Vibration analysis method, system and storage medium for the coupled structure of cylindrical shell and conical shell

Abstract

The present invention discloses a vibration analysis method, system and storage medium for a coupled structure of a cylindrical shell and a conical shell, which relates to the field of performance analysis. The method includes: S1 constructing a numerical model of the vibration of the structure under thermal load; S2 determining the vibration displacement relationship of the coupled structure between the cylindrical shell and the conical shell; S3 constructing a cone-cylindrical shell coupled system; S4 determining the Lagrangian function of the cone-cylindrical shell coupled system; S5 determining the coupling equation of the cone-cylindrical shell coupled system; S6 analyzing the free vibration and forced vibration results of the cone-cylindrical shell coupled system. By establishing a numerical model of the dynamics of the cylindrical shell and the conical shell corresponding to the action of the thermal load, and obtaining the vibration control matrix model of the coupled structure of the cylindrical shell and the conical shell according to the numerical model, and then further obtaining the vibration matrix of the cone-cylindrical shell coupled system to obtain the vibration analysis result under the thermal load, it is beneficial to improve the efficiency of the vibration analysis of the cylindrical shell and the conical shell corresponding to the action of the thermal load and reduce the overall cost.

Description

Technical Field

[0001] The present invention relates to the field of performance analysis, and particularly to a vibration analysis method, system and storage medium for a coupled structure of a cylindrical shell and a conical shell. Background Art

[0002] Vibration analysis is widely used in people's production and life. The vibration analysis of the coupled structure of a cylinder and a conical shell under thermal load plays an important role in special fields. The vibration control of the structure requires pre - vibration analysis of the structure to achieve the optimization of control. Therefore, it is necessary to analyze the vibration of the structure under thermal load.

[0003] Currently, the finite element theory is usually used for the vibration analysis of the coupled structure of a cylinder and a conical shell under thermal load. Due to problems such as a large number of grids, low calculation accuracy, and low efficiency in the finite element model, the calculation results are affected, resulting in a relatively high cost for the final vibration analysis. Summary of the Invention

[0004] The purpose of the present invention is to design a vibration analysis method, system and storage medium for a coupled structure of a cylindrical shell and a conical shell to solve the above problems.

[0005] The present invention achieves the above - mentioned purpose through the following technical solutions:

[0006] A vibration performance analysis method for a cylindrical shell and a conical shell structure, comprising:

[0007] S1. Construct a numerical model of the structure vibration under thermal load, where the numerical model includes a cylindrical shell and a conical shell, and the cylindrical shell and the conical shell are connected by a coupling spring;

[0008] S2. Obtain the vibration displacement relationship of the coupled structure between the cylindrical shell and the conical shell according to the numerical model;

[0009] S3. Introduce a three - dimensional elastic coupler with linear displacement stiffness and rotational stiffness at the common boundary of the coupled structure between the cylindrical shell and the conical shell to construct a cone - cylindrical shell coupling system;

[0010] S4. Determine the Lagrangian function of the cone - cylindrical shell coupling system;

[0011] S5. Determine the coupling equation of the cone - cylindrical shell coupling system according to the Lagrangian function and the vibration displacement relationship;

[0012] S6. Analyze the free vibration and forced vibration results of the cone - cylindrical shell coupling system based on the coupling equation.

[0013] A system for vibration performance analysis of a cylindrical shell and a conical shell structure, comprising:

[0014] A memory; used for storing a computer program;

[0015] A processor; the processor is used to execute a computer program, and when executing the computer program in the memory, it implements the steps of the vibration performance analysis method for the cylindrical shell and conical shell structures as described above.

[0016] A storage medium stores a computer program, and when the computer program is executed, it implements the steps of the vibration performance analysis method for the cylindrical shell and conical shell structures as described above.

