A kinetic analysis method for in-plane aviation hydrogen storage systems

Abstract

This invention belongs to the field of aerospace structure and structural dynamics modeling technology, specifically relating to a dynamic analysis method for in-plane aerospace hydrogen storage systems. The method first constructs a family of orthogonal displacement functions and displacement functions suitable for the aerospace hydrogen storage system. Then, based on the family of displacement functions and displacement functions, the energy equation of the aerospace hydrogen storage system is derived and solved. Finally, the mode shapes and natural frequencies are obtained based on the Rayleigh-Ritz method, and the dynamic response of the structure is calculated using the modal superposition method. This invention overcomes the shortcomings of existing semi-analytical modeling methods for aerospace hydrogen storage systems, enabling efficient and high-precision prediction and analysis of the dynamic characteristics of in-plane aerospace hydrogen storage systems.

Description

Technical Field

[0001] This invention belongs to the field of aerospace structure and structural dynamics modeling technology, specifically relating to a dynamic analysis method for an in-plane aerospace hydrogen storage system. Background Technology

[0002] In the aerospace field, hydrogen energy is emerging as a clean and efficient new energy source. Hydrogen energy boasts advantages such as low pollution and high energy density. Aviation hydrogen storage systems are responsible for the storage and transportation of hydrogen. Despite the significant advantages of hydrogen energy, the safety issues posed by hydrogen embrittlement and internal high pressure to aviation hydrogen storage systems cannot be ignored. Accurately solving the dynamic characteristics (such as mode shapes and natural frequencies) and dynamic response under external excitation of such aviation hydrogen storage systems is of significant engineering practical importance for evaluating the safety margin and functional reliability of hydrogen-powered aircraft structures, as well as for optimizing vibration reduction and noise reduction designs.

[0003] Currently, aviation hydrogen storage systems are complex beam-shell coupled structures. Research on the dynamic modeling and modal analysis of beam-shell coupled structures mainly focuses on simple beam and shell structures, such as the coupling of a straight beam with a uniform cross-section and a cylindrical shell. Existing modeling methods are mostly designed for such simple coupled structures. However, for complex beam-shell coupled structures, which consist of pipelines composed of multiple straight and curved beams coupled with a pressure-loaded composite shell, there is currently a lack of methods for studying them, and existing analysis methods heavily rely on finite element software.

[0004] In summary, existing dynamic analysis methods can only handle simple beam-shell coupled structures, lacking a dynamic analysis method for complex beam-shell coupled systems that consider pressure. Engineering practice urgently needs to develop a dynamic analysis method for complex beam-shell coupled systems such as aviation hydrogen storage systems. Summary of the Invention

[0005] The purpose of this invention is to provide a kinetic analysis method for in-plane aviation hydrogen storage systems, in order to solve the problem of the lack of specific methods for aviation hydrogen storage systems in the prior art.

[0006] This invention is implemented by providing a kinetic analysis method for an in-plane aviation hydrogen storage system, comprising the following steps: Step 1: Divide the aviation hydrogen storage system into a pipeline section and a hydrogen storage tank section. Discretize the pipeline section into a beam structure including straight beams and curved beams, and discretize the hydrogen storage tank section into a shell structure including spherical shells and cylindrical shells. Construct a family of orthogonal displacement functions suitable for aviation hydrogen storage systems, and construct displacement functions for beam structures and shell structures respectively. Step 2: Derive and solve the kinetic energy equation, potential energy equation, coupling equation, and boundary constraint equation for the beam structure and shell structure in the aviation hydrogen storage system. Step 3: Combine the kinetic energy equation, potential energy equation, coupling equation and boundary constraint equation from Step 2 to construct the total energy functional of the aviation hydrogen storage system. Solve the total energy functional based on the Rayleigh-Ritz method to obtain the mode shapes and natural frequencies of the aviation hydrogen storage system. Step 4: Based on the mode shapes and natural frequencies obtained in Step 3, the dynamic response of the aviation hydrogen storage system under external excitation is calculated using the modal superposition method, thus completing the dynamic analysis.

