Method and system for calculating natural vibration frequency of sectional type concrete fan tower tube structure

Abstract

The invention belongs to the technical field of tower drum design, and provides a sectional type concrete fan tower drum structure natural vibration frequency calculation method and system, and the method comprises the steps: building a uniform cross-section iron wood octanolean beam and a variable cross-section iron wood octanolean beam representing the tower drum structure; on the basis of the uniform-cross-section ironwood-octancarpus beam and the variable-cross-section ironwood-octancarpus beam, establishing a dynamic balance differential equation of the ironwood-octancarpus beam; on the basis of the Timoshensincaro beam dynamic balance differential equation, a homogeneous linear partial differential equation is obtained through decoupling; obtaining a characteristic value based on a homogeneous linear partial differential equation; according to the characteristic values, a rotation angle, a shearing force and a bending moment are obtained based on elastic mechanics, so that the natural vibration frequency of the fan tower drum is obtained; and compared with the eigenvalue analysis result of the Rayleigh-Ritz method, the error is reduced, and the precision requirement of the preliminary design stage is met.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of tower design, and particularly relates to a segmented concrete wind turbine tower structure natural vibration frequency calculation method and system. BACKGROUND

[0002] When the wind turbine is running, periodic excitation generated by blade rotation is coupled with the natural frequency of the tower, which will trigger a catastrophic resonance effect - especially the whole machine pendulum caused by 1P frequency will lead to the rupture of the foundation anchor bolt, and the local high-frequency vibration caused by 3P frequency will accelerate the fatigue cracking of the joint. Therefore, the natural frequency of the tower must be kept above the preset safety margin of 1P / 3P frequency, which means that the frequency prediction deviation exceeding the preset percentage may lead to the design falling into the resonance danger zone.

[0003] In current engineering practice, the natural frequency analysis of the wind turbine tower mainly relies on the finite element method (FEM). Due to the increasing complexity of the tower structure, the time for single modeling is as long as 4-6 hours, and the time for single calculation is as long as 5-10 hours. At the initial design stage, the parameters such as diameter-thickness ratio and structure height need to be adjusted repeatedly, and each modification requires re-meshing and dynamic analysis. The iteration cycle of a single scheme generally needs 24 hours, which is high in cost and long in period, and seriously restricts the design process of the tower. SUMMARY

[0004] To solve the above problems, the application provides a segmented concrete wind turbine tower structure natural vibration frequency calculation method and system. The application establishes an equal-section Timoshenko beam and a variable-section Timoshenko beam model of the tower structure. Based on the equal-section Timoshenko beam and the variable-section Timoshenko beam model, a Timoshenko beam dynamic balance differential equation is established. Based on the Timoshenko beam dynamic balance differential equation, a homogeneous linear partial differential equation is decoupled. Based on the homogeneous linear partial differential equation, eigenvalues are obtained. According to the eigenvalues, the rotation angle, shear force and bending moment are obtained based on the elasticity, so as to obtain the natural vibration frequency of the wind turbine tower. Compared with the Rayleigh-Ritz method eigenvalue analysis result, the error is reduced, and the accuracy requirement of the preliminary design stage is met.

[0005] To achieve the above purpose, the application realizes the technical scheme as follows: In a first aspect, the application provides a segmented concrete wind turbine tower structure natural vibration frequency calculation method, which comprises: establishing an equal-section Timoshenko beam and a variable-section Timoshenko beam model of the tower structure; based on the equal-section Timoshenko beam and the variable-section Timoshenko beam model, establishing a Timoshenko beam dynamic balance differential equation; based on the Timoshenko beam dynamic balance differential equation, decoupling to obtain a homogeneous linear partial differential equation; Based on the homogeneous linear partial differential equation, eigenvalues ​​are obtained; based on the eigenvalues, rotation angle, shear force, and bending moment are obtained using elasticity, thus yielding the natural frequency of the wind turbine tower.

[0006] Furthermore, in the constant cross-section Timoshenko beam and the variable cross-section Timoshenko beam, the blades, nacelles, and hubs are simplified as a single mass point.

[0007] Furthermore, for a Timoshenko beam with a uniform cross-section, its dynamic equilibrium differential equation is: ; ; in, E and G These are the elastic modulus and the shear modulus, respectively. I The moment of inertia of the cross section; A The cross-sectional area; Mass density; The coefficient of shear force non-uniformity at the cross section; For thickness; decoupling yields a fourth-order homogeneous linear partial differential equation with constant coefficients: ; For resonant excitation : ; Eigenvalues ​​can be obtained and Let the solution to the partial differential equation be: ; in, C 1. C 2. C 3 and C 4 represents the undetermined coefficients of the differential equation, which are solved based on the boundary conditions.

