A method for detecting damping loss factor of transmission pipeline

Abstract

The present application provides a method for detecting the damping loss factor of a transmission pipeline, which relates to the technical field of material mechanics. The method comprises: obtaining the measured motion response and strain response of the target cylindrical shell based on a preset vibration excitation and load applied to the target cylindrical shell; calculating the target kinetic energy of the target cylindrical shell based on the motion response, and calculating the target strain energy of the target cylindrical shell based on the strain response; calculating the Lagrangian according to the target kinetic energy and target strain energy; calculating the total energy dissipated by the target cylindrical shell through the form according to the target kinetic energy and the specific damping capacity of the target cylindrical shell; calculating the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation, and the target strain energy; and calculating the structural damping loss factor of the target cylindrical shell based on the damping loss factors in each direction according to the modal strain energy method. The present application can improve the accuracy of the damping loss factor calculation of cylindrical shell materials.

Description

Technical Field

[0001] The present application relates to the technical field of material mechanics, and in particular to a method for detecting the damping loss factor of a transmission pipeline. Background Art

[0002] The damping loss factor is a key parameter that measures the ability of a material or structure to dissipate energy during vibration. During vibration or fluctuation, some mechanical energy is converted into heat due to factors such as internal friction, air resistance, and internal friction within the material, gradually attenuating the vibration amplitude. The damping loss factor is used to quantify this energy dissipation. The damping loss factor can be understood as a system's ability to "decelerate" vibration. A larger value for this factor indicates a faster damping of the system's vibration and a greater energy loss. A smaller value indicates a longer duration of vibration and a lower energy loss.

[0003] In engineering applications, the damping loss factor is a crucial parameter in the design and analysis of vibration and noise control. By adjusting the damping characteristics of a structure, unwanted vibration and noise can be effectively reduced, thereby improving its performance and lifespan. Traditional structural damping analysis methods typically assume that the material is isotropic, assuming that the damping characteristics of the material are the same in all directions. This approach may be suitable for some simple structures or homogeneous materials, but for complex structures, especially multilayer composite materials or orthotropic materials, this assumption can lead to inaccurate analysis results. Therefore, a method is needed to improve the accuracy of the damping loss factor calculation for cylindrical shell materials. Summary of the Invention

[0004] The present application provides a method for detecting the damping loss factor of a transmission pipeline, which can improve the accuracy of calculating the damping loss factor of a cylindrical shell material.

[0005] In a first aspect of the present application, a method for detecting a damping loss factor of a transmission pipeline is provided, the method comprising:

[0006] Based on a preset vibration excitation applied to the target cylindrical shell, a motion response of the target cylindrical shell is obtained, and based on a load applied to the target cylindrical shell, a strain response of the target cylindrical shell is obtained;

[0007] Calculating a target kinetic energy of the target cylindrical shell based on the motion response, and calculating a target strain energy of the target cylindrical shell based on the strain response;

[0008] calculating a Lagrangian according to the target kinetic energy and the target strain energy;

[0009] Calculating the total energy dissipated by the target cylindrical shell in a certain manner according to the target kinetic energy and the specific damping capacity of the target cylindrical shell;

[0010] Calculating the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation and the target strain energy;

[0011] According to the modal strain energy method, based on the damping loss factors in various directions, the structural damping loss factor of the target cylindrical shell is calculated.

[0012] Optionally, the damping loss factor of the target cylindrical shell in each direction is calculated according to the Lagrangian, the total energy dissipation, and the target strain energy, and is calculated by the following formula:

[0013]

[0014] Among them, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction, ΔU is the total energy consumption, U max is the target strain energy.

[0015] Optionally, after calculating the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation, and the target strain energy, the method further includes:

[0016] According to the motion response, the stress components of the target cylindrical shell are analyzed, and then the stress vector of the target cylindrical shell is calculated, which is specifically calculated by the following formula:

[0017] {σ} T ={σ x ,σ θ ,σ xθ}

[0018] Among them, {σ} T is the stress matrix, σ x is the normal stress in the x direction, σ θ is the normal stress in the θ direction, σ xθ for x-θ Shear stress on a plane;

[0019] According to the strain response, the strain vector of the target cylindrical shell is analyzed and specifically calculated using the following formula:

[0020] {e} T ={e x , e θ , e xθ}

[0021] Among them, {e} T is the strain matrix, ex is the normal strain in the x direction, e θ is the normal strain in the θ direction, e xθ for x-θ Shear strain on a plane;

[0022] The relationship between the stress vector and the strain vector is as follows:

[0023] {σ}=[Q] T {e}

[0024] Where, {σ} is the stress vector, {e} is the strain vector, [Q] T is the reduced stiffness matrix after transformation;

[0025] The reduced stiffness matrix after the conversion is expressed as follows:

[0026]

[0027] Among them, [Q] T is the transformed reduced stiffness matrix, Q ij is the reduced stiffness, i, j∈(1,2,6).

[0028] Optionally, calculating the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation, and the target strain energy specifically includes:

[0029] The total energy consumption is calculated based on the stress vector and the strain vector, specifically using the following formula:

[0030]

[0031] Wherein, ΔU is the total energy consumption, L is the Lagrangian, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction respectively.

[0032] Optionally, the calculating of the structural damping loss factor of the target cylindrical shell based on the damping loss factors in various directions according to the modal strain energy method specifically includes:

[0033] The structural damping loss factor is calculated based on the following formula:

[0034]

[0035] Wherein, η is the structural damping loss factor, ΔU is the total energy consumption, U max is the target strain energy.

[0036] Optionally, the Lagrangian is calculated according to the target kinetic energy and the target strain energy, specifically by the following formula:

[0037] L=T max -U max

[0038] Wherein, L is the Lagrangian, T max is the target kinetic energy, U max is the target strain energy;

[0039] Obtaining the length and density of the target cylindrical shell;

[0040] The strain energy of the target cylindrical shell is calculated based on the length of the target cylindrical shell, specifically by the following formula:

[0041]

[0042] Where U is the strain energy, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix;

[0043] Based on the length and density of the target cylindrical shell, the kinetic energy of the target cylindrical shell is calculated, specifically using the following formula:

[0044]

[0045] Wherein, T is the kinetic energy, h is the length of the target cylindrical shell, ρ is the density of the target cylindrical shell, u0, v0, w0 are the displacement components of a point on the midplane (i.e., z=0) along the (x, θ, z) coordinate direction respectively.

