Synchronous force and vibration measurement dual-mode narrow-band aeroelastic model and design method

Abstract

The application discloses a synchronous force and vibration measuring double-mode narrow-band aeroelastic model and a design method thereof. The synchronous force and vibration measuring double-mode narrow-band aeroelastic model has the characteristics of large cross-sectional size, small longitudinal size, synchronous force and vibration measuring test, suitability for various vibration mode forms and synchronous simulation of two-order vertical bending mode characteristics. The model comprises a core beam, a transverse beam, an end plate, an end constraint rigid test section outer cover narrow band, a rigid compensation section outer cover narrow band, an elastic support, a concentrated mass point, a force sensor and a response measuring system. The test section outer cover is connected with the core beam through the force sensor to achieve the purpose of built-in force sensor, thereby reducing the inertia force. An equivalent theory is derived so that different scale ratios can be adopted in the longitudinal and transverse directions, the cross-sectional size of the model and the aerodynamic force on the cross section can be improved, the rigid outer cover narrow band is adopted, the inertia force is reduced, and the force and response signals at various positions in the longitudinal direction are also collected, and in the design, the target vibration mode function is directly fitted, so that the model is suitable for various vibration mode forms.

Description

Technical Field

[0001] This invention relates to the field of aerodynamics, and in particular to a synchronous force and vibration measurement dual-mode narrowband aeroelastic model and its design method. Background Technology

[0002] In the field of structural wind engineering, there is an overlap of wind speed locking zones when predicting high-order modal vortex-induced vibrations of slender flexible structures. Simulating dual-mode vortex-induced vibrations within the overlap zone and completing synchronous force and vibration measurements are key to exploring the vortex-induced vibration generation mechanism and discrimination criteria within the overlap zone. Therefore, wind tunnel tests are required to study this phenomenon.

[0003] In wind tunnel testing, while full-structure aeroelastic models can simulate a wide range of natural modes, their geometric scale is typically small due to limitations in the wind tunnel test section size. This results in the model's inability to accurately simulate structural details, and its small size is unsuitable for direct force measurement. Using a larger scale ratio often leads to excessively large longitudinal dimensions, making it difficult to meet the testing requirements of the wind tunnel test section. Simplifying the structural vibration modes to harmonic forms only allows for the simulation of a limited number of harmonic modes. Furthermore, existing aeroelastic model designs typically employ an integral outer casing, primarily suitable for vibration testing. When used for force testing, this results in excessive inertial forces, failing to meet the required testing accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a synchronous force and vibration measurement dual-mode narrowband aeroelastic model and design method to solve one or more technical problems existing in the prior art, and at least provide a beneficial option or create conditions.

[0005] The technical solution adopted to solve the above-mentioned technical problems is as follows:

[0006] This invention provides a design method for a synchronous force and vibration measurement dual-mode narrowband aeroelastic model, comprising the following steps:

[0007] Step 1: Analyze the characteristics of the target structure and convert it into an equivalent two-point elastic support structure, including a core beam, a concentrated mass point, elastic supports, and end constraints. Determine the constraint form and the relative position of the elastic supports based on the test conditions and the characteristics of the target structure.

[0008] Step 2: Based on the characteristics of the target structure, propose a finite element model and perform modal analysis to extract the modal masses of each order of the target structure. Equivalent mass of core beam Modal frequencies and mode shape , where P represents the target structure and r represents the order;

[0009] Step 3: Based on wind tunnel test requirements, similarity principles, and equivalence theory, first, the finite element model of the target structure is then... Perform overall geometric scaling; under the premise of satisfying equivalence and similarity, further scale the data longitudinally based on the overall geometric scaling. Horizontal Local geometric scaling is performed to determine the final scaling ratio, which includes: longitudinal geometric scaling ratio. Horizontal geometric scaling ratio Frequency scaling ratio Equivalent mass scaling ratio Modal mass scaling ratio Wind speed ratio Modal scaling ratio ;

