Natural vibration characteristic calculation method of corrugated steel web composite beam and related equipment

Abstract

The invention relates to the technical field of corrugated steel web composite beams, and discloses a natural vibration characteristic calculation method of a corrugated steel web composite beam and related equipment. The method comprises the following steps: constructing a mechanical model for describing the corrugated steel web composite beam based on a Zig-zag theory; constructing a natural vibration state equation according to the mechanical model, and solving the natural vibration state equation to obtain a state vector equation of the power problem of the corrugated steel web composite beam; introducing an internal force displacement continuity condition, and constructing a continuity condition equation; according to the continuity condition equation, a natural vibration frequency equation of the corrugated steel web continuous beam is constructed, the natural vibration frequency equation is solved, and the natural vibration frequency of the corrugated steel web continuous beam is obtained; according to the natural vibration frequency, the proportional relation of all components in the to-be-determined parameter column vector is determined, and the state vector equation of the dynamic problem of the corrugated steel web composite beam is solved, so that the vibration mode of the displacement and the internal force corresponding to the natural vibration frequency is determined. According to the embodiment of the invention, the natural vibration characteristic of the corrugated steel web composite beam can be accurately determined.

Description

Technical Field

[0001] The present application relates to the technical field of corrugated steel web composite beams, and in particular to a method for calculating the natural vibration characteristics of corrugated steel web composite beams and related equipment. Background Art

[0002] The composite beam with corrugated steel web is a new type of bridge structure, which consists of concrete top and bottom plates, external prestressed tendons and corrugated steel webs. Using corrugated steel plates to replace traditional concrete webs can reduce the deadweight of the structure and improve the shear resistance and durability of the structure.

[0003] How to accurately obtain the natural vibration characteristics of composite beams with corrugated steel webs is the main task of the preliminary design of composite beams with corrugated steel webs. However, due to the difference between the corrugated steel web and the concrete top and bottom plate materials, the in-plane deformation of composite beams with corrugated steel webs does not conform to the flat section assumption. In addition, the current vibration characteristic calculations of composite beams with corrugated steel webs are based on either classical beam theory or improved Timoshenko beam theory, which makes it difficult to accurately describe the differences in the in-plane deformation slopes of each layer of composite beams with corrugated steel webs. Summary of the invention

[0004] The purpose of this application is to provide a method for calculating the natural vibration characteristics of a composite beam with a corrugated steel web and related equipment, which can provide an important basis for the design of a composite beam with a corrugated steel web.

[0005] The present application provides a method for calculating the natural vibration characteristics of a composite beam with a corrugated steel web, including: Based on Zig-zag theory, a mechanical model describing the composite beam with corrugated steel webs is constructed. According to the mechanical model, a natural vibration state equation of the corrugated steel web composite beam is constructed, and the natural vibration state equation is solved to obtain a state vector equation of the dynamic problem of the corrugated steel web composite beam; the state vector equation of the dynamic problem of the corrugated steel web composite beam describes the relationship between the natural vibration state vector and the product of the column vector of undetermined parameters formed by the general solution of the natural vibration state equation and a coefficient matrix; Introducing the internal force displacement continuity condition, constructing the continuity condition equation of the corrugated steel web composite beam; According to the continuity condition equation, construct the natural frequency equation of the corrugated steel web continuous beam, solve the natural frequency equation, and obtain the natural frequency of the corrugated steel web continuous beam; Determine the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the corrugated steel web continuous beam; According to the proportional relationship between the components in the undetermined parameter column vector, the state vector equation of the dynamic problem of the corrugated steel web composite beam is solved to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam.

[0006] In some embodiments, the mechanical model describing the corrugated steel web composite beam is constructed based on the Zig-zag theory, including: Based on the material equivalence principle, the corrugated steel web composite beam is equivalent to a sandwich beam model with orthotropic layers; The interlayer continuous Zig-zag displacement assumption and the layered parabolic distribution of the in-section transverse shear stress assumption are introduced into the sandwich beam model to obtain the mechanical model of the corrugated steel web composite beam.

[0007] In some embodiments, the self-vibration state equation of the corrugated steel web composite beam is constructed based on the mechanical model, and the self-vibration state equation is solved by a numerical stability solution to obtain a state vector equation of the dynamic problem of the corrugated steel web composite beam, including: Based on Hamilton's principle, the dynamic equilibrium equation of the corrugated steel web composite beam under the action of conservative force is constructed; Based on the energy principle, the dynamic equilibrium equation is solved to obtain the equilibrium equation of the corrugated steel web composite beam; The self-vibration state vector is constructed according to the combined state information in the mechanical model; the combined state information includes the deflection, rotation angle and zig-zag displacement of the corrugated steel web composite beam and the additional bending moment caused by the section shear force, bending moment and zig-zag displacement of the energy duality; Based on the state space method, rewrite the equilibrium equation into the state equation of the corrugated steel web composite beam in the free state, substitute the natural vibration state vector into the state equation, and obtain the natural vibration state equation; Solve the self-oscillation state equation to obtain an undetermined parameter column vector and a corresponding coefficient matrix formed by the general solution of the self-oscillation state equation, and use the undetermined parameter column vector and the coefficient matrix to construct the state vector equation of the dynamic problem of the corrugated steel web composite beam.