[0046] Optionally, calculating the target kinetic energy of the target cylindrical shell based on the motion response amount, and calculating the target strain energy of the target cylindrical shell based on the strain response amount, specifically includes:

[0047] At both ends of the target cylindrical shell (x=0, h), the assumed displacement field expression is as follows:

[0048]

[0049] Where u0, v0, and w0 are the displacement components of a point on the midplane (i.e., z = 0) along the (x, θ, z) coordinate direction, A, B, and C are the magnitudes of the displacement amplitudes, m is the axial wave number, n is the circumferential wave number, and ω is the vibration angular frequency.

[0050] Based on the principle of minimum potential energy, the Lagrangian equation for the energy function is constructed as follows:

[0051]

[0052] Among them, A, B and C are the magnitudes of the displacement amplitude, T max is the target kinetic energy, U max is the target strain energy;

[0053] Based on the Lagrange equation, the control characteristic equation is obtained as follows:

[0054]

[0055] Among them, C ij are the coefficients in the equation, A, B and C are the magnitudes of the displacement amplitudes;

[0056] Solving for the roots by imposing the conditions for non-trivial solutions to the governing characteristic equation yields the following determinant:

[0057] α0ω 6 +α1ω 4 +α2ω 2 +α3=0

[0058] Among them, α i (i=0, 1, 2, 3) is a constant, ω is the angular frequency of vibration;

[0059] Solving the vibration angular frequency according to the determinant;

[0060] The vibration angular frequency is substituted into the displacement field expression to calculate the target strain energy and the target kinetic energy.

[0061] In a second aspect of the present application, a device for detecting a damping loss factor of a transmission pipeline is provided. The device includes an acquisition module and a processing module, wherein:

[0062] The acquisition module is configured to acquire a measured motion response of the target cylindrical shell based on a preset vibration excitation applied to the target cylindrical shell, and to acquire a measured strain response of the target cylindrical shell based on a load applied to the target cylindrical shell;

[0063] The processing module is configured to calculate a target kinetic energy of the target cylindrical shell based on the motion response amount, and calculate a target strain energy of the target cylindrical shell based on the strain response amount;

[0064] The processing module is configured to calculate a Lagrangian according to the target kinetic energy and the target strain energy;

[0065] The processing module is configured to calculate the total energy dissipated by the target cylindrical shell in a certain form according to the target kinetic energy and the specific damping capacity of the target cylindrical shell;

[0066] The processing module is configured to calculate the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation, and the target strain energy;

[0067] The processing module is used to calculate the structural damping loss factor of the target cylindrical shell based on the damping loss factors in various directions according to the modal strain energy method.

[0068] In the third aspect of the present application, an electronic device is provided, including a processor, a memory, a user interface and a network interface, the memory is used to store instructions, the user interface and the network interface are both used to communicate with other devices, and the processor is used to execute the instructions stored in the memory so that the electronic device performs any of the methods described above.

[0069] In a fourth aspect of the present application, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores instructions. When the instructions are executed, any one of the methods described above is executed.

[0070] In summary, one or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:

[0071] This application can improve the accuracy of the calculation of the damping loss factor of cylindrical shell materials by combining measured data with an accurate energy calculation method. The principle is to obtain the motion and strain response of the cylindrical shell based on the preset vibration excitation, thereby calculating the target kinetic energy and target strain energy respectively, and then using the Lagrangian to calculate the total energy consumption of the system. In addition, combined with the specific damping capacity, the energy dissipation is converted into the damping loss factor in each direction, thereby avoiding the error of the isotropy assumption in traditional analysis. This process more accurately reflects the true damping characteristics of the material in different directions through the modal strain energy method, thereby greatly improving the accuracy of the damping loss factor calculation.

[0072] By incorporating the anisotropic properties of materials and combining them with precise energy analysis methods, a detailed calculation of the damping loss factor for cylindrical shells in all directions is achieved. This method considers the effects of stress and strain in different directions, avoiding the errors caused by traditional methods that ignore material anisotropy. By calculating the structural damping loss factor based on the modal strain energy method, the actual damping behavior of the target cylindrical shell can be more accurately described, thereby improving the accuracy and reliability of the damping calculations and facilitating more precise structural design and performance prediction.

[0073] By precisely constructing the governing equations based on the Lagrangian and combining the vibration characteristics of the cylindrical shell with the stress-strain relationship, the kinetic energy and strain energy of the target cylindrical shell are accurately calculated. By solving the governing characteristic equations, the angular frequency of vibration is obtained, and the kinetic energy and strain energy of the structure are further calculated. This process utilizes the principle of minimum potential energy and effectively considers the influence of the energy distribution of the structure during vibration, thereby improving the accuracy of the calculation results. This method can more accurately predict the dynamic performance of the structure, facilitate design optimization, and improve structural stability and seismic resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 This is a flow chart of a method for detecting the damping loss factor of a transmission pipeline disclosed in an embodiment of the present application;

[0075] Figure 2 Schematic diagram of the structure of a target cylindrical shell disclosed in an embodiment of the present application;

[0076] Figure 3 This is a schematic diagram of an angle difference disclosed in an embodiment of the present application;

[0077] Figure 4 This is a module schematic diagram of a device for detecting the damping loss factor of a transmission pipeline disclosed in an embodiment of the present application;

[0078] Figure 5 This is a structural diagram of an electronic device disclosed in an embodiment of the present application.

[0079] Description of the accompanying drawings: 401, acquisition module; 402, processing module; 501, processor; 502, communication bus; 503, user interface; 504, network interface; 505, memory. DETAILED DESCRIPTION

[0080] In order to enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below in conjunction with the drawings in the embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this application, not all of the embodiments.