[0010] Step 4: Extract the modal masses of each order based on the finite element model of the target structure. Equivalent mass of core beam Modal frequencies and mode shape Based on the final scaling ratio, the equivalent masses of each order of the narrowband aeroelastic model are calculated. Modal quality Modal frequencies Mode shape Modal stiffness The modal stiffness is determined by the modal frequency and modal mass. ;

[0011] Step 5: Based on the principles of continuous vibration dynamics and the equivalent masses of each order of the narrow-band aeroelastic model... Modal quality Modal frequencies Mode shape Modal stiffness Based on the constraint form and the relative position of the elastic support, the target design parameters of the synchronous force and vibration measurement dual-mode narrowband aeroelastic model are calculated. These target design parameters include the target stiffness of the core beam. Elastic support target stiffness Core beam target distribution mass and target focus quality If any of the four target design parameters are negative, the relative positions of the elastic support need to be adjusted so that all the calculated values ​​are positive.

[0012] Step Six: Based on the target design parameters, design the geometric and material parameters of each component of the synchronous force and vibration measurement dual-mode narrow-band aeroelastic model, including the core beam, crossbeam, end plate, end constraint, rigid test section outer narrow band, rigid compensation section outer narrow band, elastic support, concentrated mass point, force sensor, and response measurement system material parameters and structural form.

[0013] The beneficial effects of this invention are:

[0014] This invention discloses a design method for a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model capable of simulating dual vertical bending modes. Compared to traditional segmental models, which can only simultaneously perform force and vibration measurement of first-order vertical bending and torsional modes, this invention can simultaneously perform force and vibration measurement tests of two-order vertical bending modes. By employing local geometric scaling in the longitudinal and transverse directions, the span can be further reduced by n times compared to conventional aeroelastic models, while the transverse dimensions are enlarged by n times. This avoids the defect of conventional aeroelastic models that cannot measure forces due to their small transverse scaling ratio. Therefore, the model of this invention can simultaneously perform force and vibration measurement tests, making it practical for vortex-induced vibration wind tunnel tests.

[0015] As a further improvement to the above technical solution, step six also includes:

[0016] Based on the target design parameters determined in step five and the final scaling ratio, select the material for the core beam frame, and determine its elastic modulus and density based on the selected material.

[0017] Calculate the theoretical values ​​of the moment of inertia and area of ​​the core beam section based on the target design parameters determined in step five.

[0018] Based on the theoretical values ​​of the moment of inertia and area of ​​the cross section and the requirements of the experimental structure, select the appropriate cross section form and determine the design values ​​of the moment of inertia and area of ​​the cross section;

[0019] A finite element model is established based on the determined elastic modulus and density, model parameters, design values ​​of cross-sectional moment of inertia, and design values ​​of area. Modal analysis is performed, and the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the target model are calculated. These values ​​are then compared with the equivalent mass of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness Compare and determine whether the model design is complete.

[0020] As a further improvement to the above technical solution, the step involves establishing a finite element model based on the determined elastic modulus and density, model parameters, design values ​​of the cross-sectional moment of inertia and area, performing modal analysis, and calculating the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the target model. This is then compared with the equivalent mass of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The steps for comparing and determining whether the model design is complete also include:

[0021] The judgment is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0022] If the deviations of all three judgment criteria are less than the threshold, the model design is complete.

[0023] If the deviation exceeds the threshold, adjust and verify the deviation in turn according to the following 5 adjustment schemes in a cyclical manner: 1. Adjust the design value of moment of inertia while keeping the area design value unchanged; 2. Adjust the design value of area while keeping the design value of moment of inertia unchanged; 3. Adjust the concentrated mass value while keeping the elastic support value unchanged; 4. Adjust the elastic support value while keeping the concentrated mass value unchanged; 5. Reselect materials;

[0024] After each adjustment, modal analysis is performed to obtain the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the adjusted target model. These values ​​are then compared with the equivalent masses of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The comparison is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0025] The model design is completed when the deviations of the three judgment criteria are all less than the thresholds, following the adjustment scheme and deviation evaluation method described above.