[0008] Furthermore, the rotation angle is obtained using methods of elasticity. Shear force and bending moment : ; ; .

[0009] Furthermore, for Timoshenko beams with non-uniform cross-sections, the height is discretized as follows: N Each section has undetermined coefficients for displacement, rotation, shear force, and bending moment. , , and Linear functions, a total of 4N There are several undetermined coefficients; the upper and lower interfaces of the cylinder section satisfy the conditions for continuity of displacement, rotation, shear force, and bending moment. Let the first coefficient be... n The height of each section is H n Thus, the boundary conditions for the variable cross-section Timoshenko beam are obtained.

[0010] Furthermore, when the excitation form is horizontal displacement at the bottom fixed end... At that time, add two boundary conditions: ; The above are 4 in total N A set of 4 boundary conditions are formed. N A system of linear equations of order 4, from which the fourth order is derived. N After determining the coefficients, we obtain the expressions for the displacement, rotation angle, shear force, and bending moment of each section; when the excitation mode is a bottom fixed end rotation angle At that time, the boundary conditions are: .

[0011] Furthermore, when considering the joints of concrete segments, the joints are treated as independent cylindrical sections, and a material constant for the joints is set for calculation; the first... N Fixed-end moment of each cylinder section M z=H and fixed-end shear force V z=H The fixed-end moment, fixed-end shear force, fixed-end horizontal displacement, and fixed-end rotation are: ; in, Let be the mass of the tower; the real part of the eigenvalue is the natural frequency of the wind turbine tower.

[0012] Secondly, the present invention also provides a system for calculating the natural frequency of a segmented concrete wind turbine tower structure, comprising: The Timoshenko beam creation module is configured to: create Timoshenko beams with constant cross-sections and Timoshenko beams with variable cross-sections representing the tower structure; The module for establishing dynamic equilibrium differential equations is configured to: establish dynamic equilibrium differential equations for Timoshenko beams based on Timoshenko beams with uniform cross-sections and Timoshenko beams with variable cross-sections; The module for establishing homogeneous linear partial differential equations is configured to: decouple and obtain homogeneous linear partial differential equations based on the Timoshenko beam dynamic equilibrium differential equations. The solution module is configured to: obtain eigenvalues ​​based on homogeneous linear partial differential equations; and obtain rotation angle, shear force, and bending moment based on elasticity using the eigenvalues, thereby obtaining the natural frequency of the wind turbine tower.

[0013] Thirdly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in the first aspect.

[0014] Fourthly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the program to implement the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in the first aspect.

[0015] Fifthly, the present invention also provides a computer program product, the computer program product comprising a computer program, which, when executed by a processor, implements the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in the first aspect.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention establishes models of Timoshenko beams with constant and variable cross-sections for the tower structure; based on these models, it establishes dynamic equilibrium differential equations for the Timoshenko beams; based on these equations, it decouples and obtains homogeneous linear partial differential equations; based on these equations, it obtains eigenvalues; and based on these eigenvalues, it obtains rotation angle, shear force, and bending moment using elasticity, thereby obtaining the natural frequency of the wind turbine tower. Compared with the eigenvalue analysis results of the Rayleigh-Ritz method, this invention reduces errors and meets the accuracy requirements of the preliminary design stage. Attached Figure Description

[0017] The accompanying drawings, which form part of this embodiment, are used to provide a further understanding of this embodiment. The illustrative embodiments and their descriptions are used to explain this embodiment and do not constitute an improper limitation of this embodiment.

[0018] Figure 1 This is the Timoshenko beam model of Embodiment 1 of the present invention; Figure 2 This is the calculation model for Embodiment 1 of the present invention. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0021] Timoshenko beams employ the plane section assumption and the linear assumption, but allow the deformed section to be non-perpendicular to the axis. They can simultaneously consider bending and shear deformation, making them particularly suitable for short beams.