[0081] In the description of the embodiments of this application, words such as "for example" or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "for example" or "for instance" in the embodiments of this application should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "for example" or "for instance" is intended to present the relevant concepts in a concrete manner.

[0082] In the description of the embodiments of the present application, the term "multiple" means two or more. For example, multiple systems refer to two or more systems, and multiple screen terminals refer to two or more screen terminals. In addition, the terms "first" and "second" are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly indicating the indicated technical features. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized.

[0083] This embodiment discloses a method for detecting the damping loss factor of a transmission pipeline. Figure 1 , including the following steps S110-S150:

[0084] S110 , based on a preset vibration excitation applied to the target cylindrical shell, obtaining a measured motion response of the target cylindrical shell, and based on a load applied to the target cylindrical shell, obtaining a measured strain response of the target cylindrical shell.

[0085] The target cylindrical shell in this application is a laminated cylindrical shell, which is a water delivery pipe for submarines. Figure 2 , is a cylindrical structure composed of multiple laminated composite materials, composed of steel, polyurethane and composite materials from the inside to the outside, and is mainly used as a water pipe for submarines. Because this structure has a high strength, stiffness and weight ratio, and its performance can be optimized by rationally designing the material properties of each layer. Laminated cylindrical shells are made up of multiple composite layers stacked together, and each layer usually has different fiber direction, thickness and material properties. Each layer has different mechanical properties, and the overall structure formed by these layers stacked together has complex anisotropic mechanical properties.

[0086] The target kinetic energy is the maximum kinetic energy of the target cylindrical shell. Kinetic energy is the energy possessed by an object due to its motion. For a vibrating system (such as a cylindrical shell), the kinetic energy is related to its vibration velocity and mass distribution. The maximum kinetic energy represents the maximum value the system's kinetic energy reaches during the entire vibration process. Typically, this occurs when the structure's vibration velocity is at its maximum, meaning when the vibration displacement reaches zero.

[0087] The target strain energy is the maximum strain energy of the target cylindrical shell. Strain energy is the elastic energy stored in a structure due to deformation. When an elastic body (such as a cylindrical shell) deforms due to an external force, stress and strain are generated within the material, thereby storing energy. This stored energy is strain energy. The maximum strain energy represents the strain energy at the point of maximum deformation during the entire vibration cycle. This typically occurs when the system's displacement reaches its maximum and its velocity reaches zero.

[0088] In order to calculate the target kinetic energy of the target cylindrical shell, it is necessary to apply vibration excitation to the target cylindrical shell and select an appropriate excitation method, such as frequency sweep, impact test or white noise excitation, to stimulate the vibration response of the cylindrical shell. Accelerometers, displacement sensors or strain sensors are installed at different positions of the cylindrical shell to monitor the vibration response in real time. Time domain data under excitation, such as acceleration or displacement signals, are recorded. These signals reflect the dynamic behavior of the structure at different frequencies. The time domain data is then converted to the frequency domain using fast Fourier transform (FFT) to identify the main vibration modes and frequencies, extract the displacement and acceleration data corresponding to the main vibration frequencies, and use them to calculate the kinetic energy of the target cylindrical shell.

[0089] To calculate the target strain energy of the target cylindrical shell, a mechanical loading device applies a known static or dynamic load (e.g., concentrated force, distributed force, etc.) to deform the cylindrical shell. During the loading process, strain data is measured using strain gauges or digital image correlation (DIC). Strain gauges are installed at key locations on the cylindrical shell to record strain data under different loading conditions. Digital image correlation calculates strain by taking images before and after deformation. The measured strain data is combined with the geometric characteristics of the cylindrical shell to calculate the strain energy.

[0090] S120 , calculating a target kinetic energy of the target cylindrical shell based on the motion response amount, and calculating a target strain energy of the target cylindrical shell based on the strain response amount.

[0091] For the target cylindrical shell, the strain energy expression is as follows:

[0092]

[0093] Where U is the strain energy, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix. The strain matrix and stress matrix will be explained in the following content.

[0094] The kinetic energy expression of the target cylindrical shell is as follows:

[0095]

[0096] Where T is the kinetic energy, h is the length of the target cylindrical shell, ρ is the density of the target cylindrical shell, u0, v0, and w0 are the displacement components of a point on the midplane (i.e., z = 0) along the (x, θ, z) coordinate direction.

[0097] Classical shell theory is an extension of classical laminate theory. The Kirchhoff hypothesis in classical laminate theory also applies to classical shell theory. Assumptions: (1) Lines perpendicular to the mid-plane before deformation (i.e., transverse normals) remain straight after deformation; (2) transverse normals do not elongate (i.e., are inextensible); (3) transverse normals rotate so that they remain perpendicular to the mid-plane after deformation; (4) the layers are perfectly bonded together and each layer has uniform thickness; and (5) the transverse shear stress on the top and bottom surfaces of the shell is zero.

[0098] The Kirchhoff hypothesis requires that the displacement (u, v, w) satisfies the following conditions:

[0099]

[0100] w(x,θ,z,t)=w0(x,θ,t)

[0101] where u0, v0, and w0 are the displacement components along the (x, θ, z) coordinates at a point on the midplane (i.e., z = 0). The displacement field implies that a line perpendicular to the x-θ plane before deformation remains perpendicular to the midplane after deformation. The Kirchhoff assumption is equivalent to neglecting transverse shear and transverse normal effects, meaning that deformation is entirely due to bending and in-plane stretching.

[0102] Then, at both ends of the target cylindrical shell (x = 0, h), the assumed displacement field expression is as follows:

[0103]

[0104] Among them, u0, v0, and w0 are the displacement components of a point on the midplane (i.e., z=0) along the (x, θ, z) coordinate direction, respectively. A, B, and C are the magnitudes of the displacement amplitudes. The displacement amplitude determines the intensity or amplitude of the vibration. Different vibration modes may have different displacement amplitudes. m is the axial wave number, which determines the number of vibration modes along the x direction and describes the periodic characteristics of the vibration, that is, how many wave periods there are in the length direction of the shell. n is the circumferential wave number, which determines the number of vibration modes along the θ direction. Different n values ​​will lead to different vibration modes, such as symmetric modes and antisymmetric modes. ω is the angular frequency of vibration, which describes the frequency characteristics of the cylindrical shell in free vibration. It determines the vibration speed or periodicity of the system and is an important indicator of the natural frequency of the structure.