[0026] As a further improvement to the above technical solution, in step one, the target structure is equivalent to a two-point elastic support structure, the end constraint form of the model corresponds to the target structure, the mass of the target structure includes the core beam distributed mass and the simulation of concentrated mass points of the two-point elastic support structure, and the stiffness is mainly simulated by the core beam stiffness and elastic support.

[0027] As a further improvement to the above technical solution, in step three, two scaling-ups are performed based on the similarity principle, equivalence theory, and experimental requirements. The first scaling-up is an overall geometric scaling-up, and the second scaling-up is a partial geometric scaling-up (Part) in the longitudinal and transverse directions to meet experimental requirements. Note: Subscript m1 represents the model parameters after the first overall geometric scaling-up, subscript m2 represents the model parameters after the partial geometric scaling-up, and subscript p represents the actual bridge parameters. The first overall geometric scaling-up ratio is determined to be 1: Select a suitable wind speed ratio 1: The overall geometric scaling process is as follows:

[0028] (1) Geometric similarity:

[0029]

[0030] (2) Equivalent quality is similar:

[0031]

[0032] (3) Modal mass similarity:

[0033]

[0034] (4) Select the wind speed ratio according to the test conditions:

[0035]

[0036] (5) Similar frequencies:

[0037]

[0038] (6) Similar vibration modes:

[0039]

[0040] Overall geometric scaling results:

[0041]

[0042] To meet the experimental requirements, based on the overall geometric scaling, and according to the longitudinal... Horizontal Local geometric scaling is performed to further reduce the longitudinal length of the model.

[0043] (1) Longitudinal reduction:

[0044]

[0045] (2) If the total mass remains constant, then the equivalent mass scaling ratio is:

[0046]

[0047] (3) Maintain consistent modal quality:

[0048]

[0049] (4) Based on the similarity of lift, the lateral reduction is:

[0050]

[0051] (5) The longitudinal scaling ratio is Then the horizontal scaling will be:

[0052]

[0053] (6) Similar frequencies: , The frequency is kept the same by adjusting the distributed stiffness and the support stiffness.

[0054] (7) Similar wind speeds:

[0055]

[0056] (8) Similar vibration modes:

[0057]

[0058] Local geometric scaling results:

[0059] .

[0060] As a further improvement to the above technical solution, the core beam target stiffness in the aeroelastic model is calculated based on the principle of continuous vibration dynamics. Elastic support target stiffness Core beam target distribution mass and target focus quality During the calculation, the mode shape function is obtained by fitting the mode shape data. The parameters of the aeroelastic model are calculated as follows:

[0061]

[0062] As a further improvement to the above technical solution, step six also includes a force sensor for measuring the inertial force of the rigid test section outer narrow strip, and the force sensor is installed between the core beam and the rigid test section outer narrow strip.

[0063] As a further improvement to the above technical solution, in step six, a transverse beam is set at the center position and elastic support point position of each rigid test section outer narrow strip and rigid compensation section outer narrow strip.

[0064] As a further improvement to the above technical solution, in step six, the concentrated mass is arranged at the location of the elastic support point.