[0008] In some embodiments, the introduction of internal force displacement continuity conditions to construct the continuity condition equation of the corrugated steel web composite beam includes: According to the internal force displacement continuity condition, the continuity condition equation of the beam span and the continuity condition equation of the support of the corrugated steel web composite beam are constructed, and the corresponding end boundary conditions are determined; The continuity condition equation of the beam span, the continuity condition equation of the support and the end boundary condition are combined to obtain the continuity condition equation of the corrugated steel web composite beam.

[0009] In some embodiments, constructing the natural frequency equation of the corrugated steel web continuous beam according to the continuity condition equation, solving the natural frequency equation, and obtaining the natural frequency of the corrugated steel web continuous beam includes: Solving the continuity condition equation to obtain the natural frequency equation; The natural frequency of the continuous beam with corrugated steel web is obtained by solving the natural frequency equation at several modal orders using a dichotomy method.

[0010] In some embodiments, determining the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the corrugated steel web continuous beam includes: The natural frequency of the corrugated steel web continuous beam is substituted into the natural frequency equation, and the non-zero solution of the undetermined parameter column vector is calculated to determine the proportional relationship between the components in the undetermined parameter column vector.

[0011] In some embodiments, solving the state vector equation of the dynamic problem of the corrugated steel web composite beam according to the proportional relationship of each component in the undetermined parameter column vector to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam includes: According to the proportional relationship between the components in the undetermined parameter column vector, the undetermined parameter column vector that conforms to the proportional relationship of the components is determined and substituted into the state vector equation of the dynamic problem of the corrugated steel web composite beam to obtain the natural vibration state vector of the vibration mode corresponding to the displacement and internal force of the natural vibration frequency of the corrugated steel web continuous beam.

[0012] The embodiment of the present application also provides a device for calculating the natural vibration characteristics of a corrugated steel web composite beam, comprising: The first module is used to construct a mechanical model describing the composite beam with corrugated steel webs based on the Zig-zag theory; The second module is used to construct the self-vibration state equation of the corrugated steel web composite beam according to the mechanical model, and solve the self-vibration state equation by a numerical stability solution method to obtain the state vector equation of the dynamic problem of the corrugated steel web composite beam; the state vector equation of the dynamic problem of the corrugated steel web composite beam describes the relationship between the self-vibration state vector and the product of the column vector of undetermined parameters formed by the general solution of the self-vibration state equation and a coefficient matrix; The third module is used to introduce the internal force displacement continuity condition and construct the continuity condition equation of the corrugated steel web composite beam; The fourth module is used to construct the natural frequency equation of the corrugated steel web continuous beam according to the continuity condition equation, solve the natural frequency equation, and obtain the natural frequency of the corrugated steel web continuous beam; The fifth module is used to determine the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the corrugated steel web continuous beam; The sixth module is used to solve the state vector equation of the dynamic problem of the corrugated steel web composite beam according to the proportional relationship between the components in the unknown parameter column vector, so as to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam.

[0013] An embodiment of the present application further provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the above-mentioned method for calculating the natural vibration characteristics of the corrugated steel web composite beam when executing the computer program.

[0014] An embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for calculating the natural vibration characteristics of the corrugated steel web composite beam is implemented.

[0015] The beneficial effects of the present application are as follows: a mechanical model describing a composite beam with corrugated steel webs is constructed based on the Zig-zag theory, a natural vibration state equation is constructed based on the mechanical model, a numerical stable solution is used to solve the natural vibration state equation, and a state vector equation of the dynamic problem of the composite beam with corrugated steel webs is obtained, the internal force displacement continuity condition is introduced, and a continuity condition equation is constructed, and based on the continuity condition equation, a natural vibration frequency equation of a continuous beam with corrugated steel webs is constructed, and the natural vibration frequency equation is solved to obtain the natural vibration frequency of the continuous beam with corrugated steel webs, and based on the natural vibration frequency, the proportional relationship between each component in the column vector of the unknown parameters is determined and the state vector equation of the dynamic problem of the composite beam with corrugated steel webs is solved to determine the vibration mode of the displacement and the internal force corresponding to the natural vibration frequency. The embodiment of the present application determines the natural vibration characteristics of the composite beam with corrugated steel web based on the Zig-zag theory and the state space method, breaking through the flat section assumption in the classical beam theory, and can improve the calculation accuracy and efficiency of the natural vibration characteristics of the composite beam with corrugated steel web. It can cope with the complex variable cross-section forms and different constraint types in actual engineering, meet the needs of the initial design stage of the composite beam with corrugated steel web, and is an important basis for the structural design of the composite beam with corrugated steel web. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of a method for calculating the natural vibration characteristics of a corrugated steel web composite beam provided in an embodiment of the present application.

