Method for determining constraint constant of end part of structural rod piece
By using the finite element model and frequency calculation formula, the constraint constants at the ends of the members are derived, solving the problem of difficulty in accurate matching under complex support conditions using traditional methods, and realizing accurate calculation of structural vibration response.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-28
- Publication Date
- 2026-03-24
AI Technical Summary
In existing technologies, when connecting members to elastic support beams and truss braces, the actual constraint is in a transitional state between hinged and fixed support. Traditional lookup table methods are difficult to match accurately, affecting the accuracy of structural vibration response.
By establishing a finite element model, performing modal analysis, transient dynamic analysis, and Fourier transform, and combining the formula for calculating the vibration frequency of the members, the end constraint constants of the structural members are derived in reverse.
The end constraint constants of members under complex support conditions were accurately determined, which improved the accuracy and rationality of structural vibration response calculation.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of structural member vibration analysis technology, and particularly relates to a method for determining the end constraint constants of structural members. Background Technology
[0002] During structural design, it is necessary to evaluate the vibration response of the structure under various dynamic loads (such as earthquakes, wind loads, and machine vibrations), including displacement, velocity, and acceleration. This response data helps engineers determine whether the structure will experience excessive deformation or stress due to vibration, thereby assessing the structure's safety. Specifically, for vibration problems of structural members, it is often necessary to introduce the end constraint constants of the members as input conditions for member vibration evaluation.
[0003] Existing methods typically simplify the end constraints of members to ideal hinged or fixed supports in order to select the corresponding constraint constants, leading to calculation errors. In actual engineering projects, when members are connected to elastic support beams or truss braces, their actual constraints are in a transitional state between hinged and fixed supports. Traditional lookup table methods are difficult to match accurately, which in turn affects the results of structural vibration response.
[0004] Therefore, there is an urgent need to design a method for determining the end constraint constants of structural members to solve the problems mentioned above. Summary of the Invention
[0005] To address the technical problem mentioned in the background art, where the actual constraint of structural members is in a transitional state between hinged and fixed support when connected to elastic support beams or truss braces, making it difficult to accurately match using table lookup methods and thus affecting the structural vibration response, a method for determining the end constraint constants of structural members is provided to solve the problem of accurately determining the end constraint constants of structural members.
[0006] To achieve the above objectives, the specific technical solution of the method for determining the end constraint constants of structural members according to the present invention is as follows: A method for determining the end constraint constants of structural members mainly includes the following steps: S1. Establish the finite element model of the target structure; S2. Set the finite element properties of the structural frame; S3. Conduct modal analysis and extract modal data of the target member; S4. Select modal data to calculate the Rayleigh damping coefficient required for structural dynamic analysis; S5. Obtain the time history curve of the vibration of the target rod through transient dynamic analysis; S6. Obtain the fundamental frequency of free vibration of the target rod through Fourier transform; S7. By using the formula for calculating the vibration frequency of structural members, the end constraint constant of the target member can be derived.
[0007] Furthermore, in S1, the finite element model of the target structure includes the target structure members, the related members connected to its ends, and the nodes between them.
[0008] Furthermore, in S2, the finite element properties refer to setting the elastic modulus, shear modulus, yield strength, and mass density of the members in the frame.
[0009] Furthermore, only the mass density of the target member is retained, while the mass density of the surrounding members is corrected to 0, so as to obtain the vibration characteristics of the target member in the subsequent modal analysis.
[0010] Furthermore, in S3, parameters including natural frequency, mode shape, and modal participation factor are obtained through finite element software. The selection of the modal order must ensure that the mass participation rate of the target member reaches more than 90%.
[0011] Furthermore, in S4, when selecting modes, modes with larger mode participation factors are preferred to better reflect the damping characteristics of the target structure.
[0012] Furthermore, in S5, the duration of the transient analysis must be sufficient to observe the vibration response of the target member until its vibration tends to stabilize or decays to a negligible level.
[0013] Furthermore, in S6, the vibration data in the time domain is converted to the frequency domain through Fourier transform to obtain a spectrum. In the spectrum, the frequency corresponding to the peak with the largest amplitude is found. This frequency is the fundamental frequency of the free vibration of the target rod.