[0065] This invention also provides a synchronous force and vibration measurement dual-mode narrowband aeroelastic model, including a core beam frame and a support structure. The core beam frame includes two core beams and multiple transverse beams. The two core beams are arranged side by side, and the multiple transverse beams are spaced apart between the two core beams along the extension direction of the core beams. The core beam frame has multiple outer narrowband segments spaced apart along the extension direction of the core beams. The outer narrowband segments are all wrapped with outer narrowbands. The multiple outer narrowband segments include multiple rigid compensation segments and multiple rigid test segments. The rigid test segments are distributed between two adjacent rigid compensation segments. The support structure includes two end supports and at least two elastic supports. The two end supports are respectively connected to both ends of the core beams. The at least two elastic supports are spaced apart between the two end supports along the extension direction of the core beams. The at least two elastic supports are respectively located between any two of the rigid compensation segments. The elastic supports are connected to the core beam frame. Attached Figure Description

[0066] The present invention will be further described below with reference to the accompanying drawings and embodiments;

[0067] Figure 1 This is a schematic diagram of the structure of a synchronous force and vibration measurement dual-mode narrowband aeroelastic model as described in the embodiment;

[0068] Figure 2 This is a cross-sectional schematic diagram of the outer casing of a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model compensation section as described in the embodiment;

[0069] Figure 3 This is a cross-sectional schematic diagram of the outer garment of a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model test section as described in the embodiment;

[0070] Figure 4 This is an elevation view of a synchronous force and vibration measurement dual-mode narrowband aeroelastic model as described in the embodiment;

[0071] Figure 5 This is a plan view of a synchronous force and vibration measurement dual-mode narrowband aeroelastic model as described in the embodiment;

[0072] Figure 6 This is a cross-sectional schematic diagram of the position of the transverse beam of the outer garment of a test section of a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model as described in the embodiment;

[0073] Figure 7 This is a non-transverse diaphragm beam for the outer casing of a test section of a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model, as described in the embodiment.

[0074] A cross-sectional diagram of the location;

[0075] Figure 8This is a cross-sectional schematic diagram of the position of the outer transverse beam of the compensation section of a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model as described in the embodiment;

[0076] Figure 9 This is a schematic cross-sectional view of the non-transverse diaphragm position of the outer garment of the compensation section of a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model as described in the embodiment;

[0077] Figure 10 This is a flowchart illustrating the design method of a synchronous force and vibration measurement dual-mode narrowband aeroelastic model as described in the embodiment. Detailed Implementation

[0078] This section will describe in detail specific embodiments of the present invention. Preferred embodiments of the present invention are shown in the accompanying drawings. The purpose of the drawings is to supplement the textual description with graphics, so that people can intuitively and vividly understand each technical feature and overall technical solution of the present invention, but they should not be construed as limiting the scope of protection of the present invention.

[0079] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0080] In the description of this invention, if there are words such as "several", they mean one or more, "multiple" means two or more, "greater than", "less than", "exceeding" etc. are understood to exclude the number itself, and "above", "below", "within" etc. are understood to include the number itself.

[0081] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0082] Reference Figures 1 to 10 The present invention provides a synchronous force and vibration measurement dual-mode narrowband aeroelastic model and design method, which is embodied in the following embodiments:

[0083] The design method for a synchronous force and vibration measurement dual-mode narrowband aeroelastic model includes the following steps:

[0084] Step 1: Analyze the characteristics of the target structure and convert it into a two-point elastic support structure, including core beam 1, concentrated mass point 8, elastic support 7 and end constraint 4. Determine the constraint form and the relative position of elastic support 7 according to the test conditions and the characteristics of the target structure.

[0085] Step one also includes: equating the target structure to a two-point elastic support structure, with the end constraint form of the model corresponding to the target structure, the mass of the target structure being simulated by the distributed mass of the core beam 1 and the concentrated mass point 8 of the two-point elastic support structure, and the stiffness being simulated by the stiffness of the core beam and the elastic support 7.

[0086] Step 2: Establish a finite element model based on the characteristics of the target structure and perform modal analysis to extract the modal masses of each order of the target structure. Equivalent mass of core beam Modal frequencies and mode shape , where P represents the target structure and r represents the order;

[0087] Step 3: Based on wind tunnel test requirements, similarity principles, and equivalence theory, first, the finite element model of the target structure is then... Perform overall geometric scaling; under the premise of satisfying equivalence and similarity, further scale the data longitudinally based on the overall geometric scaling. Horizontal Local geometric scaling is performed to determine the final scaling ratio, which includes: longitudinal geometric scaling ratio. Horizontal geometric scaling ratio Frequency scaling ratio Equivalent mass scaling ratio Modal mass scaling ratio Wind speed ratio Modal scaling ratio .