[0017] Figure 2 It is a flowchart of the specific method of step S102 provided in an embodiment of the present application.

[0018] Figure 3 It is a structural schematic diagram of a device for calculating the natural vibration characteristics of a corrugated steel web composite beam provided in an embodiment of the present application.

[0019] Figure 4 It is a schematic diagram of the hardware structure of the electronic device provided in the embodiment of the present application.

[0020] Figure 5 It is a schematic diagram of the beam segment division of the corrugated steel web composite beam provided in the embodiment of the present application.

[0021] Figure 6 It is a schematic diagram of the Zig-zag displacement field and transverse shear stress distribution provided in the embodiments of the present application.

[0022] Figure 7 It is a schematic diagram of the first three vibration modes of the corrugated steel web composite beam provided in the embodiment of the present application. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0024] It should be noted that, although the functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown can be performed in a different order than the module division in the device or the order in the flowchart. The terms "first", "second" and the like in the specification, claims and drawings are used to distinguish similar objects, and are not used to describe a specific order or sequence.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0026] Figure 1 is a flow chart of a method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs provided in an embodiment of the present application. Figure 1 The method may specifically include steps S101 to S106.

[0027] Step S101, based on the Zig-zag theory, construct a mechanical model describing the corrugated steel web composite beam.

[0028] In some embodiments, step S101 specifically converts the corrugated steel web composite beam into an equivalent sandwich beam model with an orthotropic layer, establishes a spatial rectangular coordinate system along the span direction, beam width direction and beam height direction of the composite beam, determines the height of the top plate, web and bottom plate of the corrugated steel web composite beam, the width of the top plate and the bottom plate and the thickness of the web, and determines the equivalent elastic modulus, shear modulus, density, deflection, rotation, zig-zag displacement of each layer of the corrugated steel web composite beam and the internal force dual to the energy of the corrugated steel web composite beam, thereby establishing a mechanical model of the corrugated steel web composite beam.

[0029] Step S102, constructing the natural vibration state equation of the composite beam with corrugated steel webs according to the mechanical model, solving the natural vibration state equation, and obtaining the state vector equation of the dynamic problem of the composite beam with corrugated steel webs.

[0030] The state vector equation of the dynamic problem of the composite beam with corrugated steel webs describes the relationship between the natural vibration state vector and the product of the column vector of undetermined parameters formed by the general solution of the natural vibration state equation and a coefficient matrix.

[0031] In some embodiments, step S102 specifically establishes the self-oscillation state equation of the corrugated steel web composite beam based on the Hamilton principle without considering the external load. In order to avoid the numerical instability problem in the traditional transfer matrix solution, a numerical stable solution is adopted to solve the self-oscillation state equation. Through matrix transformation, the column vector of undetermined parameters in the general solution of the self-oscillation state equation is used as the basic unknown quantity to replace the state variable in the transfer matrix solution. The relationship between the corresponding state vector and the column vector of undetermined coefficients in the beam section of the corrugated steel web composite beam is described by the coefficient matrix, and the state vector equation of the dynamic problem of the corrugated steel web composite beam is obtained.

[0032] Step S103, introducing the internal force displacement continuity condition, and constructing the continuity condition equation of the corrugated steel web composite beam.

[0033] In some embodiments, step S103 specifically follows the displacement and internal force continuity conditions between beam segments without loss of generality, establishes continuity condition equations between beam segments of a composite beam with corrugated steel webs, considers that the internal forces and displacements of adjacent beam segments on the left and right of the middle support are continuous at the support position, and the vertical displacement is constrained, and there are 6×(n-1) continuity condition equations at the n-1 hinged supports, and considers the boundary conditions at the end support position. Common boundary conditions in engineering are simply supported, fixed, and free. Taking the simply supported boundary as an example, the corresponding vertical displacement w, bending moment M, and internal force P at the end support position are all 0, and 6 boundary condition equations can be obtained for the two end supports, thereby obtaining the continuity condition equation of the composite beam with corrugated steel webs.

[0034] Step S104, constructing a natural frequency equation of the continuous beam with corrugated steel webs according to the continuity condition equation, solving the natural frequency equation, and obtaining the natural frequency of the continuous beam with corrugated steel webs.

[0035] In some embodiments, step S104 is specifically based on the continuity condition equation, so that the column vector of the unknown parameters is a non-zero solution to construct the natural frequency equation of the corrugated steel web continuous beam, and the natural frequency equation is solved by the bisection method, and the solution of the natural frequency equation is solved under several modal orders to obtain the natural frequency of the corrugated steel web continuous beam.