[0014] Furthermore, in S7, based on the relationship between the fundamental frequency of the member and the constraint constant at the end of the member, the fundamental frequency of the member obtained from S1-S6 is used as the input condition and substituted into the formula: The end constraint constants of the member are obtained by reverse calculation; where C is the end constraint constant of the member, L is the length of the member, E is Young's modulus, I is the moment of inertia of the member section, and W is the effective mass per unit length of the member.
[0015] Furthermore, after determining the constraint constant, this formula can be used to quickly obtain the vibration frequency of the rod after the change in rod parameters, length, or mass under the same support conditions.
[0016] The method for determining the end constraint constants of structural members according to the present invention has the following advantages: The constraint constants at the ends of structural members under complex support conditions were obtained through numerical calculation and formula derivation. This avoids the existing practice of simplifying the constraints at the ends of members to ideal hinged or fixed supports to determine the constraint constants. This makes the values of the constraint coefficients at the ends of members under complex support conditions more accurate and improves the accuracy and rationality of the calculation and analysis results. Attached Figure Description
[0017] Figure 1 The flowchart of the method for determining the end constraint constants of structural members in this invention is shown below; Figure 2 This is a finite element model diagram of the framework of this invention.
[0018] Explanation of markings in the diagram: 1. Structural frame; 2. Target member; 3. Related members. Detailed Implementation
[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0020] Those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, in the claims, any of the claimed embodiments can be used in any combination.
[0021] The following is a reference to the appendix. Figure 1 To be continued Figure 2 The present invention describes a method for determining the end constraint constants of structural members.
[0022] It should be understood that, for ease of description, the dimensions of the various components shown in the accompanying drawings are not drawn to actual scale; for example, the thickness or width of some layers may be exaggerated relative to other layers.
[0023] like Figure 1 As shown, the method for determining the end constraint constants of structural members in this invention mainly includes the following steps: S1. Establish the finite element model of the target structure; It should be noted that the finite element model of the target structure mentioned in step 1 is the structural frame 1, which includes the target member 2, related members 3 connected to its ends, and the nodes between them.
[0024] S2. Set the finite element properties of the structural frame; It should be noted that setting the finite element properties of structural frame 1 mentioned in step 2 refers to setting the elastic modulus, shear modulus, yield strength, and mass density of the members in structural frame 1. Specifically, only the mass density of the target member 2 is retained, while the mass density of the related member 13 is corrected to 0, so as to better obtain the vibration characteristics of the target member 12 in the subsequent modal analysis.
[0025] S3. Conduct modal analysis and extract modal data of the target member; It should be noted that the modal analysis mentioned in step 3, which involves extracting the modal data of the target member 2, refers to obtaining parameters including natural frequencies, mode shapes, and modal participation factors through finite element software. The selection of the modal order should ensure that the mass participation rate of the target member 2 reaches more than 90%.
[0026] S4. Select modal data to calculate the Rayleigh damping coefficient required for structural dynamic analysis; It should be noted that, in step 4, when selecting modal data to calculate the Rayleigh damping coefficient required for structural dynamic analysis, modes with larger modal participation factors should be prioritized to better reflect the damping characteristics of the target member 2. Generally, the first and second modal parameters can be selected as inputs for damping calculation.
[0027] S5. Obtain the time history curve of the vibration of the target rod through transient dynamic analysis; It should be noted that in step 5, the time history curve of the vibration of the target rod 2 is obtained through transient dynamic analysis. The duration of the transient analysis must be sufficient, and the vibration response of the target rod 2 should be observed until its vibration tends to stabilize or decays to a negligible level.
[0028] S6. Obtain the fundamental frequency of free vibration of the target rod through Fourier transform; It should be noted that obtaining the fundamental frequency of free vibration of the target rod 2 through Fourier transform in step 6 refers to converting the vibration data in the time domain to the frequency domain using Fourier transform to obtain a spectrum. In the spectrum, the frequency corresponding to the peak with the largest amplitude is found; this frequency is usually the fundamental frequency of free vibration of the target rod 2.