[0017] The beneficial effects of the present invention are as follows: The present invention can establish a numerical model of the dynamics of the cylindrical shell and conical shell corresponding to the action of thermal load, and obtain the vibration control matrix model of the cylindrical shell and conical shell coupling structure according to the numerical model, and then further obtain the vibration matrix of the cone-cylindrical shell coupling system to obtain the vibration analysis result under the thermal load. The implementation method is simple, the cost is low, and the calculation process is efficient, which is beneficial to improving the efficiency of vibration analysis of the cylindrical shell and conical shell corresponding to the action of thermal load and reducing the overall cost. Description of the Drawings

[0018] Figure 1 It is a schematic diagram of the numerical model of the present invention;

[0019] Figure 2 It is a schematic flow diagram of the vibration performance analysis method for the cylindrical shell and conical shell structures of the present invention;

[0020] Figure 3 It is a schematic diagram of the free vibration mode of the cylindrical shell and conical shell corresponding to the action of thermal load of the present invention;

[0021] Figure 4 It is a schematic diagram of the forced vibration of the cylindrical shell and conical shell corresponding to the action of thermal load of the present invention. Detailed Embodiments

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0023] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0024] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0025] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings.

[0026] Vibration performance analysis methods for cylindrical and conical shell structures, including:

[0027] S1. Construct a numerical model of structural vibration under thermal load, the numerical model includes a cylindrical shell and a conical shell, and the cylindrical shell and the conical shell are connected by a coupling spring;

[0028] S2. The vibration displacement relationship of the coupling structure between the cylindrical shell and the conical shell is obtained according to the numerical model; specifically:

[0029] The vibration displacement of the cylindrical shell is expressed as:

[0030]

[0031]

[0032]

[0033] The vibration displacement of a conical shell is expressed as:

[0034]

[0035]

[0036]

[0037] Among them, λ lm =mπ / L l ,λ ln =nπ / ψ,λ cm =mπ / L c ,λ cn =nπ / ψ, where L l and L c are the generatrix lengths of cylindrical shell and conical shell respectively, ψ is the angle of the toroidal shell structure, The vector of unknown coefficients representing the series expansion of the displacement functions for cylindrical and conical shells.

[0038] S3. A three-dimensional elastic coupler with linear displacement stiffness and rotation stiffness is introduced at the common boundary of the coupling structure between the cylindrical shell and the conical shell to construct a cone-cylindrical shell coupling system;

[0039] S4. Determine the Lagrangian function of the cone-shell coupling system; the Lagrangian function of the cone-shell coupling system includes the strain energy, kinetic energy of the substructures, the potential energy stored in the boundary coupling springs, the potential energy stored in the circumferential boundary three-dimensional elastic couplers, and the coupling potential energy between the substructures.

[0040] The strain energy is the work done by the thermal load on the conical shell and is expressed as:

[0041]

[0042] The maximum kinetic energy of the conical shell structure is expressed as:

[0043]

[0044] The potential energy stored in the boundary coupling springs of the conical shell is expressed as:

[0045]

[0046] When the rotation angle ψ of the conical shell structure is 2π, a virtual coupling spring needs to be introduced, and the stiffness value of the constraint spring at the coupling boundary becomes zero. Then the potential energy stored in the boundary coupling springs is expressed as:

[0047]

[0048] The potential energy stored in the circumferential boundary three-dimensional elastic couplers of the conical shell and the coupling potential energy between the substructures are expressed as:

[0049]

[0050] The maximum kinetic energy of the cylindrical shell structure can be expressed as:

[0051]

[0052] The potential energy stored in the boundary constraint springs can be expressed as:

[0053]

[0054] When the rotation angle ψ of the cylindrical shell structure is 2π, virtual coupling springs need to be introduced at the coincidence of the boundaries ψ = 0 and ψ = 2π, which also include three groups of linear displacement constraint springs and one group of rotational coupling springs To ensure the continuity of the cylindrical shell structure at the circumferential coupling boundary; meanwhile, the stiffness value of the constraint spring at the coupling boundary becomes zero. The potential energy stored in the coupling constraint springs can be expressed as:

[0055]

[0056] The work done by the thermal load on the cylindrical shell can be expressed as:

[0057]

[0058] The strain energy of the cylindrical shell structure is as follows:

[0059]

[0060] Then the Lagrangian function is expressed as:

[0061]

[0062] S5. Determine the coupling equation of the cone-cylindrical shell coupling system according to the relationship between the Lagrangian function and the vibration displacement. Perform a variational operation on the Lagrangian function, truncate the infinite expansion series at m = M and n = N, and obtain a linear equation system with a dimension of 2×(M + 5)×(N + 5)+3×(M + 3)×(N + 3). In matrix form, it is the coupling equation, expressed as (K - ω 2 M)E = 0, where M = diag[M cc M ll , E = [W c , U c , V c , W l , U l , V l T , where K is the system stiffness matrix, M is the system mass matrix, and E is the vector of unknown coefficients in the series expansion of the displacement function, that is

[0063] S6. Analyze the free vibration and forced vibration results of the cone-cylindrical shell coupling system according to the coupling equation; specifically: obtain the vibration displacement according to the vibration displacement expressions of the cylindrical shell and the conical shell under the thermal load, and then draw the vibration mode and the forced vibration results according to the displacement function to obtain the vibration results of the cone-cylindrical shell coupling system.

[0064] In view of the coupling structure vibration performance analysis method provided by the present invention, when dealing with different boundary conditions, only the installation stiffness value at the boundary needs to be adjusted. Therefore, it is very easy to obtain the vibration results under different boundary conditions. Therefore, the present invention has the advantage of the influence law of different installation boundaries on the vibration of cylindrical structures under thermal load.

[0065] ​It can be seen that the present invention can establish a numerical model of the dynamics of a cylindrical shell and a conical shell corresponding to the action of thermal load, obtain the vibration matrix of the coupled structure of the cylindrical shell and the conical shell according to the numerical model, and then further obtain the vibration analysis result of the coupled structure under the thermal load from the vibration matrix of the coupled structure of the cylindrical shell and the conical shell. The implementation method is simple, the cost is low, and the measurement process is efficient, which is beneficial to improving the efficiency of vibration analysis of the cylindrical shell and the conical shell corresponding to the action of thermal load and reducing the overall cost.

[0066] A system for analyzing the vibration performance of a cylindrical shell and a conical shell structure, comprising:

[0067] A memory; for storing a computer program;

[0068] A processor; the processor is used to execute the computer program, and when executing the computer program in the storage, it realizes the steps of the vibration performance analysis method for the cylindrical shell and the conical shell structure as described above.

[0069] A storage medium stores a computer program, and when the computer program is executed, it realizes the steps of the vibration performance analysis method for the cylindrical shell and the conical shell structure as described above.

[0070] The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and any technical deformation made according to the technical solution of the present invention falls within the protection scope of the present invention.

Claims

1. A method for analyzing the vibration of a coupled structure of a cylindrical shell and a conical shell, characterized in that, Including: S1. Construct a numerical model of the structural vibration under thermal load. The numerical model includes a cylindrical shell and a conical shell, and the cylindrical shell and the conical shell are connected by a coupling spring; S2. Obtain the vibration displacement relationship of the coupling structure between the cylindrical shell and the conical shell according to the numerical model. The vibration displacement of the cylindrical shell is expressed as: The vibration displacement of the conical shell is expressed as: where λ lm = mπ / L l , λ ln = nπ / ψ, λ cm = mπ / L c , λ cn = nπ / ψ, where L l and L c are the generatrix lengths of the cylindrical shell and the conical shell respectively, and ψ is the angle of the toroidal shell structure, represent the unknown coefficient vectors of the series expansion of the displacement functions of the cylindrical shell and the conical shell; S3. Introduce a three-dimensional elastic coupler with linear displacement stiffness and rotational stiffness at the common boundary of the coupling structure between the cylindrical shell and the conical shell to construct a cone-cylindrical shell coupling system; S4. Determine the Lagrangian function of the cone-cylindrical shell coupling system; S5. Determine the coupling equation of the cone-cylindrical shell coupling system according to the Lagrangian function and the vibration displacement relationship; S6. Analyze the free vibration and forced vibration results of the cone-cylindrical shell coupling system based on the coupling equation.