[0007] Preferably, step 1 specifically includes: Step 1.1: Assume the displacement function of the straight beam is as follows: ; Where i=1 and 2 represent the first straight beam and the second straight beam on the pipeline section, respectively. The first straight beam and the second straight beam are the straight pipe sections at the beginning and end of the pipeline section, respectively. , and These represent points on the straight beam. , and Displacement of the axis, , and These represent points on the straight beam. , and angular displacement of the shaft, , , , , and It is the displacement function of the straight beam. This indicates the truncation order of the straight beam displacement function. , , , , and These are the unknown coefficients of an orthogonal polynomial. , , , , and Represents an orthogonal polynomial. Angular frequency, t For time, , , , , and Represents the time function of a straight beam; Assume the displacement function of the curved beam is as follows: ; Among them, the curved beam is the connection part between the first straight beam and the second straight beam in the pipeline section; , and They represent points on the curved beam. , and Displacement of the axis, , and They represent points on the curved beam. , and angular displacement of the shaft, , , , , and It is the corresponding displacement function of the curved beam. This indicates the truncation order of the displacement function of the curved beam. , , , , and These are the unknown coefficients of an orthogonal polynomial. , , , , and Represents the time function of the curved beam; Assume the displacement function of the shell structure is as follows: ; Where i=1, 2 and c represent the first spherical shell, the second spherical shell and the cylindrical shell of the hydrogen storage tank, respectively. The first spherical shell and the second spherical shell are the shell structures at the bottom and top of the hydrogen storage tank, respectively, and the cylindrical shell is the shell structure of the main body of the hydrogen storage tank. , and These represent points on the surface of the shell structure. , and Displacement of the axis, and These represent points on the surface of the shell structure. and Angular displacement of the shaft; and This indicates the truncation order of the displacement function of the shell structure. , , , and These are the unknown coefficients of an orthogonal polynomial; , , , and It is the corresponding displacement function of the shell structure. , , , and The time function representing the shell structure; Step 1.2: Construct a family of characteristic functions. Set a normalized first-order orthogonal displacement function satisfying the boundary conditions as the initial basis function. Construct higher-order orthogonal displacement functions through the following recursive relationship: The formula for calculating the intermediate variable is as follows: ; Among them, symbols P ( x ) represents the weight function, defined as P ( x = 1; Step 1.3: Calculate the 2-norm of the higher-order orthogonal displacement function, expressed as: ; By normalizing the orthogonal polynomial series, we can construct the standardized orthogonal basis functions: ; The standardized orthogonal basis functions satisfy the following Kronecker orthogonality relation: ; in, The Kronecker function is used to obtain a family of orthogonal displacement functions applicable to the aviation hydrogen storage system.