[0029] S7. By using the formula for calculating the vibration frequency of structural members, the end constraint constant of the target member can be derived. It should be noted that the step 7, in which the end constraint constant of target member 2 is derived from the formula for calculating the vibration frequency of structural members, is based on the relationship between the fundamental frequency of the member and the end constraint constant. The fundamental frequency of the member obtained from S1-S6 is used as the input condition and substituted into the formula. The end constraint constants of the member are obtained by reverse calculation.
[0030] Where C is the end constraint constant of the member, L is the length of the member, E is Young's modulus, I is the moment of inertia of the member section, and W is the effective mass per unit length of the member.
[0031] After determining the constraint constants, for cases where the parameters (length, mass, etc.) of the rod change under the same support conditions, the vibration frequency of the rod after the change can be quickly obtained using the above formula.
[0032] Based on the method for determining the end constraint constants of structural members, this invention obtains the end constraint constants of structural members under complex support conditions through numerical calculation and formula derivation. This avoids the existing practice of simplifying the end constraint of the target member 2 to an ideal hinge or fixed support to determine the constraint constant, thus making the end constraint coefficient of the member under complex support conditions more accurate and improving the accuracy and rationality of the calculation and analysis results.
[0033] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.
Claims
1. A method for determining the end constraint constants of structural members, characterized in that, The main steps include: S1. Establish the finite element model of the target structure; S2. Set the finite element properties of the structural frame; S3. Conduct modal analysis and extract modal data of the target member; S4. Select modal data to calculate the Rayleigh damping coefficient required for structural dynamic analysis; S5. Obtain the time history curve of the vibration of the target rod through transient dynamic analysis; S6. Obtain the fundamental frequency of free vibration of the target rod through Fourier transform; S7. By using the formula for calculating the vibration frequency of structural members, the end constraint constant of the target member can be derived.
2. The method for determining the end constraint constants of structural members according to claim 1, characterized in that, In S1, the finite element model of the target structure includes the target structure members, the related members connected to its ends, and the nodes between them.
3. The method for determining the end constraint constants of structural members according to claim 1, characterized in that, In S2, the finite element properties refer to setting the elastic modulus, shear modulus, yield strength, and mass density of the members in the frame.
4. The method for determining the end constraint constants of structural members according to claim 3, characterized in that, Only the mass density of the target member is retained, while the mass density of the surrounding members is corrected to 0, so as to obtain the vibration characteristics of the target member in the subsequent modal analysis.
5. The method for determining the end constraint constants of structural members according to claim 1, characterized in that, In S3, parameters including natural frequency, mode shape, and modal participation factor are obtained through finite element software. The selection of the modal order should ensure that the mass participation rate of the target member reaches more than 90%.
6. The method for determining the end constraint constants of structural members according to claim 1, characterized in that, In S4, when selecting modes, modes with larger mode participation factors are preferred to better reflect the damping characteristics of the target structure.
7. The method for determining the end constraint constants of structural members according to claim 1, characterized in that, In S5, the duration of the transient analysis must be sufficient to observe the vibration response of the target member until its vibration tends to stabilize or decays to a negligible level.
8. The method for determining the end constraint constants of structural members according to claim 1, characterized in that, In S6, the vibration data in the time domain is converted to the frequency domain through Fourier transform to obtain a spectrum. In the spectrum, the frequency corresponding to the peak with the largest amplitude is found. This frequency is the fundamental frequency of the free vibration of the target rod.
9. The method for determining the end constraint constants of structural members according to claim 1, characterized in that, In S7, based on the relationship between the fundamental frequency of the member and the constraint constant at the end of the member, the fundamental frequency of the member obtained from S1-S6 is used as the input condition and substituted into the formula: The end constraint constants of the member are obtained by reverse calculation; where C is the end constraint constant of the member, L is the length of the member, E is Young's modulus, I is the moment of inertia of the member section, and W is the effective mass per unit length of the member.
10. The method for determining the end constraint constants of structural members according to claim 9, characterized in that, After determining the constraint constants, this formula can be used to quickly obtain the vibration frequency of the rod after the change in rod parameters, length, or mass under the same support conditions.