[0105] S130: Calculate the Lagrangian according to the target kinetic energy and the target strain energy.

[0106] In analytical mechanics, the Lagrangian of a dynamic system, also known as the Lagrangian function, or "Lagrangian" for short, is a function that describes the dynamic state of the entire physical system. For general classical physical systems, it is usually defined as kinetic energy minus potential energy. For the target cylindrical shell, the Rayleigh-Ritz method is used to calculate the natural frequency of the cylindrical shell. This is a variational method that derives the system's equation of motion and natural frequency by constructing the Lagrangian equation and combining it with the principle of minimum potential energy. First, the Rayleigh method constructs an energy functional, the Lagrangian, based on the relationship between the maximum values ​​of kinetic energy T and strain energy U:

[0107] L=T max -U max

[0108] Where L is the Lagrangian, T max is the target kinetic energy, U max is the target strain energy.

[0109] Based on the principle of minimum potential energy, the Lagrangian equation for the energy function is constructed as follows:

[0110]

[0111] Among them, A, B and C are the magnitudes of the displacement amplitude, T max is the target kinetic energy, U max is the target strain energy.

[0112] The principle of minimum potential energy is a key principle in the calculus of variations in mechanics. It states that for a statically balanced system, the total potential energy of the system is at its minimum in equilibrium. This principle is widely used in structural analysis and design optimization, particularly in solid mechanics, elasticity, and structural mechanics, to solve problems such as structural deformation, displacement, and stress distribution. In elasticity, total potential energy (also known as the potential energy functional) typically consists of two components: strain energy (representing the energy within the system) and the work done by external forces.

[0113] In dynamic problems, the Lagrange equation introduces the difference between kinetic energy T and potential energy U, the so-called Lagrange quantity L, which is expressed as: L = TU. For a vibrating system, using the principle of minimum potential energy, the Lagrange equation can be constructed in the form of:

[0114]

[0115] Here, A, B, and C are the displacement amplitudes of the system. Solving these equations yields the system's equilibrium position or vibration mode. In this context, the principle of minimum potential energy essentially involves finding the system's stable state under given conditions—that is, finding the conditions under which the Lagrangian L reaches its stationary value (minimum or maximum).

[0116] According to the Lagrange equation, kinetic energy expression and strain energy expression, the control characteristic equation is obtained as follows:

[0117]

[0118] Among them, C ij are the coefficients in the equation, and A, B, and C are the magnitudes of the displacement amplitudes. The roots are solved by imposing nontrivial solution conditions on the governing characteristic equation, which is the determinant [C ij ] is equal to zero, we can get the following determinant:

[0119] α0ω 6 +α1ω 4 +α2ω 2 +α3=0

[0120] Among them, α i (i=0, 1, 2, 3) is a constant, and ω is the vibration angular frequency. By using the eigenvalue and eigenvector functions of matlab, the above is about ω 2 The third-order equation has three pairs of different angular frequencies, three positive roots and three negative roots, where the three positive roots represent the three angular frequencies of the cylindrical shell in the axial, circumferential and radial directions respectively. The minimum angular frequency is given priority. By substituting the obtained vibration angular frequency ω into the displacement field expression, the corresponding target strain energy U can be calculated. max and target kinetic energy T max , the calculation of these two energies is based on the previous integral expressions.

[0121] S140 , calculating the total energy dissipated by the target cylindrical shell in the form of a damping device according to the target kinetic energy and the specific damping capacity of the target cylindrical shell.

[0122] In a free vibration system, there is an energy exchange between kinetic energy and strain energy. When the system vibrates within a vibration cycle, kinetic energy and strain energy are periodically converted to each other. In the ideal case of no damping, this conversion is complete and there is no energy loss. However, in a real system with damping, a portion of the energy is dissipated due to the damping effect in each vibration cycle. The specific damping capacity (SDC) of a structure can be defined as the ratio of the total energy dissipated by the system in each stress cycle (i.e., dissipated energy) to the maximum strain energy of the system, which can be obtained as follows:

[0123]

[0124] Where, ψ is the specific damping capacity, η is the structural damping loss factor, ΔU is the total energy consumption, U max is the target strain energy.

[0125] According to the influence of the damping loss factor in different directions on energy dissipation, the dissipated energy in each direction can be expressed as:

[0126] ΔU x =2πη 11 U max

[0127] ΔU y =2πη 22 U max

[0128] ΔU xy =2πη 12 U max

[0129] The total energy dissipation ΔU is the sum of the energy dissipated in all directions, representing the energy dissipated by the system due to internal damping during the entire cycle. The total energy dissipation is expressed as follows:

[0130]

[0131] Among them, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction, ΔU is the total energy consumption, U max is the target strain energy.

[0132] In one possible implementation, for general orthotropic layers, the constitutive relation for laminated cylindrical shells under plane stress conditions is as follows:

[0133] {σ}=[Q] T {e}

[0134] Where {σ} is the stress vector, {e} is the strain vector, [Q] T is the reduced stiffness matrix after transformation.

[0135] Specifically, the Love shell theory is a type of classical elastic shell theory that is suitable for describing the deformation behavior of thin shell structures under external forces. A shell is a special structural form in which one dimension (thickness) is much smaller than the other two dimensions (length and width). Shells can withstand complex load conditions, including bending, torsion, tension, and compression. An important feature of thin shell structures is that their deformation mainly depends on geometric nonlinear effects. Using the Love shell theory, the strain components of the target cylindrical shell are defined as follows:

[0136] e x =e1+zk1

[0137] e θ =e2+zk2

[0138] e xθ =γ+2zτ

[0139] Where e1, e2 and γ are surface strains, and k1, k2 and τ are surface curvatures. Surface strain and surface curvature are defined as follows:

[0140]

[0141] Where u0, v0, and w0 are the displacement components of a point on the mid-plane (i.e., z = 0) along the (x, θ, z) coordinate direction, R is the radius of the target cylindrical shell, e1, e2, and γ are the surface strains, and k1, k2, and τ are the surface curvatures.