[0022] Example 1: As the global energy structure accelerates its transformation towards cleaner and lower-carbon energy, wind power, as one of the most technologically mature and commercially viable renewable energy sources, is ushering in unprecedented development opportunities. In wind turbine systems, the tower, as the core load-bearing structure supporting the 100-meter-long blades and heavy nacelle, has its dynamic characteristics directly impacting the overall safety and service life of the turbine. Tower structural failures account for up to one-third of wind farm accidents, with fatigue damage caused by resonance being a significant contributing factor. When the wind turbine is running, the periodic excitation generated by the blade rotation coincides with the tower's natural frequency, triggering a catastrophic resonance effect—especially since whole-machine swaying caused by 1 times the rotational frequency (1P frequency) can lead to foundation anchor bolt fracture, while localized high-frequency vibrations excited by 3 times the rotational frequency (3P frequency) can accelerate joint fatigue cracking. Therefore, the tower's natural frequency must maintain a safety margin of ±10% or more compared to the 1P / 3P frequencies. This means that frequency prediction deviations can cause the structural frequency to fall into the resonance danger zone.

[0023] As described in the background section, current engineering practice primarily relies on the finite element method (FEM) for analyzing the natural frequency of wind turbine towers. While this method ensures accuracy in the detailed design phase, it faces significant challenges in the preliminary design stage. Due to the increasing complexity of tower structures, a single modeling session can take 4-6 hours, and a single calculation can take 5-10 hours. Furthermore, in the initial design phase, parameters such as the diameter-to-thickness ratio and structural height need repeated adjustments, requiring re-meshing and dynamic analysis for each modification. The iteration cycle for a single design typically takes 24 hours. This high-cost, long-cycle analysis model severely restricts the modern design process of "rapid solution verification → parameter sensitivity analysis → economic trade-offs," especially given the trend towards larger wind turbines, necessitating the development of new computational tools within the industry.

[0024] To address at least one of the aforementioned problems, this embodiment provides a method for calculating the natural frequency of a segmented concrete wind turbine tower structure, aiming to provide reliable data and an efficient, scientific solution for the preliminary design stage of tower engineering. The method is based on Timoshenko beam theory, establishing an equivalent stiffness matrix to describe the variable cross-section characteristics. For the unique transverse joint structure of concrete towers, an innovative joint embedding method is proposed. The method specifically includes: S1. The tower structure is simplified to a variable cross-section Timoshenko beam, and the blades, nacelle, and hub are simplified as a point mass. The tower structure height is... H Thickness is t The outer radius of the base is The outer radius of the top surface is The tower structure material parameters are mass density. shear wave velocity Viscous damping coefficient The total mass of the blades, nacelle, and hub is .

[0025] S2. This embodiment mainly includes two parts: the first part is the calculation method of the uniform cross-section Timoshenko beam, and the second part is the dynamic analysis of the variable cross-section tower and the treatment method of the joint of the concrete tower section.

[0026] S2.1, Part One is described as follows: set up z For height variables, t For time variables, u ( z , t () represents the horizontal displacement. For the rotation angle, the dynamic equilibrium differential equation of the Timoshenko beam with uniform cross-section is: ; ; in, E and G These are the elastic modulus and the shear modulus, respectively. I The moment of inertia of the cross section; A The cross-sectional area; Mass density; The shear force non-uniformity coefficient represents the actual shear stiffness relative to the nominal shear stiffness. GA The magnification factor is 2 for thin-walled circular rings.

[0027] Decoupling the above equation yields a fourth-order homogeneous linear partial differential equation with constant coefficients: ; For resonant excitation (circular frequency) Its characteristic equation is: ; This yields the eigenvalues. and Suppose that the solution to the partial differential equation is of the following form: ; in, C 1. C 2. C 3 and C 4 represents the undetermined coefficients of the differential equation, which are solved based on the boundary conditions.

[0028] The rotation angle is obtained by the method of elasticity. Shear force and bending moment The expression is as follows: ; ; ; When considering material damping, the complex modulus of elasticity is used. E * and shear modulus G * Replacing the real modulus: .

[0029] S2.2, Part Two is described as follows: For a Timoshenko beam with a non-uniform cross section, discretize it along its height as follows: N Each section has undetermined coefficients for displacement, rotation, shear force, and bending moment. , , and linear functions ( n =1, 2, … , N ), a total of 4 N There are several undetermined coefficients. The upper and lower interfaces of the cylinder section should satisfy the conditions for continuity of displacement, rotation, shear force, and bending moment. Let the first coefficient be... n The height of each section is H n The boundary conditions for the variable cross-section Timoshenko beam can be obtained as follows: ; When the excitation mode is horizontal displacement of the bottom fixed end At this time, two boundary conditions need to be added: ; The above are 4 in total N A set of 4 boundary conditions can be formed. N A system of linear equations of order 4, from which the fourth order is derived. N After determining the undetermined coefficients, the expressions for the displacement, rotation angle, shear force, and bending moment of each section can be obtained. When the excitation mode is a fixed-end rotation angle at the bottom... When (the corner is located) xoz (Plane), boundary conditions are: ; The same steps can be used to determine the undetermined coefficients and obtain the expressions for each physical quantity.