[0008] Further preferably, step 2 specifically includes: Step 2.1: Based on Timoshenko beam theory, derive the potential energy equation of the straight beam in the global coordinate system. The expression is: ; In the formula, n Indicates the number of straight beams. Indicates the first i The length of the straight beam section This represents the elastic modulus of the beam structure. This represents the shear correction factor for the beam structure. This represents the shear modulus of the beam structure. and They are and Moment of inertia of the axis, A Represents the cross-sectional area of ​​the beam structure. J Represents the torsional moment of inertia of the cross section; Step 2.2: Derive the kinetic energy equation of the straight beam, the expression of which is: ; In the formula, Indicates the density of the beam structure. yes Moment of inertia of the axis; Step 2.3: Based on Timoshenko beam theory, derive the potential energy equation within the curved beam structure, the expression of which is: ; In the formula, m Indicates the number of curved beams. For the central angle of the curved beam, Indicates the radius of the curved beam; Step 2.4: Derive the potential energy equation outside the curved beam structure, the expression is: ; In the formula, Represents the moment of inertia; Step 2.5: Derive the in-plane kinetic energy equation for the curved beam structure, the expression of which is: ; Step 2.6: Derive the out-of-plane kinetic energy equation for the curved beam structure, the expression of which is: ; Step 2.7: Based on the first-order shear deformation theory, derive the equations for the tensile potential energy, bending potential energy, and bending-tension coupled potential energy of the first and second spherical shells. The expressions are as follows: ; ; ; in, Indicates spherical shell i radius, , and These represent the tension, tension-bending coupling, and bending stiffness coefficients, respectively. Step 2.8: Derive the kinetic energy equations for the first and second spherical shells, the expressions are as follows: ; in, , , Represents the inertia constant; Step 2.9: Based on the first-order shear deformation theory, derive the equations for the tensile potential energy, bending potential energy, and bending-tension coupled potential energy of the cylindrical shell. The expressions are as follows: ; ; ; in, Indicates the radius of the cylindrical shell; Step 2.10: Derive the kinetic energy equation for the cylindrical shell, the expression is: ; Step 2.11: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the straight beam, the expression of which is: ; ; In the formula, , , , , , , , , , , and These are the boundary spring stiffnesses at the end of the first straight beam and three-quarters of the way through the second straight beam, respectively. Step 2.12: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the curved beam, the expression of which is: ; In the formula, , , , , and The boundary spring stiffness at the starting end of the curved beam; Step 2.13: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the spherical shell, the expression of which is: ; In the formula, h The thickness of the shell structure, and Representing the spherical shell i exist The starting and ending angles of the direction; , , , , , , , , and These are the boundary spring stiffnesses at the beginning and end of the cylindrical shell, respectively. Step 2.14: Establish the boundary spring potential energy equation for the cylindrical shell structure, the expression of which is: ; In the formula, , , , , , , , , and These are the boundary spring stiffnesses at the beginning and end of the cylindrical shell, respectively. Step 2.15: Establish the beam-beam coupled spring potential energy equation for the beam structure, the expression of which is: ; ; In the formula, , , , , , , , , , , and These are the spring stiffness of the first straight beam coupled with the curved beam and the spring stiffness of the curved beam coupled with the second straight beam, respectively. Step 2.16: Under the condition of multi-point arbitrary stiffness constraint, establish the shell-shell coupled spring potential energy equation of the shell structure, the expression of which is: ; ; In the formula, , , , , , , , , and These represent the spring stiffness of the coupling between the first spherical shell and the cylindrical shell, and the spring stiffness of the coupling between the cylindrical shell and the second spherical shell, respectively. Step 2.17: Based on the deformation compatibility relationship, construct the sixth degree of freedom of the second spherical shell, expressed as: ; Step 2.18: Based on the relationship between the local coordinate system and the global coordinate system of the second spherical shell, construct the expression for the displacement of the second spherical shell structure in the global coordinate system. The expression is as follows: ; In the formula, Indicates the first q The angle of each coupling point; Step 2.19: Establish the potential energy equation for the beam-shell coupled spring, its expression is: ; In the formula, , , , , and Represents the stiffness of the beam-shell coupled spring; Step 2.20: Establish the pressure potential energy equation, the expression of which is: ; in, This is a function of internal pressure, where the internal pressure is uniform. =P, where P is a constant.

[0009] Further preferably, step 3 specifically includes: Step 3.1: Substitute the family of orthogonal displacement functions into the potential energy equation, kinetic energy equation, and boundary spring potential energy equation respectively to construct the total energy functional of the system; ; Step 3.2: Based on the Rayleigh-Ritz method, calculate the partial derivatives of each Ritz parameter in the total energy functional and set them to zero to derive the eigenvalue equations of the system: ; In the formula, K The total stiffness matrix satisfies , , , and These are the stiffness matrices generated by structural potential energy, pressure potential energy, boundary potential energy, and coupling potential energy, respectively. Let Ritz be the vector containing unknown modal coefficients; Step 3.3: Solve the eigenvalue equations using a matrix factorization algorithm to obtain the natural frequency vector and modal coefficient matrix of the aviation hydrogen storage system, and then combine them with the orthogonal displacement function family to obtain the mode shape functions of each order.

[0010] Further preferably, step 4 specifically includes: Step 4.1: Based on the obtained mode shape functions and the Lagrange equations, establish the dynamic differential equations of the aviation hydrogen storage system: ; In the formula, , and Let these represent the mass matrix, damping matrix, and stiffness matrix, respectively. This represents the excitation force vector applied at any location on the beam structure. Represents the generalized displacement vector; Step 4.2: By combining coordinate transformation with modal orthogonality, the dynamic differential equation is decoupled to the modal coordinate system, so that the mass matrix and stiffness matrix are converted into diagonal matrix form; Step 4.3: Solve the decoupled dynamic differential equations using a numerical solution algorithm to obtain the dynamic response of the aviation hydrogen storage system.