[0036] Step S105, determining the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the continuous beam with corrugated steel webs.

[0037] In some embodiments, step S105 specifically involves substituting the natural frequency of the corrugated steel web continuous beam into the continuity condition equation to determine the proportional relationship between the components in the undetermined parameter column vector.

[0038] Step S106, solving the state vector equation of the dynamic problem of the corrugated steel web composite beam according to the proportional relationship of each component in the undetermined parameter column vector, so as to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam.

[0039] In some embodiments, step S106 specifically solves the state vector equation of the dynamic problem of the corrugated steel web composite beam after determining the proportional relationship between the components in the unknown parameter column vector, so as to determine the natural vibration state vector that satisfies the proportional relationship conditions of the components in the unknown parameter column vector, and determines the vibration mode of the displacement and internal force corresponding to the natural vibration frequency of the corrugated steel web continuous beam according to the components of the natural vibration state vector.

[0040] In a specific embodiment, step S101 specifically includes: based on the material equivalence principle, the corrugated steel web composite beam is equivalent to a sandwich beam model with orthotropic layers; on the sandwich beam model, the interlayer continuous Zig-zag displacement assumption and the layered parabolic distribution of the cross-sectional transverse shear stress assumption are introduced to obtain the mechanical model of the corrugated steel web composite beam. The structure of the corrugated steel web composite beam is as follows: Figure 5 shown.

[0041] In the specific implementation, according to the material equivalence principle, the composite beam with corrugated steel web can be equivalent to a sandwich beam model with orthotropic layers of width b0, ρ k 、E k , μ k and G k are the equivalent density, elastic modulus, k=1,2,3, Poisson's ratio and shear modulus of the kth layer respectively, and the equivalent formula is: , , , , , , , Among them, n csw is the number of corrugated steel webs in the beam, α w 、b w 、c w 、h w ,t w and θ w are the straight plate width, inclined plate projection width, inclined plate width, wave height, plate thickness and wave angle of the corrugated steel web, ρ, E and μ represent density, elastic modulus and Poisson's ratio, respectively. Subscripts c and s correspond to concrete and steel, respectively. b1, h1, b3 and h3 represent the top plate width, top plate thickness, bottom plate width and bottom plate thickness, respectively. h2 is the height of the corrugated steel web, t is the web thickness, and i is a positive integer (i=1,2,3).

[0042] The Zig-zag displacement s is introduced to describe the discontinuity of the displacement slope of each layer in the plane of the corrugated steel web composite beam between layers. At the same time, it is assumed that the shear stress on the section is distributed in a layered parabola, and the mechanical model of the corrugated steel web composite beam is obtained, as shown in Figure 6. The Zig-zag theoretical displacement field and the in-plane transverse shear stress are: , , in, is the displacement component of the kth layer of the corrugated steel web composite beam in the x direction, is the displacement component of the kth layer of the corrugated steel web composite beam in the z direction, u(x) is the displacement in the x direction at the position z=0, is the cross-sectional rotation angle, s is the zig-zag displacement amplitude, is the dimensionless coordinate of the kth layer of the corrugated steel web composite beam, , w(x) is the vertical deflection of the composite beam with corrugated steel webs, is the in-plane transverse shear stress of the kth layer of the corrugated steel web composite beam in the x direction, τ k-1 and τ k are the in-plane transverse shear stresses on the upper and lower surfaces of the kth layer of the corrugated steel web composite beam, τ0 and τ3 are the in-plane transverse shear stresses on the upper and lower surfaces of the composite beam with corrugated steel webs, Q k is the in-plane transverse shear stress of the kth layer of the corrugated steel web composite beam.

[0043] Figure 2 is a flowchart of a specific method of step S102 provided in an embodiment of the present application. Figure 2 The method includes but is not limited to steps S201 to S205.

[0044] Step S201: Based on Hamilton's principle, a dynamic equilibrium equation of the corrugated steel web composite beam under the action of conservative force is constructed.

[0045] Step S202, based on the energy principle, solve the dynamic equilibrium equation to obtain the equilibrium equation of the corrugated steel web composite beam.

[0046] Step S203, constructing a natural vibration state vector according to the combined state information in the mechanical model.

[0047] The combined state information includes the deflection, rotation and zig-zag displacement of the composite beam with corrugated steel webs and the additional bending moment caused by the section shear force, bending moment and zig-zag displacement of the energy duality.

[0048] Step S204, based on the state space method, rewrite the equilibrium equation into the state equation of the corrugated steel web composite beam in the free state, substitute the natural vibration state vector into the state equation, and obtain the natural vibration state equation.