[0030] When considering the splice joints of concrete segments, the splice joint is treated as an independent cylindrical section, and a material constant for the splice joint is set for calculation.

[0031] Find the first N Fixed-end moment of each cylinder section Mz=H and fixed-end shear force V z=H The fixed-end moment, fixed-end shear force, fixed-end horizontal displacement, and fixed-end rotation angle are expressed in the following forms: ; in, m s The mass of the tower can be calculated based on its geometric dimensions and density.

[0032] The right side of the above equation has eigenvalues, and the eigenvalue with the smallest modulus is meaningful to the problem. The real part of the eigenvalue is the natural frequency of the wind turbine tower. ,Right now The natural frequency of a wind turbine tower is typically 0.2Hz-1Hz. An initial value of 0.2Hz can be used for iterative calculations. Alternatively, the incident frequency can be traversed within the range of 0-2Hz. The incident frequency that maximizes the absolute values ​​of shear force and bending moment is the structural frequency of the wind turbine tower.

[0033] S3. Verification and Examples: The Rayleigh-Ritz method is an approximate numerical method based on variational principles, which can calculate the natural frequencies and mode shapes of beams and plates. The first-order natural frequency of a straight bar with a uniform cross-section calculated using the Rayleigh-Ritz method is: ; Let the length of the annular concrete straight bar with uniform cross-section be... H The concrete grade is C80, and the mass density is 2500. The elastic modulus is 38 GPa, Poisson's ratio is 0.18, and the damping coefficient is 0.03; or the length of a straight rod with a uniform cross-section made of ring steel is... H The steel grade is Q355, and the mass density is 7850. The elastic modulus is 206 GPa, Poisson's ratio is 0.3, and the damping coefficient is 0.02. Table 1 shows a comparison between the first-order natural frequencies calculated by the method in this embodiment and those calculated by the Rayleigh-Ritz method. Table 1 Comparison of First-Order Natural Frequencies

[0034] A certain wind turbine tower is a steel-concrete wind turbine tower, with concrete grade C80 and mass density of 2500. The elastic modulus is 38 GPa, Poisson's ratio is 0.18, and the damping coefficient is 0.03; the steel grade is Q355, and the mass density is 7850. The elastic modulus is 206 GPa, Poisson's ratio is 0.3, and the damping coefficient is 0.02. The concrete tower section consists of 30 sections with a joint width of 10 mm. The joint adhesive has an elastic modulus of 8 GPa, a Poisson's ratio of 0.3, and a damping coefficient of 0.03. The total mass of the blades, nacelle, and hub at the top of the tower structure is... The natural frequencies of the wind turbine tower under various common operating conditions are shown in Table 2.

[0035] Table 2 Natural frequencies of wind turbine towers under various common operating conditions

[0036] Example 2: A system for calculating the natural frequency of a segmented concrete wind turbine tower structure includes: The Timoshenko beam creation module is configured to: create Timoshenko beam models with constant cross-section and Timoshenko beam models with variable cross-section for tower structures; The module for establishing dynamic equilibrium differential equations is configured to: establish dynamic equilibrium differential equations for Timoshenko beams based on constant cross-section Timoshenko beam and variable cross-section Timoshenko beam models; The module for establishing homogeneous linear partial differential equations is configured to: decouple and obtain homogeneous linear partial differential equations based on the Timoshenko beam dynamic equilibrium differential equations. The solution module is configured to: obtain eigenvalues ​​based on homogeneous linear partial differential equations; and obtain rotation angle, shear force, and bending moment based on elasticity using the eigenvalues, thereby obtaining the natural frequency of the wind turbine tower.

[0037] The working method of the system is the same as the method for calculating the natural frequency of the segmented concrete wind turbine tower structure in Example 1, and will not be repeated here.

[0038] Example 3: This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in Embodiment 1.

[0039] Example 4: This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the program, it implements the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in Embodiment 1.