[0011] Compared with the prior art, the advantages of the present invention are as follows: 1. This invention provides a dynamic analysis method for complex beam-shell coupled structures considering the influence of pressure. It can effectively and accurately analyze the mode shapes, natural frequencies and dynamic responses of complex beam-shell coupled structures considering the influence of pressure, thus providing a dynamic analysis method for complex beam-shell coupled structures considering the influence of pressure. 2. This invention uses the Rayleigh-Ritz method based on the energy principle combined with the modal superposition method for solving the problem. It does not require complex mesh generation and preprocessing operations. Compared with the traditional finite element method, it significantly reduces the preprocessing workload and computational resource consumption, and greatly improves the computational efficiency. Attached Figure Description

[0012] Figure 1 This invention provides a schematic diagram of an aviation hydrogen storage system in the aerospace field. Figure 2 A schematic flowchart of the kinetic analysis method for aviation hydrogen storage systems provided by the present invention; Figure 3 This is a schematic diagram of the modal vibration results provided by the present invention; Figure 4 A schematic diagram comparing the dynamic response and finite element simulation results provided by this invention. Detailed Implementation

[0013] The technical solutions of this invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0014] like Figure 2 As shown, this invention provides a dynamic analysis method for an in-plane aviation hydrogen storage system, taking the structure of a certain type of aircraft aviation hydrogen storage system (such as...) as an example. Figure 1 The following is an explanation of the application objects (shown in the figure).

[0015] Step 1 specifically includes: Step 1.1: Assume the displacement function of the straight beam is as follows: ; Where i=1 and 2 represent the first straight beam 1 and the second straight beam 2 on the pipeline section, respectively. The first straight beam and the second straight beam are the straight pipe sections at the beginning and end of the pipeline section, respectively. , and These represent points on the straight beam. , and Displacement of the axis, , and These represent points on the straight beam. , and angular displacement of the shaft, , , , , and It is the displacement function of the straight beam. This indicates the truncation order of the straight beam displacement function. , , , , and These are the unknown coefficients of an orthogonal polynomial. , , , , and Represents an orthogonal polynomial. Angular frequency, t For time, , , , , and Represents the time function of a straight beam; Assume the displacement function of the curved beam 3 is as follows: ; Among them, the curved beam 3 is the connection part between the first straight beam 1 and the second straight beam 2 in the pipeline section; , and They represent points on the curved beam. , and Displacement of the axis, , and They represent points on the curved beam. , and angular displacement of the shaft, , , , , and It is the corresponding displacement function of the curved beam. This indicates the truncation order of the displacement function of the curved beam. , , , , and These are the unknown coefficients of an orthogonal polynomial. , , , , and Represents the time function of the curved beam; Assume the displacement function of the shell structure is as follows: ; Where i=1, 2 and c represent the first spherical shell 4, the second spherical shell 5 and the cylindrical shell 6 of the hydrogen storage tank, respectively. The first spherical shell 4 and the second spherical shell 5 are the shell structures of the bottom and top of the hydrogen storage tank, respectively, and the cylindrical shell 6 is the shell structure of the main body of the hydrogen storage tank. , and These represent points on the surface of the shell structure. , and Displacement of the axis, and These represent points on the surface of the shell structure. and Angular displacement of the shaft; and This indicates the truncation order of the displacement function of the shell structure. , , , and These are the unknown coefficients of an orthogonal polynomial; , , , and It is the corresponding displacement function of the shell structure. , , , and The time function representing the shell structure; Step 1.2: Construct a family of characteristic functions. Set a normalized first-order orthogonal displacement function satisfying the boundary conditions as the initial basis function. Construct higher-order orthogonal displacement functions through the following recursive relationship: The formula for calculating the intermediate variable is as follows: ; Among them, symbols P ( x ) represents the weight function, defined as P ( x = 1; Step 1.3: Calculate the 2-norm of the higher-order orthogonal displacement function, its expression is: ; By normalizing the orthogonal polynomial series, we can construct the standardized orthogonal basis functions: ; The standardized orthogonal basis functions satisfy the following Kronecker orthogonality relation: ; In the formula, Let Kronecker function be used; thus, a family of orthogonal displacement functions applicable to the aforementioned aviation hydrogen storage system is obtained.

