthogonality of the augmented eigenvectors, that is: Inner product of the volume dynamics equations of a carrier-based aircraft multi-flexible body system To decouple them, we obtain the dynamic equations of the multi-flexible body system of each order that are independent under the generalized coordinate system: In the formula, The symbol for Kronecker. For the p-th modal mass of the carrier-based aircraft multi-flexible body system, For the p-th modal stiffness of the carrier-based aircraft multi-flexible body system, For the P-th order augmented eigenvector, It is the p-th natural frequency; Let be the generalized coordinates at any time t. For the damping ratio, The resultant external force on the multi-flexible body system of carrier-based aircraft; , They are respectively The first and second derivatives. Step 4-4: Based on the initial conditions of the carrier-based aircraft multi-soft-body system, the generalized coordinates of the carrier-based aircraft multi-soft-body system at any time t are obtained using the numerical integration method. Thus, the displacement coordinate array of the first input terminals of each body element in the multi-flexible body system of the carrier-based aircraft is obtained. , which is the dynamic response of the carrier-based aircraft's multi-flexible-body system at any time t.

10. The rapid calculation method for shipborne aircraft dynamics according to claim 9, characterized in that, For the F-type subsystem, its augmented eigenvector and mode shape are: In the formula, This is the reduced-order matrix of the Craig-Bampton mode reduction. For the augmented feature vector of the F-class subsystem, Let a be the a-order displacement and rotation array of all nodes in the F-type subsystem, which is the mode shape of the left and right tires; Substitute these steps 4-1 to 4-4 into the equation to obtain the dynamic response of the flexible tire.

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