2. The vibration analysis method of the cylindrical shell and conical shell coupling structure according to claim 1, characterized in that In S4, the Lagrangian function of the cone-cylindrical shell coupling system includes the strain energy, kinetic energy of the substructure, potential energy stored in the boundary coupling spring, potential energy stored in the circumferential boundary three-dimensional elastic coupler, and coupling potential energy between the substructures; The strain energy is the work done by the thermal load on the conical shell, expressed as: The maximum kinetic energy of the conical shell structure is expressed as: The potential energy stored in the boundary coupling spring of the conical shell is expressed as: When the rotation angle ψ of the conical shell structure is 2π, a virtual coupling spring needs to be introduced, and the stiffness value of the constraint spring at the coupling boundary becomes zero. Then the potential energy stored in the boundary coupling spring is expressed as: The potential energy stored in the circumferential boundary three-dimensional elastic coupler of the conical shell and the coupling potential energy between the substructures are expressed as: The maximum kinetic energy of the cylindrical shell structure can be expressed as: The potential energy stored in the boundary constraint spring of the cylindrical shell can be expressed as: When the rotation angle ψ of the cylindrical shell structure is ψ = 2π, virtual coupling springs need to be introduced at the coincidence of the boundaries ψ = 0 and ψ = 2π, and it also includes three groups of linear displacement constraint springs and a group of rotational coupling springs to ensure the continuity of the cylindrical shell structure at the circumferential coupling boundary; meanwhile, the stiffness value of the constraint spring at the coupling boundary becomes zero, and the potential energy stored in the coupling constraint spring can be expressed as: The work done by the thermal load on the cylindrical shell can be expressed as: The strain energy of the cylindrical shell structure is: Then the Lagrangian function of the coupling structure of the cylindrical shell and the conical shell is expressed as:

3. The vibration analysis method of the cylindrical shell and conical shell coupling structure according to claim 1, characterized in that In S5, a variational operation is performed on the Lagrangian function, and the infinite expansion series is truncated at m = M and n = N to obtain a linear equation system with a dimension of 2×(M + 5)×(N + 5) + 3×(M + 3)×(N + 3). In matrix form, it is the coupling equation, expressed as (K - ω 2 M)E = 0, where M = diag[M cc M ll , E = [W c , U c , V c , W l , U l , V l T , where K is the system stiffness matrix, M is the system mass matrix, and E is the vector of unknown coefficients in the series expansion of the displacement function, that is ​ 4. The vibration analysis method of the cylindrical shell and conical shell coupling structure according to claim 1, characterized in that In S6, obtain the vibration displacement according to the vibration displacement expressions of the cylindrical shell and the conical shell under thermal load, and then draw the vibration mode and forced vibration results according to the displacement function to obtain the vibration results of the cone-cylindrical shell coupling system.

5. A system for analyzing the vibration performance of cylindrical shell and conical shell structures, characterized in that, Including: A memory; For storing a computer program; A processor. The processor is used to execute the computer program. When executing the computer program in the memory, the steps of the vibration analysis method of the coupling structure of the cylindrical shell and the conical shell as described in any one of claims 1-4 are implemented.

6. A storage medium, characterized in that, A computer program is stored in a storage medium. When the computer program is executed, the steps of the vibration performance analysis method for the cylindrical shell and the conical shell structure as described in any one of claims 1-4 are implemented.

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