[0016] Step 2 specifically includes: Step 2.1: Based on Timoshenko beam theory, derive the potential energy equation of the straight beam in the global coordinate system. The expression is: ; In the formula, n Indicates the number of straight beams. Indicates the first i The length of the straight beam section This represents the elastic modulus of the beam structure. This represents the shear correction factor for the beam structure. This represents the shear modulus of the beam structure. and They are and Moment of inertia of the axis, A Represents the cross-sectional area of ​​the beam structure. J This represents the torsional moment of inertia of the cross section. In this embodiment, the beam material is steel, and the length of the first straight beam is... =100mm, length of the second straight beam L b2 =300mm, Young's modulus = 200 GPa, shear modulus =76.92, Poisson's ratio ν = 0.3, density ρ = 7850 kg / m 3 .

[0017] Step 2.2: Derive the kinetic energy equation of the straight beam structure, its expression is: ; In the formula, Indicates the density of the beam structure. yes Moment of inertia of the axis; Step 2.3: Based on Timoshenko beam theory, derive the potential energy equation within the curved beam structure surface. Its expression is: ; In the formula, m Indicates the number of curved beams. For the central angle of the curved beam, Indicates the radius of the curved beam; Step 2.4: Derive the potential energy equation outside the curved beam structure, the expression is: ; In the formula, Represents the moment of inertia; Step 2.5: Derive the in-plane kinetic energy equation for the curved beam structure, the expression of which is: ; Step 2.6: Derive the out-of-plane kinetic energy equation for the curved beam structure, the expression of which is: ; Step 2.7: Based on the first-order shear deformation theory, derive the equations for the tensile potential energy, bending potential energy, and bending-tension coupled potential energy of the first and second spherical shells. The expressions are as follows: ; ; ; in, Indicates spherical shell i radius, , and These represent the tensile, tensile-bending coupling, and bending stiffness coefficients, respectively. In this embodiment, both the spherical and cylindrical shells are made of inner steel and outer composite materials, with 8 inner layers and 2 outer layers, each with a single layer thickness of 0.25 mm. Composite material parameters include: elastic modulus. =140 GPa =7 GPa, Poisson's ratio =0.38, shear modulus =5 GPa.

[0018] Step 2.8: Derive the kinetic energy equations for the first and second spherical shells, the expressions are as follows: ; in, , , Represents the inertia constant; Step 2.9: Based on the first-order shear deformation theory, derive the equations for the tensile potential energy, bending potential energy, and bending-tension coupled potential energy of the cylindrical shell. The expressions are as follows: ; ; ; in, This represents the radius of the cylindrical shell; in this embodiment... =89.25mm; Step 2.10: Derive the kinetic energy equation for the cylindrical shell, the expression is: ; Step 2.11: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the straight beam, the expression of which is: ; ; In the formula, , , , , , , , , , , and These are the boundary spring stiffnesses at the end of the first straight beam and three-quarters of the way through the second straight beam, respectively. In this embodiment, constraints exist only at the connection between the first straight beam and the curved beam, and at 1 / 4 of the length of the second straight beam in the direction of the end; the constraint type is fixed constraint. = The stiffness of the remaining boundary constraint springs and coupling springs is the same as that at this location.

[0019] Step 2.12: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the curved beam, the expression of which is: ; In the formula, , , , , and The boundary spring stiffness at the starting end of the curved beam; Step 2.13: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the spherical shell, the expression of which is: ; In the formula, h The thickness of the shell structure, and Representing the spherical shell i exist The starting and ending angles of the direction; , , , , , , , , and These are the boundary spring stiffnesses at the beginning and end of the cylindrical shell, respectively. Step 2.14: Establish the boundary spring potential energy equation for the cylindrical shell structure, the expression of which is: ; In the formula, , , , , , , , , and These are the boundary spring stiffnesses at the beginning and end of the cylindrical shell, respectively. Step 2.15: Establish the beam-beam coupled spring potential energy equation for the beam structure, the expression of which is: ; ; In the formula, , , , , , , , , , , and These are the spring stiffness of the first straight beam coupled with the curved beam and the spring stiffness of the curved beam coupled with the second straight beam, respectively. Step 2.16: Under the condition of multi-point arbitrary stiffness constraint, establish the shell-shell coupled spring potential energy equation of the shell structure, the expression of which is: ; ; In the formula, , , , , , , , , and These represent the spring stiffness of the coupling between the first spherical shell and the cylindrical shell, and the spring stiffness of the coupling between the cylindrical shell and the second spherical shell, respectively. Step 2.17: Based on the deformation compatibility relationship, construct the sixth degree of freedom of the second spherical shell, expressed as: ; Step 2.18: Based on the relationship between the local coordinate system and the global coordinate system of the second spherical shell, construct the expression for the displacement of the second spherical shell structure in the global coordinate system. The expression is as follows: ; In the formula, Indicates the first q The angle of each coupling point; Step 2.19: Establish the potential energy equation for the beam-shell coupled spring, its expression is: ; In the formula, , , , , and This represents the stiffness of the beam-shell coupled spring; in this embodiment, q=2.