[0040] Example 5: This embodiment provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in Embodiment 1.

[0041] The above description is merely a preferred embodiment of this practice and is not intended to limit the scope of this practice. Various modifications and variations can be made to this practice by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this practice should be included within the protection scope of this practice.

Claims

1. A method for calculating the natural frequency of a segmented concrete wind turbine tower structure, characterized in that, include: Models of constant-section and variable-section Timoshenko beams for tower structures were established. Based on Timoshenko beams with constant and variable cross sections, the dynamic equilibrium differential equations of Timoshenko beams are established. Based on the Timoshenko beam dynamic equilibrium differential equation, the homogeneous linear partial differential equation is obtained by decoupling. Based on the homogeneous linear partial differential equation, the eigenvalues ​​are obtained; Based on the eigenvalues, the rotation angle, shear force, and bending moment are obtained using elasticity mechanics, thus yielding the natural frequency of the wind turbine tower.

2. The method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in claim 1, characterized in that, In the constant cross-section Timoshenko beam and the variable cross-section Timoshenko beam, the blades, nacelles, and hubs are simplified as a single mass point.

3. The method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in claim 1, characterized in that, For a Timoshenko beam with a uniform cross-section, the dynamic equilibrium differential equation is: ； ； in, E and G These are the elastic modulus and the shear modulus, respectively. I The moment of inertia of the cross section; A The cross-sectional area; Mass density; The coefficient of shear force non-uniformity at the cross section; t For thickness; decoupling yields a fourth-order homogeneous linear partial differential equation with constant coefficients: ； For resonant excitation : ； This yields the eigenvalues. and Let the solution to the partial differential equation be: ； in, C 1. C 2. C 3 and C 4 represents the undetermined coefficients of the differential equation, which are solved based on the boundary conditions.

4. The method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in claim 3, characterized in that, The rotation angle is obtained by the method of elasticity. Shear force and bending moment : ； ； 。 5. The method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in claim 3, characterized in that, For a Timoshenko beam with a non-uniform cross section, discretized along the height as follows: N Each section has undetermined coefficients for displacement, rotation, shear force, and bending moment. , , and Linear functions, a total of 4 N There are several undetermined coefficients; the upper and lower interfaces of the cylinder section satisfy the conditions for continuity of displacement, rotation, shear force, and bending moment. Let the first coefficient be... n The height of each section is H n Thus, the boundary conditions for the variable cross-section Timoshenko beam are obtained.

6. The method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in claim 5, characterized in that, When the excitation mode is horizontal displacement of the bottom fixed end At that time, two boundary conditions are added: ； The above are 4 in total N A set of 4 boundary conditions are formed. N A system of linear equations of order 4, from which the fourth order is derived. N After determining the coefficients, we obtain the expressions for the displacement, rotation angle, shear force, and bending moment of each section; when the excitation mode is a bottom fixed end rotation angle At that time, the boundary conditions are: 。 7. The method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in claim 6, characterized in that, When considering the splices of concrete segments, the splices are treated as independent cylindrical sections, and a material constant for the splices is set for calculation; the first... N Fixed-end moment of each cylinder section M z=H and fixed-end shear force V z=H The fixed-end moment, fixed-end shear force, fixed-end horizontal displacement, and fixed-end rotation are: ； in, Let be the mass of the tower; the real part of the eigenvalue is the natural frequency of the wind turbine tower.

8. A system for calculating the natural frequency of a segmented concrete wind turbine tower structure, characterized in that, include: The Timoshenko beam creation module is configured to: create Timoshenko beams with constant cross-sections and Timoshenko beams with variable cross-sections representing the tower structure; The module for establishing dynamic equilibrium differential equations is configured to: establish dynamic equilibrium differential equations for Timoshenko beams based on Timoshenko beams with uniform cross-sections and Timoshenko beams with variable cross-sections; The module for establishing homogeneous linear partial differential equations is configured to: decouple and obtain homogeneous linear partial differential equations based on the Timoshenko beam dynamic equilibrium differential equations. The solution module is configured to obtain eigenvalues ​​based on homogeneous linear partial differential equations. Based on the eigenvalues, the rotation angle, shear force, and bending moment are obtained using elasticity mechanics, thus yielding the natural frequency of the wind turbine tower.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the program, it implements the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the steps of the method for calculating the natural frequency of a segmented concrete wind turbine tower structure as described in any one of claims 1-6.

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