[0142] Once the mid-surface displacements (u0, v0, w0) are known, the strain at any point in the target cylindrical shell can be calculated using the equations above. The definition of the strain components for the target cylindrical shell shows that all strain components vary linearly with the thickness and are independent of the material variation through the shell thickness. For a fixed z value, the strain is typically a nonlinear function of x and θ, and for dynamic problems, it is time-dependent.

[0143] For general orthotropic layers, the constitutive relation of laminated cylindrical shells under plane stress conditions is as follows:

[0144] {σ}=[Q] T {e}

[0145] Where {σ} is the stress vector, {e} is the strain vector, [Q] T is the reduced stiffness matrix after transformation.

[0146] Orthotropic materials are materials with varying mechanical properties in different directions. These materials typically consist of fibers or laminates with varying physical properties in multiple directions. Orthotropic layers are a common model in composite material analysis. In an orthotropic layer, the material exhibits varying elastic moduli, shear moduli, and Poisson's ratio along three mutually perpendicular principal directions (commonly referred to as the 1, 2, and 3 directions).

[0147] A stress vector is a vector that contains the internal stress components of a structure or material. Under plane stress conditions, the stress matrix of the stress vector of an orthotropic material is usually expressed as:

[0148] {σ} T ={σ x ,σ θ ,σ xθ}

[0149] Among them, {σ} T is the stress matrix, σ xis the normal stress in the x direction, σ θ is the normal stress in the θ direction, σ xθ for x-θ Shear stress on a plane. The components of the stress vector represent the magnitude of the tensile, compressive, or shear stress experienced by the material in different directions. Understanding stress distribution is important for analyzing the behavior of a material under external loads.

[0150] The strain vector describes the degree of deformation of the material under stress. For a plane stress state, the strain matrix of the strain vector is usually expressed as:

[0151] {e} T ={e x , e θ , e xθ}

[0152] Among them, {e} T is the strain matrix, e x is the normal strain in the x direction, e θ is the normal strain in the θ direction, e xθ for x-θ Shear strain on a plane. The strain vector reflects the deformation of a material under load and is the key to describing the geometric changes of the material.

[0153] The reduced stiffness matrix is ​​a matrix used to describe the stress-strain relationship of an orthotropic material under plane stress conditions. It is the core part of the material constitutive relationship and characterizes the stiffness of the material in different directions. The reduced stiffness matrix is ​​usually expressed as:

[0154]

[0155] Among them, [Q] T is the transformed reduced stiffness matrix, Q ij is the reduced stiffness, i,j∈(1,2,6). For orthotropic materials, the stiffness matrix usually needs to undergo coordinate transformation (i.e. conversion) to adapt to the different laying directions of the material layer. The converted reduced stiffness matrix [Q] T Reflects the stiffness characteristics of the material at a specific laying angle.

[0156] Specifically, for orthotropic materials, the reduced stiffness Q ij (i, j = 1, 2, 6) can be expressed as:

[0157]

[0158] Among them E 11 and E 22 is Young's modulus, G 12 is the shear modulus; v 12and v 21 is Poisson's ratio; for orthotropic materials, the shell coordinate system is not consistent with the material coordinate system. In addition, refer to Figure 3 ,These laminated shells have multiple layers, and the material coordinates of each layer have different orientations relative to the shell coordinates, with an angle difference α, so the reduced stiffness needs to be converted.

[0159] After coordinate transformation, the stress and strain relationship of a single layer of material becomes:

[0160]

[0161] Among them, σ x is the normal stress in the x direction, σ θ is the normal stress in the θ direction, σ xθ for x-θ Shear stress on the plane, e x is the normal strain in the x direction, e θ is the normal strain in the θ direction, e xθ for x-θ Shear strain on the plane, Q ij is the reduced stiffness, i, j∈(1,2,6).

[0162] S150: Calculate the damping loss factor of the target cylindrical shell in each direction based on the Lagrangian, the total energy dissipation, and the target strain energy.

[0163] According to the expression formula of total energy consumption, stress matrix and strain matrix, the calculation formula of total energy consumption is obtained:

[0164]

[0165] Where ΔU is the total energy consumption, L is the Lagrangian, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction.

[0166] Damping loss factor η ij Describes the energy dissipation characteristics of the material in all directions. In the structural analysis of cylindrical shells, the damping loss factor usually affects the total energy dissipation of the system. The damping loss factor is expressed in matrix form:

[0167]

[0168] Among them, η 11 represents the damping loss factor of the target cylindrical shell in the x direction, η 22represents the damping loss factor of the target cylindrical shell in the θ direction, η 12 represents the shear damping loss factor of the target cylindrical shell in the x-θ plane.

[0169] The total energy dissipation formula represents the energy dissipated by the system through damping during a stress cycle. Integration calculates the total energy loss across the entire cylindrical shell structure. The damping loss factor matrix [η] converts strain energy into dissipated energy, ultimately yielding the total energy dissipation ΔU. This calculation method is suitable for analyzing complex structures, particularly those made of multilayer composite materials and laminated cylindrical shells. The combination of stress, strain, and damping factors allows for a precise description of the energy dissipation behavior of the structure.

[0170] S160: Calculate the structural damping loss factor of the target cylindrical shell based on the damping loss factors in various directions according to the modal strain energy method.

[0171] The modal strain energy method is a commonly used method for estimating the damping loss factor of a structure, and is particularly widely used in complex structures such as composite structures and laminate shells. This method is based on modal analysis and uses modal strain energy to calculate the energy distribution and dissipated energy of the structure during vibration, thereby obtaining the damping characteristics of the system. Modal analysis is a basic method for solving the vibration characteristics of a structure. Through modal analysis, the natural frequency and modal shape of the structure (that is, the vibration mode corresponding to each natural frequency) can be determined. For each mode (vibration mode), the total strain energy and kinetic energy of the system in this mode can be solved separately. The damping loss factor indicates the proportion of energy lost by the system to the total energy of the system in each vibration cycle. The modal strain energy method estimates the damping loss factor of the entire system by calculating the modal strain energy and corresponding loss factors of different parts.