[0049] Step S205, solving the natural vibration state equation, obtaining the undetermined parameter column vector and the corresponding coefficient matrix formed by the general solution of the natural vibration state equation, and constructing the state vector equation of the dynamic problem of the corrugated steel web composite beam using the undetermined parameter column vector and the coefficient matrix.

[0050] In specific implementation, based on Hamilton's principle, the dynamic equilibrium equation of the composite beam with corrugated steel web under the action of conservative force is: , , , Where L = ∏ d -∏ R is the Lagrangian function, ∏ d is the system kinetic energy of the composite beam with corrugated steel webs, ∏ R is the functional of the generalized potential energy. A dot above the letter indicates the time derivative. is the kth layer rotation angle of the corrugated steel web composite beam, is the mass per unit length of the entire corrugated steel web composite beam section, is the moment of inertia of the entire cross-section of the composite beam with corrugated steel webs, t0 and t1 are time nodes, and h k is the thickness of the kth layer, I k is the moment of inertia of the k-th layer section.

[0051] According to the energy principle, the dynamic equilibrium equation of the composite beam with corrugated steel web is solved, and the equilibrium equation of the composite beam with corrugated steel web is obtained as follows: , , , , , Among them, the superscript symbol represents the derivative of coordinate x, is the second-order derivative of the rotation angle with respect to time t, is the second-order derivative of the zig-zag displacement s with respect to time t, I is the section inertia moment, A is the cross-sectional area, and the corresponding boundary conditions are: , , , , Among them, Q, M, N and P are the shear stress, bending moment, axial force and additional bending moment on the entire cross section of the corrugated steel web composite beam, represents the variation, l is the span of the bridge, and the internal force displacement relationship is: , , , The relationship between the interlaminar shear stress and the cross section is: , Among them, τ0 and τ3 are the in-plane transverse shear stresses on the upper and lower surfaces of the corrugated steel web composite beam, respectively, so τ0=τ3=0.

[0052] Considering that the composite beam with corrugated steel web is not subjected to external axial force, that is, N=0, the axial force N and axial displacement μ are eliminated. Based on the state space method, the deflection w, rotation angle φ and zig-zag displacement s of the composite beam with corrugated steel web, and the additional bending moment P caused by the section shear force Q, bending moment M and zig-zag displacement of its energy duality are taken as state vectors. The equilibrium equation of the composite beam with corrugated steel web is combined, and the equilibrium equation of the composite beam with corrugated steel web is controlled in a matrix form. The state equation of the composite beam with corrugated steel web in the free state is obtained: , In the state equation of the corrugated steel web composite beam in the free state, , , , , , , , , Among them, H ij is the element corresponding to the i-th row and j-th column in the matrix H, A i , B j and C2 are constants related to geometric dimensions and material parameters, i∈[1,3], j∈[1,4], A i , B j The calculation formulas for C and C2 are: , , , , , , , , For free vibration, the natural vibration state vector can be constructed as: , Where v is the natural oscillation state vector, , , , and are the vibration mode functions of the deflection, rotation, zig-zag displacement, shear stress, bending moment and additional bending moment of the composite beam with corrugated steel webs, ω is the circular frequency of free vibration of the composite beam with corrugated steel webs, e is a natural constant, and T represents the transpose of the matrix.

[0053] Substituting the constructed natural vibration state vector into the state equation of the corrugated steel web composite beam in the free state, the natural vibration state equation is obtained: , In the self-oscillating state equation, , Considering numerical stability, the natural vibration state equation is solved by numerical stability method, and the state vector equation of the dynamic problem of the corrugated steel web composite beam is obtained: , in, is the natural vibration state vector of the beam segment in the i-th span and the j-th segment, is the column vector of unknown parameters, for The corresponding coefficient matrix.

[0054] In a specific embodiment, step S103 specifically includes: constructing the continuity condition equation of the beam span and the continuity condition equation of the support of the corrugated steel web composite beam based on the internal force displacement continuity condition, and determining the corresponding end boundary conditions; combining the continuity condition equation of the beam span, the continuity condition equation of the support and the end boundary conditions to obtain the continuity condition equation of the corrugated steel web composite beam.

[0055] According to the jth beam segment and j+1th beam segment adjacent to the i-th beam span at the node Continuity conditions for internal forces and displacements at You can get: , Where i=1,2,3,...n, j=1,2,3,...m i -1.

[0056] The continuity condition equation of the beam span can be obtained within the entire beam span: , Where D is determined by the beam segment coefficient matrix, c is the column vector to be determined, where: , , , There are n-1 intermediate supports for an n-span continuous beam. The adjacent beam segments on the left and right of the i-th intermediate support are located at the support nodes. The continuity conditions of internal forces and displacements at are: , , , , , The above formula can be expressed in matrix form, that is, the continuity condition equation of the support, which is: , In the formula, , , Taking the composite beam with corrugated steel webs as an example, the corresponding boundary conditions are: , , , , , , written in matrix form, i.e. the end boundary condition, is: , In the formula, , in, and The constant matrix that determines the continuity conditions for the intermediate supports, To determine the constant matrix of boundary conditions, For the nth span The coefficient matrix corresponding to the beam segment is: For the nth span The coordinates of the right end node of the beam segment.