[0020] Step 2.20: Establish the pressure potential energy equation, the expression of which is: ; in, This is a function of internal pressure, where the internal pressure is uniform. =P, where P is a constant; in this embodiment, P = 70 MPa; Step 3 specifically includes: Step 3.1: Substitute the family of orthogonal displacement functions into the potential energy equation, kinetic energy equation, and boundary spring potential energy equation respectively to construct the total energy functional of the system: ; Step 3.2: Based on the Rayleigh-Ritz method, calculate the partial derivatives of each Ritz parameter in the total energy functional and set them to zero to derive the eigenvalue equations of the system: ; In the formula, K The total stiffness matrix satisfies , , , and These are the stiffness matrices generated by structural potential energy, pressure potential energy, boundary potential energy, and coupling potential energy, respectively. Let Ritz be the vector containing unknown modal coefficients; Step 3.3: Solve the eigenvalue equations using a matrix factorization algorithm to obtain the natural frequency vector and modal coefficient matrix of the aviation hydrogen storage system. Then, combine this with the orthogonal displacement function family to obtain the mode shape functions for each order, such as... Figure 3 As shown.

[0021] Step 4 specifically includes: Step 4.1: Based on the obtained mode shape functions and the Lagrange equations, establish the dynamic differential equations of the aviation hydrogen storage system: ; In the formula, , and Let these represent the mass matrix, damping matrix, and stiffness matrix, respectively. This represents the excitation force vector applied at any location on the beam structure. Represents the generalized displacement vector; in this embodiment, F is a 7N sinusoidal excitation; damping matrix A proportional damping model is adopted, and the damping ratio is taken as follows: ξ =0.05; Step 4.2: By combining coordinate transformation with modal orthogonality, the dynamic differential equation is decoupled to the modal coordinate system, so that the mass matrix and stiffness matrix are converted into diagonal matrix form; Step 4.3: Solve the decoupled dynamic differential equations using a numerical solution algorithm to obtain the dynamic response of the aviation hydrogen storage system; In step 4.3, the transfer function method is used to solve the decoupled dynamic differential equations to obtain the amplitude-frequency response curve of the aviation hydrogen storage system under harmonic excitation, as shown below. Figure 4 As shown. For transient excitation conditions, the following is adopted: The time-domain dynamic response of the aviation hydrogen storage system was obtained by numerical solution. The above description is merely an embodiment of the present invention and is not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for in-plane kinetic analysis of an aerial hydrogen storage system, characterized in that, Includes the following steps: Step 1: Divide the aviation hydrogen storage system into a pipeline section and a hydrogen storage tank section. Discretize the pipeline section into a beam structure including straight beams and curved beams, and discretize the hydrogen storage tank section into a shell structure including spherical shells and cylindrical shells. Construct a family of orthogonal displacement functions suitable for aviation hydrogen storage systems, and construct displacement functions for beam structures and shell structures respectively. Step 2: Derive and solve the kinetic energy equation, potential energy equation, coupling equation, and boundary constraint equation for the beam structure and shell structure in the aviation hydrogen storage system. Step 3: Combine the kinetic energy equation, potential energy equation, coupling equation and boundary constraint equation from Step 2 to construct the total energy functional of the aviation hydrogen storage system. Solve the total energy functional based on the Rayleigh-Ritz method to obtain the mode shapes and natural frequencies of the aviation hydrogen storage system. Step 4: Based on the mode shapes and natural frequencies obtained in Step 3, the dynamic response of the aviation hydrogen storage system under external excitation is calculated using the modal superposition method, thus completing the dynamic analysis.