[0172] First, the natural frequencies and corresponding modal shapes of the structure are solved by finite element analysis or other numerical methods. Each mode represents the vibration mode of the structure at a specific frequency. For each mode, the modal strain energy of different parts of the structure is calculated. For example, if it is a laminate structure, the strain energy of each layer of material needs to be calculated. The modal strain energy U j Through integration, we can get:

[0173]

[0174] Among them, {∈ j} is the strain generated by the modal shape in this part, and [C] is the elastic stiffness matrix of the material. Based on the constitutive damping characteristics of each part of the material (such as the material loss factor η of each layer), i), calculate the local damping loss factor of the part. Generally speaking, energy dissipation is related to the intrinsic damping performance of the material. According to the modal strain energy and local damping loss factor of each part, the modal damping loss factor of the overall structure η total It can be calculated by weighted average:

[0175]

[0176] Among them, U i is the modal strain energy of the i-th part, η i is the material loss factor of this part. In this way, the damping loss factor of the entire structure can be calculated.

[0177] According to the above principles, the structural damping loss factor is calculated based on the following formula:

[0178]

[0179] Among them, η is the structural damping loss factor, ΔU is the total energy consumption, U max is the target strain energy.

[0180] This application can improve the accuracy of the calculation of the damping loss factor of cylindrical shell materials by combining measured data with an accurate energy calculation method. The principle is to obtain the motion and strain response of the cylindrical shell based on the preset vibration excitation, thereby calculating the target kinetic energy and target strain energy respectively, and then using the Lagrangian to calculate the total energy consumption of the system. In addition, combined with the specific damping capacity, the energy dissipation is converted into the damping loss factor in each direction, thereby avoiding the error of the isotropy assumption in traditional analysis. This process more accurately reflects the true damping characteristics of the material in different directions through the modal strain energy method, thereby greatly improving the accuracy of the damping loss factor calculation.

[0181] This embodiment also discloses a device for detecting the damping loss factor of a transmission pipeline, referring to Figure 4 The device includes an acquisition module 401401 and a processing module 402402, wherein:

[0182] The acquisition module 401 is used to acquire the measured motion response of the target cylindrical shell based on the preset vibration excitation applied to the target cylindrical shell, and acquire the measured strain response of the target cylindrical shell based on the load applied to the target cylindrical shell.

[0183] The processing module 402 is configured to calculate the target kinetic energy of the target cylindrical shell based on the motion response, and calculate the target strain energy of the target cylindrical shell based on the strain response.

[0184] The processing module 402 is used to calculate the Lagrangian according to the target kinetic energy and the target strain energy.

[0185] The processing module 402 is used to calculate the total energy dissipated by the target cylindrical shell through the form according to the target kinetic energy and the specific damping capacity of the target cylindrical shell.

[0186] The processing module 402 is used to calculate the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation and the target strain energy.

[0187] The processing module 402 is configured to calculate the structural damping loss factor of the target cylindrical shell based on the damping loss factors in various directions according to the modal strain energy method.

[0188] In a possible implementation, the processing module 402 is configured to calculate the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation, and the target strain energy, using the following formula:

[0189]

[0190] Among them, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction, ΔU is the total energy consumption, U max is the target strain energy.

[0191] In one possible implementation, the processing module 402 is configured to analyze the stress components of the target cylindrical shell according to the motion response, and then calculate the stress vector of the target cylindrical shell, specifically using the following formula:

[0192] {σ} T ={σ x ,σ θ ,σ xθ}

[0193] Among them, {σ} T is the stress matrix, σ x is the normal stress in the x direction, σ θ is the normal stress in the θ direction, σ xθ for x-θ Shear stress on a plane.

[0194] The processing module 402 is used to analyze the strain vector of the target cylindrical shell according to the strain response, and is specifically calculated using the following formula:

[0195] {e} T ={e x , e θ , e xθ}

[0196] Among them, {e} T is the strain matrix, ex is the normal strain in the x direction, e θ is the normal strain in the θ direction, e xθ for x-θ Shear strain on a plane.

[0197] The relationship between stress vector and strain vector is as follows:

[0198] {σ}=[Q] T {e}

[0199] Where {σ} is the stress vector, {e} is the strain vector, [Q] T is the reduced stiffness matrix after transformation.

[0200] The converted reduced stiffness matrix is ​​expressed as follows:

[0201]

[0202] Among them, [Q] T is the transformed reduced stiffness matrix, Q ij is the reduced stiffness, i, j∈(1,2,6).

[0203] In a possible implementation, the processing module 402 is configured to calculate the total energy consumption according to the stress vector and the strain vector, specifically using the following formula:

[0204]

[0205] Where ΔU is the total energy consumption, L is the Lagrangian, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction.

[0206] In a possible implementation, the processing module 402 is configured to calculate the structural damping loss factor based on the following formula:

[0207]

[0208] Among them, η is the structural damping loss factor, ΔU is the total energy consumption, U max is the target strain energy.

[0209] In a possible implementation, the processing module 402 is configured to calculate the Lagrangian according to the target kinetic energy and the target strain energy, specifically using the following formula:

[0210] L=T max -Umax

[0211] Where L is the Lagrangian, T max is the target kinetic energy, U max is the target strain energy.

[0212] The acquisition module 401 is used to acquire the length and density of the target cylindrical shell.

[0213] The processing module 402 is used to calculate the strain energy of the target cylindrical shell based on the length of the target cylindrical shell, specifically using the following formula:

[0214]

[0215] Where U is the strain energy, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix.

[0216] The processing module 402 is used to calculate the kinetic energy of the target cylindrical shell based on the length and density of the target cylindrical shell, specifically using the following formula:

[0217]

[0218] Where T is the kinetic energy, h is the length of the target cylindrical shell, ρ is the density of the target cylindrical shell, u0, v0, and w0 are the displacement components of a point on the midplane (i.e., z = 0) along the (x, θ, z) coordinate direction.