[0057] Without loss of generality, other boundary conditions can always be written in the form of the above formula. Finally, the continuity condition equation of the beam span, the continuity condition equation of the support and the end boundary conditions are combined and written in matrix form to obtain the continuity condition equation of the corrugated steel web composite beam: , Among them, K is Order square array.

[0058] In a specific embodiment, step S104 specifically includes: solving the continuity condition equation to obtain the natural frequency equation; using the dichotomy method to solve the natural frequency equation at several modal orders to obtain the natural frequency of the corrugated steel web continuous beam.

[0059] The continuity condition equation of the composite beam with corrugated steel web is a homogeneous linear algebraic equation system. The condition for its non-zero solution is that the determinant K of the coefficient matrix must be 0, that is: , The above formula is the natural frequency equation of the composite beam with corrugated steel webs. It is a transcendental equation about ω and has infinite solutions. The binary method is used to solve it. After solving the solutions under several modal orders, the natural frequency of the continuous beam with corrugated steel webs is obtained. As shown in Table 1, the errors of the natural frequencies of the first three orders of the composite beam with corrugated steel webs obtained by the method of this application and the finite element calculation method are all within 5%, and the consistency is good. In addition, Figure 7 As shown, the calculation results of the first three modes of the corrugated steel web composite beam are given. The analytical method of the present invention is in good agreement with the ABAQUS numerical calculation results.

[0060]

[0061] Table 1 In a specific embodiment, step S105 specifically includes: substituting the natural frequency of the corrugated steel web continuous beam into the natural frequency equation, calculating the non-zero solution of the undetermined parameter column vector to determine the proportional relationship between the components in the undetermined parameter column vector.

[0062] In a specific embodiment, step S106 specifically includes: according to the proportional relationship between the components in the undetermined parameter column vector, determining the undetermined parameter column vector that conforms to the proportional relationship of the components and substituting it into the state vector equation of the dynamic problem of the corrugated steel web composite beam, and obtaining the natural vibration state vector of the vibration mode that characterizes the displacement and internal force corresponding to the natural vibration frequency of the corrugated steel web continuous beam.

[0063] See also Figure 3 The embodiment of the present application further provides a device for calculating the natural vibration characteristics of a composite beam with a corrugated steel web, which can implement the method for calculating the natural vibration characteristics of the composite beam with a corrugated steel web, and the device includes: The first module 301 is used to construct a mechanical model describing a composite beam with corrugated steel webs based on the Zig-zag theory; The second module 302 is used to construct the self-oscillation state equation of the corrugated steel web composite beam according to the mechanical model, solve the self-oscillation state equation, and obtain the state vector equation of the dynamic problem of the corrugated steel web composite beam; the state vector equation of the dynamic problem of the corrugated steel web composite beam describes the relationship between the self-oscillation state vector and the product of the column vector of undetermined parameters formed by the general solution of the self-oscillation state equation and a coefficient matrix; The third module 303 is used to introduce the internal force displacement continuity condition and construct the continuity condition equation of the corrugated steel web composite beam; The fourth module 304 is used to construct a natural frequency equation of the continuous beam with corrugated steel webs according to the continuity condition equation, solve the natural frequency equation, and obtain the natural frequency of the continuous beam with corrugated steel webs; The fifth module 305 is used to determine the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the continuous beam with corrugated steel webs; The sixth module 306 is used to solve the state vector equation of the dynamic problem of the corrugated steel web composite beam according to the proportional relationship between the components in the undetermined parameter column vector, so as to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam.

[0064] The specific implementation of the device for calculating the natural vibration characteristics of the corrugated steel web composite beam is basically the same as the specific implementation of the method for calculating the natural vibration characteristics of the corrugated steel web composite beam mentioned above, and will not be repeated here.

[0065] Figure 4 It is a block diagram of an electronic device according to an exemplary embodiment.

[0066] Refer to the following Figure 4 The electronic device 400 according to this embodiment of the present disclosure is described. Figure 4 The electronic device 400 shown is merely an example and should not bring any limitation to the functions and scope of use of the embodiments of the present disclosure.

[0067] like Figure 4 As shown, the electronic device 400 is in the form of a general computing device. The components of the electronic device 400 may include, but are not limited to: at least one processing unit 410, at least one storage unit 420, a bus 430 connecting different system components (including the storage unit 420 and the processing unit 410), a display unit 440, etc.

[0068] The storage unit stores program codes, which can be executed by the processing unit 410, so that the processing unit 410 executes the steps described in the above-mentioned method for calculating the natural vibration characteristics of the corrugated steel web composite beam according to various exemplary embodiments of the present disclosure.