[0088] Based on wind tunnel testing requirements, similarity principles, and equivalence theory, first proceed according to... Perform overall geometric scaling, and then, under the premise of satisfying equivalence and similarity, scale it down longitudinally. Horizontal Perform local geometric scaling to obtain the scaling ratio: longitudinal geometric scaling ratio Horizontal geometric scaling ratio Frequency scaling ratio Equivalent mass scaling ratio Modal mass scaling ratio Wind speed ratio Modal scaling ratio .

[0089] Based on the principles of similarity, equivalence theory, and experimental requirements, two scaling operations were performed. The first was a full geometry scale, and the second was a partial geometry scale in both the longitudinal and transverse directions to meet the experimental requirements. Note: Subscript m1 (model1) represents the model parameters after the first full geometry scale, subscript m2 (model2) represents the model parameters after the second partial geometry scale, and subscript p (prototype) represents the actual bridge parameters. The first full geometry scale ratio was determined to be (1: Select a suitable wind speed ratio (1: The overall geometric scaling process is as follows:

[0090] (1) Geometric similarity:

[0091]

[0092] (2) Equivalent quality is similar:

[0093]

[0094] (3) Modal mass similarity:

[0095]

[0096] (4) Select the wind speed ratio according to the test conditions:

[0097]

[0098] (5) Similar frequencies:

[0099]

[0100] (6) Similar vibration modes:

[0101]

[0102] Overall geometric scaling results:

[0103]

[0104] To meet the experimental requirements, based on the overall geometric scaling, and according to the longitudinal... Horizontal Local geometric scaling is performed to further reduce the longitudinal length of the model.

[0105] (1) Longitudinal reduction:

[0106]

[0107] (2) If the total mass remains constant, then the equivalent mass scaling ratio is:

[0108]

[0109] (3) Maintain consistent modal quality:

[0110]

[0111] (4) Based on the similarity of lift, the lateral reduction is:

[0112]

[0113] (5) The longitudinal scaling ratio is Then the horizontal scaling will be:

[0114]

[0115] (6) Similar frequencies: , The frequency is kept the same by adjusting the distributed stiffness and the support stiffness.

[0116] (7) Similar wind speeds:

[0117]

[0118] (8) Similar vibration modes:

[0119]

[0120] Local geometric scaling results:

[0121]

[0122] Step 4: Extract the modal masses of each order based on the finite element model of the target structure. Equivalent mass of core beam (1) Modal frequencies and mode shape Based on the final scaling ratio, the equivalent masses of each order of the narrowband aeroelastic model are calculated. Modal quality Modal frequencies Mode shape Modal stiffness The modal stiffness is determined by the modal frequency and modal mass. ;

[0123] Step 5: Based on the principles of continuous vibration dynamics and the equivalent masses of each order of the narrow-band aeroelastic model... Modal quality Modal frequencies Mode shape Modal stiffness Based on the constraint form and the relative position of the elastic support 7, the target design parameters of the synchronous force and vibration measurement dual-mode narrowband aeroelastic model are calculated. The target design parameters include the target stiffness of the core beam. Elastic support target stiffness Core beam target distribution mass and target focus quality If any of the four target design parameters are negative, the relative position of the elastic support 7 needs to be adjusted so that all the calculated values ​​are positive.