2. The kinetic analysis method for an in-plane aviation hydrogen storage system according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Assume the displacement function of the straight beam is as follows: ； Where i=1 and 2 represent the first straight beam and the second straight beam on the pipeline section, respectively. The first straight beam and the second straight beam are the straight pipe sections at the beginning and end of the pipeline section, respectively. , and These represent points on the straight beam. , and Displacement of the axis, , and These represent points on the straight beam. , and angular displacement of the shaft, , , , , and It is the displacement function of the straight beam. This indicates the truncation order of the straight beam displacement function. , , , , and These are the unknown coefficients of an orthogonal polynomial. , , , , and Represents an orthogonal polynomial. Angular frequency, t For time, , , , , and Represents the time function of a straight beam; Assume the displacement function of the curved beam is as follows: ； Among them, the curved beam is the connection part between the first straight beam and the second straight beam in the pipeline section; , and They represent points on the curved beam. , and Displacement of the axis, , and They represent points on the curved beam. , and angular displacement of the shaft, , , , , and It is the corresponding displacement function of the curved beam. This indicates the truncation order of the displacement function of the curved beam. , , , , and These are the unknown coefficients of an orthogonal polynomial. , , , , and Represents the time function of the curved beam; Assume the displacement function of the shell structure is as follows: ； Where i=1, 2 and c represent the first spherical shell, the second spherical shell and the cylindrical shell of the hydrogen storage tank, respectively. The first spherical shell and the second spherical shell are the shell structures at the bottom and top of the hydrogen storage tank, respectively, and the cylindrical shell is the shell structure of the main body of the hydrogen storage tank. , and These represent points on the surface of the shell structure. , and Displacement of the axis, and These represent points on the surface of the shell structure. and Angular displacement of the shaft; and This indicates the truncation order of the displacement function of the shell structure. , , , and These are the unknown coefficients of an orthogonal polynomial; , , , and It is the corresponding displacement function of the shell structure. , , , and The time function representing the shell structure; Step 1.2: Construct a family of characteristic functions. Set a normalized first-order orthogonal displacement function satisfying the boundary conditions as the initial basis function. Construct higher-order orthogonal displacement functions through the following recursive relationship: The formula for calculating the intermediate variable is as follows: ； Among them, symbols P ( x ) represents the weight function, defined as P ( x = 1; Step 1.3: Calculate the 2-norm of the higher-order orthogonal displacement function, expressed as: ； By normalizing the orthogonal polynomial series, we can construct the standardized orthogonal basis functions: ； The standardized orthogonal basis functions satisfy the following Kronecker orthogonality relation: ； in, The Kronecker function is used to obtain a family of orthogonal displacement functions applicable to the aviation hydrogen storage system.