[0069] The storage unit 420 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 4201 and / or a cache storage unit 4202 , and may further include a read-only storage unit (ROM) 4203 .

[0070] The storage unit 420 may also include a program / utility 4204 having a set (at least one) of program modules 4205, such program modules 4205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0071] Bus 430 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0072] The electronic device 400 may also communicate with one or more external devices 400' (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 400, and / or communicate with any device that enables the electronic device 400 to communicate with one or more other computing devices (e.g., routers, modems, etc.). Such communication may be performed via an input / output (I / O) interface 450. In addition, the electronic device 400 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) via a network adapter 460. The network adapter 460 may communicate with other modules of the electronic device 400 via the bus 430. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 400, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0073] An embodiment of the present application further provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for calculating the natural vibration characteristics of the corrugated steel web composite beam.

[0074] The embodiments of the present application provide a method for calculating the natural vibration characteristics of a composite beam with a corrugated steel web and related equipment. A mechanical model describing the composite beam with a corrugated steel web is constructed based on the Zig-zag theory, a natural vibration state equation is constructed according to the mechanical model, a numerical stability solution is used to solve the natural vibration state equation, and a state vector equation of the dynamic problem of the composite beam with a corrugated steel web is obtained. An internal force-displacement continuity condition is introduced to construct a continuity condition equation. Based on the continuity condition equation, a natural vibration frequency equation of a continuous beam with a corrugated steel web is constructed. The natural vibration frequency equation is solved to obtain the natural vibration frequency of the continuous beam with a corrugated steel web. Based on the natural vibration frequency, the proportional relationship between the components in the column vector of the unknown parameters is determined and the state vector equation of the dynamic problem of the composite beam with a corrugated steel web is solved to determine the vibration mode of the displacement and the internal force corresponding to the natural vibration frequency. The embodiment of the present application determines the natural vibration characteristics of the composite beam with corrugated steel web based on the Zig-zag theory and the state space method, breaking through the flat section assumption in the classical beam theory, and can improve the calculation accuracy and efficiency of the natural vibration characteristics of the composite beam with corrugated steel web. It can cope with the complex variable cross-section forms and different constraint types in actual engineering, meet the needs of the initial design stage of the composite beam with corrugated steel web, and is an important basis for the structural design of the composite beam with corrugated steel web.

[0075] Through the description of the above implementation, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software, or by software combined with necessary hardware. Therefore, the technical solution according to the implementation of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, including several instructions to enable a computing device (which can be a personal computer, a server, or a network device, etc.) to execute the above method according to the implementation of the present disclosure.

[0076] The program product may use any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0077] Computer readable storage media may include data signals propagated in baseband or as part of a carrier wave, wherein readable program codes are carried. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, device, or device. The program codes contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination thereof.

[0078] Those skilled in the art will appreciate that the above modules can be distributed in the device according to the description of the embodiment, or can be changed accordingly and only used in one or more devices different from the embodiment. The modules of the above embodiments can be combined into one module, or further divided into multiple sub-modules.

[0079] The exemplary embodiments of the present disclosure are specifically shown and described above. It should be understood that the present disclosure is not limited to the detailed structures, configurations or implementations described herein; on the contrary, the present disclosure is intended to cover various modifications and equivalent configurations included in the spirit and scope of the appended claims.

Claims

1. A method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs, characterized in that: include: Based on Zig-zag theory, a mechanical model describing the composite beam with corrugated steel webs is constructed. According to the mechanical model, a natural vibration state equation of the corrugated steel web composite beam is constructed, and the natural vibration state equation is solved to obtain a state vector equation of the dynamic problem of the corrugated steel web composite beam; the state vector equation of the dynamic problem of the corrugated steel web composite beam describes the relationship between the natural vibration state vector and the product of the column vector of undetermined parameters formed by the general solution of the natural vibration state equation and a coefficient matrix; Introducing the internal force displacement continuity condition, constructing the continuity condition equation of the corrugated steel web composite beam; According to the continuity condition equation, construct the natural frequency equation of the corrugated steel web continuous beam, solve the natural frequency equation, and obtain the natural frequency of the corrugated steel web continuous beam; Determine the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the corrugated steel web continuous beam; According to the proportional relationship between the components in the undetermined parameter column vector, the state vector equation of the dynamic problem of the corrugated steel web composite beam is solved to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam.

2. The method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs according to claim 1, characterized in that: The mechanical model for describing the corrugated steel web composite beam is constructed based on the Zig-zag theory, including: Based on the material equivalence principle, the corrugated steel web composite beam is equivalent to a sandwich beam model with orthotropic layers; The interlayer continuous Zig-zag displacement assumption and the layered parabolic distribution of the in-section transverse shear stress assumption are introduced into the sandwich beam model to obtain the mechanical model of the corrugated steel web composite beam.