[0219] In a possible implementation, the processing module 402 is configured to assume the following displacement field expressions at both ends of the target cylindrical shell (x=0, h):

[0220]

[0221] Where u0, v0, and w0 are the displacement components of a point on the midplane (i.e., z = 0) along the (x, θ, z) coordinate direction, A, B, and C are the magnitudes of the displacement amplitudes, m is the axial wave number, n is the circumferential wave number, and ω is the vibration angular frequency.

[0222] The processing module 402 is used to construct the Lagrangian equation for the energy function based on the minimum potential energy principle. The Lagrangian equation is as follows:

[0223]

[0224] Among them, A, B and C are the magnitudes of the displacement amplitude, T max is the target kinetic energy, U max is the target strain energy.

[0225] The processing module 402 is used to obtain the control characteristic equation based on the Lagrange equation as follows:

[0226]

[0227] Among them, C ij are the coefficients in the equation, and A, B, and C are the magnitudes of the displacement amplitudes.

[0228] The processing module 402 is configured to solve the roots by applying the condition of a non-trivial solution to the governing characteristic equation, and obtain the following determinant:

[0229] α0ω 6 +α1ω 4 +α2ω 2 +α3=0

[0230] Among them, α i (i=0, 1, 2, 3) is a constant, and ω is the vibration angular frequency.

[0231] The processing module 402 is used to solve the vibration angular frequency according to the determinant.

[0232] The processing module 402 is used to substitute the vibration angular frequency into the displacement field expression to calculate the target strain energy and the target kinetic energy.

[0233] It should be noted that the above embodiments provide devices that implement their functions using only the division of the above functional modules as examples. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the device and method embodiments provided in the above embodiments are based on the same concept. The specific implementation process is detailed in the method embodiment and will not be repeated here.

[0234] This embodiment also discloses an electronic device, referring to Figure 5 The electronic device may include: at least one processor 501 , at least one communication bus 502 , a user interface 503 , a network interface 504 , and at least one memory 505 .

[0235] The communication bus 502 is used to implement the connection and communication between these components.

[0236] The user interface 503 may include a display screen (Display) and a camera (Camera). Optionally, the user interface 503 may also include a standard wired interface and a wireless interface.

[0237] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a WI-FI interface).

[0238] The processor 501 may include one or more processing cores. The processor 501 utilizes various interfaces and lines to connect various parts of the entire server, and executes various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 505, as well as calling data stored in the memory 505. Optionally, the processor 501 may be implemented in the form of at least one hardware component selected from digital signal processing (DSP), field-programmable gate array (FPGA), and programmable logic array (PLA). The processor 501 may integrate one or a combination of a central processing unit (CPU), a graphics processing unit (GPU), and a modem. The CPU primarily processes the operating system, user interface, and application programs; the GPU is responsible for rendering and drawing the content to be displayed on the display screen; and the modem is used to handle wireless communications. It is understood that the modem may not be integrated into the processor 501 and may be implemented separately on a single chip.

[0239] The memory 505 may include a random access memory (RAM) or a read-only memory (ROM). Optionally, the memory includes a non-transitory computer-readable storage medium. The memory 505 may be used to store instructions, programs, codes, code sets, or instruction sets. The memory 505 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as a touch function, a sound playback function, an image playback function, etc.), instructions for implementing the above-mentioned various method embodiments, etc.; the data storage area may store data involved in the above-mentioned various method embodiments, etc. The memory 505 may also be at least one storage device located away from the aforementioned processor 501. The memory 505, as a computer storage medium, may include an operating system, a network communication module, a user interface 503 module, and an application program for a method for detecting the damping loss factor of a conveying pipeline.

[0240] exist Figure 5In the electronic device shown, the user interface 503 is mainly used to provide an input interface for the user and obtain data input by the user; and the processor 501 can be used to call an application stored in the memory 505 for a method for detecting the damping loss factor of a transmission pipeline. When executed by one or more processors 501, the electronic device executes one or more methods in the above-mentioned embodiments.

[0241] It should be noted that for the aforementioned method embodiments, for simplicity of description, they are all expressed as a series of action combinations, but those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required for this application.

[0242] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0243] In the several embodiments provided in this application, it should be understood that the disclosed devices can be implemented in other ways. For example, the device embodiments described above are merely schematic, such as the division of units, which is only a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some service interface, and the indirect coupling or communication connection of devices or units can be electrical or other forms.

[0244] Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0245] In addition, the functional units in the various embodiments of the present application may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0246] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a memory 505 and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the various embodiments of the present application. The aforementioned memory 505 includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a magnetic disk, or an optical disk.

[0247] The present application also discloses a computer-readable storage medium storing instructions, which, when executed by one or more processors 501, enable an electronic device to execute one or more of the methods described in the above embodiments.

[0248] The above is only an exemplary embodiment of the present disclosure and cannot be used to limit the scope of the present disclosure. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the disclosure of the specification and the truth of practice, those skilled in the art will easily think of other embodiments of the present disclosure. This application is intended to cover any variation, use or adaptive change of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the art that are not recorded in the present disclosure. The description and examples are to be regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

Claims

1. A method for detecting the damping loss factor of a transmission pipeline, characterized in that: The method comprises: Based on a preset vibration excitation applied to the target cylindrical shell, a motion response of the target cylindrical shell is obtained, and based on a load applied to the target cylindrical shell, a strain response of the target cylindrical shell is obtained; Calculating a target kinetic energy of the target cylindrical shell based on the motion response, and calculating a target strain energy of the target cylindrical shell based on the strain response; calculating a Lagrangian according to the target kinetic energy and the target strain energy; Calculating the total energy dissipated by the target cylindrical shell in a certain manner according to the target kinetic energy and the specific damping capacity of the target cylindrical shell; Calculating the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation and the target strain energy; According to the modal strain energy method, based on the damping loss factors in various directions, the structural damping loss factor of the target cylindrical shell is calculated.