[0124] Specifically, this also includes: calculating the target stiffness of the core beam in a synchronous force and vibration measurement dual-mode narrowband aeroelastic model based on the principles of continuous vibration dynamics and the model modal parameters obtained in step four. Elastic support target stiffness Core beam target distribution mass and target focus quality The model is considered as a single main beam with elastic supports 7 in the calculation. Two concentrated mass points 8 are distributed on the main beam, and the positions of the concentrated mass points 8 are the suspension points of the two elastic supports 7. The entire structure is perfectly symmetrical, therefore the concentrated mass and the stiffness of the elastic supports 7 are the same. The final model uses a double main beam, with the two core beams 1 connected in parallel. Therefore, the stiffness, distributed mass, concentrated mass point 8, and stiffness of the elastic supports 7 of a single core beam 1 are half of the calculated values ​​for the single main beam model. The mode shape function is directly obtained by fitting the mode shape data from the actual bridge modal analysis and is applicable to all types of mode shapes.

[0125]

[0126]

[0127] Step Six: Design the geometric and material parameters of each component of the synchronous force and vibration measurement dual-mode narrow-band aeroelastic model according to the target design parameters, including the material parameters and structural form of the core beam 1, crossbeam 2, end plate 3, end constraint 4, rigid test section outer narrow band 5, rigid compensation section outer narrow band 6, elastic support 7, concentrated mass point 8, force sensor 9, and response measurement system 10.

[0128] Reference Figure 10 Step six also includes:

[0129] Based on the target design parameters determined in step five and the final scaling ratio, select the material for the core beam 1 frame, and determine its elastic modulus and density based on the selected material.

[0130] Calculate the theoretical values ​​of the moment of inertia and area of ​​the core beam 1 section based on the target design parameters determined in step five.

[0131] Based on the theoretical values ​​of the moment of inertia and area of ​​the cross section and the requirements of the experimental structure, select the appropriate cross section form and determine the design values ​​of the moment of inertia and area of ​​the cross section;

[0132] A finite element model is established based on the determined elastic modulus and density, model parameters, design values ​​of cross-sectional moment of inertia, and design values ​​of area. Modal analysis is performed, and the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the target model are calculated. These values ​​are then compared with the equivalent mass of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The comparison and judgment of whether the model design is complete also includes:

[0133] The judgment is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0134] If the deviations of all three judgment criteria are less than the threshold, the model design is complete.

[0135] If the deviation exceeds the threshold, adjust and verify the deviation in turn according to the following 5 adjustment schemes in a cyclical manner: 1. Adjust the design value of moment of inertia while keeping the area design value unchanged; 2. Adjust the design value of area while keeping the design value of moment of inertia unchanged; 3. Adjust the concentrated mass value while keeping the elastic support value unchanged; 4. Adjust the elastic support value while keeping the concentrated mass value unchanged; 5. Reselect materials;

[0136] After each adjustment, modal analysis is performed to obtain the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the adjusted target model. These values ​​are then compared with the equivalent masses of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The comparison is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0137] The model design is completed when the deviations of the three judgment criteria are all less than the thresholds, following the adjustment scheme and deviation evaluation method described above.

[0138] More specific adjustment plans and procedures include:

[0139] The judgment is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0140] If all deviations are less than the threshold, the model design is complete.

[0141] If the deviation exceeds the threshold, the design value of the area should be kept unchanged while the design value of the moment of inertia is adjusted.

[0142] After adjustment, modal analysis is performed to obtain the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the adjusted target model. These values ​​are then compared with the equivalent mass of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The comparison is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0143] If the deviations of all three judgment criteria are less than the threshold, then the model design is complete.

[0144] If the deviation exceeds the threshold, the design value of the moment of inertia will remain unchanged while the design value of the area will be adjusted.

[0145] After adjustment, modal analysis is performed to obtain the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the adjusted target model. These values ​​are then compared with the equivalent mass of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The comparison is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0146] If the deviations of all three judgment criteria are less than the threshold, then the model design is complete.

[0147] After adjustment, modal analysis is performed to obtain the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the adjusted target model. These values ​​are then compared with the equivalent mass of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The comparison is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0148] If all three conditions are met, the model design is complete.