3. The method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs according to claim 1, characterized in that: The method of constructing the natural vibration state equation of the corrugated steel web composite beam based on the mechanical model and solving the natural vibration state equation to obtain the state vector equation of the dynamic problem of the corrugated steel web composite beam includes: Based on Hamilton's principle, the dynamic equilibrium equation of the corrugated steel web composite beam under the action of conservative force is constructed; Based on the energy principle, the dynamic equilibrium equation is solved to obtain the equilibrium equation of the corrugated steel web composite beam; The self-vibration state vector is constructed according to the combined state information in the mechanical model; the combined state information includes the deflection, rotation angle and zig-zag displacement of the corrugated steel web composite beam and the additional bending moment caused by the section shear force, bending moment and zig-zag displacement of the energy duality; Based on the state space method, rewrite the equilibrium equation into the state equation of the corrugated steel web composite beam in the free state, substitute the natural vibration state vector into the state equation, and obtain the natural vibration state equation; Solve the self-oscillation state equation to obtain an undetermined parameter column vector and a corresponding coefficient matrix formed by the general solution of the self-oscillation state equation, and use the undetermined parameter column vector and the coefficient matrix to construct the state vector equation of the dynamic problem of the corrugated steel web composite beam.

4. The method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs according to claim 1, characterized in that: The introduction of internal force displacement continuity conditions to construct the continuity condition equation of the corrugated steel web composite beam includes: According to the internal force displacement continuity condition, the continuity condition equation of the beam span and the continuity condition equation of the support of the corrugated steel web composite beam are constructed, and the corresponding end boundary conditions are determined; The continuity condition equation of the beam span, the continuity condition equation of the support and the end boundary condition are combined to obtain the continuity condition equation of the corrugated steel web composite beam.

5. The method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs according to claim 1, characterized in that: The method of constructing the natural frequency equation of the corrugated steel web continuous beam according to the continuity condition equation and solving the natural frequency equation to obtain the natural frequency of the corrugated steel web continuous beam includes: Solving the continuity condition equation to obtain the natural frequency equation; The natural frequency of the continuous beam with corrugated steel web is obtained by solving the natural frequency equation at several modal orders using a dichotomy method.

6. The method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs according to claim 1, characterized in that: Determining the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the corrugated steel web continuous beam includes: The natural frequency of the corrugated steel web continuous beam is substituted into the natural frequency equation, and the non-zero solution of the undetermined parameter column vector is calculated to determine the proportional relationship between the components in the undetermined parameter column vector.

7. The method for calculating the natural vibration characteristics of a composite beam with corrugated steel webs according to claim 1, characterized in that: The method of solving the state vector equation of the dynamic problem of the corrugated steel web composite beam according to the proportional relationship of each component in the undetermined parameter column vector to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam comprises: According to the proportional relationship between the components in the undetermined parameter column vector, the undetermined parameter column vector that conforms to the proportional relationship of the components is determined and substituted into the state vector equation of the dynamic problem of the corrugated steel web composite beam to obtain the natural vibration state vector of the vibration mode corresponding to the displacement and internal force of the natural vibration frequency of the corrugated steel web continuous beam.

8. A device for calculating the natural vibration characteristics of a composite beam with corrugated steel webs, characterized in that: include: The first module is used to construct a mechanical model describing the composite beam with corrugated steel webs based on the Zig-zag theory; The second module is used to construct the self-oscillation state equation of the corrugated steel web composite beam according to the mechanical model, solve the self-oscillation state equation, and obtain the state vector equation of the dynamic problem of the corrugated steel web composite beam; the state vector equation of the dynamic problem of the corrugated steel web composite beam describes the relationship between the self-oscillation state vector and the product of the column vector of undetermined parameters formed by the general solution of the self-oscillation state equation and a coefficient matrix; The third module is used to introduce the internal force displacement continuity condition and construct the continuity condition equation of the corrugated steel web composite beam; The fourth module is used to construct the natural frequency equation of the corrugated steel web continuous beam according to the continuity condition equation, solve the natural frequency equation, and obtain the natural frequency of the corrugated steel web continuous beam; The fifth module is used to determine the proportional relationship of each component in the undetermined parameter column vector according to the natural frequency of the corrugated steel web continuous beam; The sixth module is used to solve the state vector equation of the dynamic problem of the corrugated steel web composite beam according to the proportional relationship between the components in the unknown parameter column vector, so as to determine the vibration mode of the displacement and internal force corresponding to the natural frequency of the corrugated steel web continuous beam.

9. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and the processor implements the method for calculating the natural vibration characteristics of the corrugated steel web composite beam according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for calculating the natural vibration characteristics of the corrugated steel web composite beam according to any one of claims 1 to 7 is implemented.

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