2. The method for detecting the damping loss factor of a transmission pipeline according to claim 1, characterized in that: The damping loss factor of the target cylindrical shell in each direction is calculated according to the Lagrangian, the total energy consumption and the target strain energy, and is calculated by the following formula: ； Among them, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction, ΔU is the total energy consumption, U max is the target strain energy.

3. The method for detecting the damping loss factor of a transmission pipeline according to claim 2, characterized in that: After calculating the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation, and the target strain energy, the method further includes: According to the motion response, the stress components of the target cylindrical shell are analyzed, and then the stress vector of the target cylindrical shell is calculated, which is specifically calculated by the following formula: ； Among them, {σ} T is the stress matrix, σ x is the normal stress in the x direction, σ θ is the normal stress in the θ direction, σ xθ for x-θ Shear stress on a plane; According to the strain response, the strain vector of the target cylindrical shell is analyzed and specifically calculated using the following formula: ； Among them, {e} T is the strain matrix, e x is the normal strain in the x direction, e θ is the normal strain in the θ direction, e xθ for x-θ Shear strain on a plane; The relationship between the stress vector and the strain vector is as follows: ； Where, {σ} is the stress vector, {e} is the strain vector, [Q] T is the reduced stiffness matrix after transformation; The reduced stiffness matrix after the conversion is expressed as follows: ； Among them, [Q] T is the transformed reduced stiffness matrix, Q ij is the reduced stiffness, i, j∈(1,2,6).

4. The method for detecting the damping loss factor of a transmission pipeline according to claim 3, characterized in that: Calculating the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy dissipation, and the target strain energy specifically includes: The total energy consumption is calculated based on the stress vector and the strain vector, specifically using the following formula: ； Wherein, ΔU is the total energy consumption, L is the Lagrangian, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix, η 11 ,η 12 ,η 22 are the damping loss factors of the target cylindrical shell in each direction, and R is the radius of the target cylindrical shell.

5. The method for detecting the damping loss factor of a transmission pipeline according to claim 1, characterized in that: The method of calculating the structural damping loss factor of the target cylindrical shell based on the damping loss factors in various directions according to the modal strain energy method specifically includes: The structural damping loss factor is calculated based on the following formula: ； Wherein, η is the structural damping loss factor, ΔU is the total energy consumption, U max is the target strain energy.

6. The method for detecting the damping loss factor of a transmission pipeline according to claim 1, characterized in that: The Lagrangian is calculated based on the target kinetic energy and the target strain energy, specifically using the following formula: ； Wherein, L is the Lagrangian, T max is the target kinetic energy, U max is the target strain energy; Obtaining the length and density of the target cylindrical shell; The strain energy of the target cylindrical shell is calculated based on the length of the target cylindrical shell, specifically by the following formula: ； Where U is the strain energy, h is the length of the target cylindrical shell, {e} T is the strain matrix, {σ} T is the stress matrix, R is the radius of the target cylindrical shell; Based on the length and density of the target cylindrical shell, the kinetic energy of the target cylindrical shell is calculated, specifically using the following formula: ； Wherein, T is the kinetic energy, h is the length of the target cylindrical shell, ρ is the density of the target cylindrical shell, u0, v0, and w0 are the displacement components of a point on the mid-plane (i.e., z=0) along the (x, θ, z) coordinate direction, respectively.

7. The method for detecting the damping loss factor of a transmission pipeline according to claim 6, characterized in that: The calculating the target kinetic energy of the target cylindrical shell based on the motion response, and the calculating the target strain energy of the target cylindrical shell based on the strain response, specifically includes: At both ends of the target cylindrical shell (x=0, h), the assumed displacement field expression is as follows: ； Where u0, v0, and w0 are the displacement components of a point on the midplane (i.e., z = 0) along the (x, θ, z) coordinate directions, A, B, and C are the magnitudes of the displacement amplitudes, m is the axial wave number, n is the circumferential wave number, and ω is the vibration angular frequency. Based on the principle of minimum potential energy, the Lagrangian equation for the energy function is constructed as follows: ； Among them, A, B and C are the magnitudes of the displacement amplitude, T max is the target kinetic energy, U max is the target strain energy; Based on the Lagrange equation, the control characteristic equation is obtained as follows: ； Among them, C ij are the coefficients in the equation, A, B and C are the magnitudes of the displacement amplitudes; Solving for the roots by imposing the conditions for non-trivial solutions to the governing characteristic equation yields the following determinant: ； Among them, α i (i=0, 1, 2, 3) is a constant, ω is the angular frequency of vibration; Solving the vibration angular frequency according to the determinant; The vibration angular frequency is substituted into the displacement field expression to calculate the target strain energy and the target kinetic energy.

8. A device for detecting the damping loss factor of a transmission pipeline, characterized in that: The device comprises an acquisition module (401) and a processing module (402), wherein: The acquisition module (401) is used to acquire a measured motion response of the target cylindrical shell based on a preset vibration excitation applied to the target cylindrical shell, and to acquire a measured strain response of the target cylindrical shell based on a load applied to the target cylindrical shell; The processing module (402) is used to calculate the target kinetic energy of the target cylindrical shell based on the motion response amount, and calculate the target strain energy of the target cylindrical shell based on the strain response amount; The processing module (402) is used to calculate the Lagrangian according to the target kinetic energy and the target strain energy; The processing module (402) is used to calculate the total energy dissipated by the target cylindrical shell in a certain form according to the target kinetic energy and the specific damping capacity of the target cylindrical shell; The processing module (402) is used to calculate the damping loss factor of the target cylindrical shell in each direction according to the Lagrangian, the total energy consumption and the target strain energy; The processing module (402) is used to calculate the structural damping loss factor of the target cylindrical shell based on the damping loss factors in various directions according to the modal strain energy method.

9. An electronic device, characterized in that: The electronic device comprises a processor (501), a communication bus (502), a user interface (503), a network interface (504) and a memory (505), wherein the memory (505) is used to store instructions, the user interface (503) and the network interface (504) are both used to communicate with other devices, and the processor (501) is used to execute the instructions stored in the memory (505) so that the electronic device executes the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores instructions, and when the instructions are executed, the method according to any one of claims 1 to 7 is executed.

Images