3. The kinetic analysis method for an in-plane aviation hydrogen storage system according to claim 2, characterized in that, Step 2 specifically includes: Step 2.1: Based on Timoshenko beam theory, derive the potential energy equation of the straight beam in the global coordinate system. The expression is: ； In the formula, n Indicates the number of straight beams. Indicates the first i The length of the straight beam section This represents the elastic modulus of the beam structure. This represents the shear correction factor for the beam structure. This represents the shear modulus of the beam structure. and They are and Moment of inertia of the axis, A Represents the cross-sectional area of ​​the beam structure. J Represents the torsional moment of inertia of the cross section; Step 2.2: Derive the kinetic energy equation of the straight beam, the expression of which is: ； In the formula, Indicates the density of the beam structure. yes Moment of inertia of the axis; Step 2.3: Based on Timoshenko beam theory, derive the potential energy equation within the curved beam structure, the expression of which is: ； In the formula, m Indicates the number of curved beams. For the central angle of the curved beam, Indicates the radius of the curved beam; Step 2.4: Derive the potential energy equation outside the curved beam structure, the expression is: ； In the formula, Represents the moment of inertia; Step 2.5: Derive the in-plane kinetic energy equation for the curved beam structure, the expression of which is: ； Step 2.6: Derive the out-of-plane kinetic energy equation for the curved beam structure, the expression of which is: ； Step 2.7: Based on the first-order shear deformation theory, derive the equations for the tensile potential energy, bending potential energy, and bending-tension coupled potential energy of the first and second spherical shells. The expressions are as follows: ； ； ； in, Indicates spherical shell i radius, , and These represent the tension, tension-bending coupling, and bending stiffness coefficients, respectively. Step 2.8: Derive the kinetic energy equations for the first and second spherical shells, the expressions are as follows: ； in, , , Represents the inertia constant; Step 2.9: Based on the first-order shear deformation theory, derive the equations for the tensile potential energy, bending potential energy, and bending-tension coupled potential energy of the cylindrical shell. The expressions are as follows: ； ； ； in, Indicates the radius of the cylindrical shell; Step 2.10: Derive the kinetic energy equation for the cylindrical shell, the expression is: ； Step 2.11: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the straight beam, the expression of which is: ； ； In the formula, , , , , , , , , , , and These are the boundary spring stiffnesses at the end of the first straight beam and three-quarters of the way through the second straight beam, respectively. Step 2.12: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the curved beam, the expression of which is: ； In the formula, , , , , and The boundary spring stiffness at the starting end of the curved beam; Step 2.13: Under the condition of multi-point arbitrary stiffness constraint, establish the boundary spring potential energy equation of the spherical shell, the expression of which is: ； In the formula, h The thickness of the shell structure, and Representing the spherical shell i exist The starting and ending angles of the direction; , , , , , , , , and These are the boundary spring stiffnesses at the beginning and end of the cylindrical shell, respectively. Step 2.14: Establish the boundary spring potential energy equation for the cylindrical shell structure, the expression of which is: ； In the formula, , , , , , , , , and These are the boundary spring stiffnesses at the beginning and end of the cylindrical shell, respectively. Step 2.15: Establish the beam-beam coupled spring potential energy equation for the beam structure, the expression of which is: ； ； In the formula, , , , , , , , , , , and These are the spring stiffness of the first straight beam coupled with the curved beam and the spring stiffness of the curved beam coupled with the second straight beam, respectively. Step 2.16: Under the condition of multi-point arbitrary stiffness constraint, establish the shell-shell coupled spring potential energy equation of the shell structure, the expression of which is: ； ； In the formula, , , , , , , , , and These represent the spring stiffness of the coupling between the first spherical shell and the cylindrical shell, and the spring stiffness of the coupling between the cylindrical shell and the second spherical shell, respectively. Step 2.17: Based on the deformation compatibility relationship, construct the sixth degree of freedom of the second spherical shell, expressed as: ； Step 2.18: Based on the relationship between the local coordinate system and the global coordinate system of the second spherical shell, construct the expression for the displacement of the second spherical shell structure in the global coordinate system. The expression is as follows: ； In the formula, Indicates the first q The angle of each coupling point; Step 2.19: Establish the potential energy equation for the beam-shell coupled spring, its expression is: ； In the formula, , , , , and Represents the stiffness of the beam-shell coupled spring; Step 2.20: Establish the pressure potential energy equation, the expression of which is: ； in, This is a function of internal pressure, where the internal pressure is uniform. =P, where P is a constant.

4. The kinetic analysis method for an in-plane aviation hydrogen storage system according to claim 3, characterized in that, Step 3 specifically includes: Step 3.1: Substitute the family of orthogonal displacement functions into the potential energy equation, kinetic energy equation, and boundary spring potential energy equation respectively to construct the total energy functional of the system; ； Step 3.2: Based on the Rayleigh-Ritz method, calculate the partial derivatives of each Ritz parameter in the total energy functional and set them to zero to derive the eigenvalue equations of the system: ； In the formula, K The total stiffness matrix satisfies , , , and These are the stiffness matrices generated by structural potential energy, pressure potential energy, boundary potential energy, and coupling potential energy, respectively. Let Ritz be the vector containing unknown modal coefficients; Step 3.3: Solve the eigenvalue equations using a matrix factorization algorithm to obtain the natural frequency vector and modal coefficient matrix of the aviation hydrogen storage system, and then combine them with the orthogonal displacement function family to obtain the mode shape functions of each order.

5. The kinetic analysis method for an in-plane aviation hydrogen storage system according to claim 4, characterized in that, Step 4 specifically includes: Step 4.1: Based on the obtained mode shape functions and the Lagrange equations, establish the dynamic differential equations of the aviation hydrogen storage system: ； In the formula, , and Let these represent the mass matrix, damping matrix, and stiffness matrix, respectively. This represents the excitation force vector applied at any location on the beam structure. Represents the generalized displacement vector; Step 4.2: By combining coordinate transformation with modal orthogonality, the dynamic differential equation is decoupled to the modal coordinate system, so that the mass matrix and stiffness matrix are converted into diagonal matrix form; Step 4.3: Solve the decoupled dynamic differential equations using a numerical solution algorithm to obtain the dynamic response of the aviation hydrogen storage system.

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