[0149] If the deviation exceeds the threshold, the elastic support value is adjusted to ensure that the concentrated mass value remains unchanged.

[0150] After adjustment, modal analysis is performed to obtain the actual equivalent mass, modal mass, modal frequency, mode shape, and modal stiffness of the adjusted target model. These values ​​are then compared with the equivalent mass of the narrowband aeroelastic model obtained in step five. Modal quality Modal frequencies Mode shape Modal stiffness The comparison is made based on three criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shapes are consistent.

[0151] If the deviations of all three judgment criteria are less than the threshold, then the model design is complete.

[0152] If the deviation still exceeds the threshold, then the material should be redesigned, that is, the density and elastic modulus should be reselected.

[0153] Specifically, based on the scaling ratio, since the model is scaled twice, the cross-sectional scaling ratio is greater than the longitudinal scaling ratio. Using a double-core beam is beneficial to the stability of the model. The two core beams are connected by a crossbeam to form a frame structure.

[0154] Based on the target stiffness of the core beam Elastic support target stiffness Core beam target distribution mass and target focus quality The model's target value is used to determine the material of the core beam 1, including its scaling ratio. Steel or aluminum is chosen as the core beam material. If steel is chosen, the cross-sectional dimensions of the core beam 1 are determined based on the model's target value. To ensure the balance can be stably mounted on the core beam 1, it needs to be designed as a flat shape. If the cross-section of the steel core beam 1 is smaller than the balance base size while meeting the model's target value, aluminum can be chosen as the core beam material. Again, the cross-sectional dimensions of the core beam 1 are determined based on the model's target value, taking into account the balance's dimensions, and the core beam 1 is then chosen as a flat shape. The balance can be understood as a type of force sensor.

[0155] Reference Figure 1 , Figure 2 , Figure 3 and Figure 5 The specific structure of the synchronous force and vibration measurement dual-mode narrowband aeroelastic model includes a core beam frame and an end support structure.

[0156] The core beam frame comprises two core beams 1 and multiple transverse diaphragms 2. The two core beams 1 are arranged side by side, and the multiple transverse diaphragms 2 are spaced apart between the two core beams 1 along the extension direction of the core beams 1. The core beam frame has multiple outer garment narrow strips spaced apart along the extension direction of the core beams 1. Each outer garment narrow strip is wrapped with an outer garment narrow strip. The multiple outer garment narrow strips include multiple rigid compensation sections and multiple rigid test sections. The rigid test sections are distributed between two adjacent rigid compensation sections. For ease of understanding, the rigid compensation section is referred to as the rigid compensation section outer garment narrow strip 6 in this embodiment, and the rigid test section is referred to as the rigid test section outer garment narrow strip 5 in this embodiment. The model outer garment adopts the form of a rigid narrow strip to ensure sufficient rigidity of the test section, reduce inertial forces, and also help to collect force and response signals at various longitudinal positions, facilitating force measurement and demonstrating good practicality in wind tunnel testing.

[0157] Specifically, the outer garment narrow strap includes a lightweight yet rigid outer skin and a lightweight frame, with the lightweight yet rigid outer skin set within the lightweight frame, as shown in the reference. Figure 6 and Figure 7 The outer narrow strip of the rigid test section is integrally machined, and a core beam frame groove is set in the center of the outer narrow strip, through which the core beam frame passes.

[0158] Reference Figure 8 and Figure 9 The rigid compensation section's outer narrow band includes a first wrapping band and a second wrapping band that overlap each other. The first and second wrapping bands are respectively located on both sides of the core beam frame, and the first and second wrapping bands are detachably connected. During installation, the upper and lower first and second wrapping bands are separated and fastened to the upper and lower sides of the core beam frame, respectively, and then bolts are connected. The transverse diaphragm 2 is designed using the same material as the core beam 1, which facilitates welding. The rigid compensation section's outer narrow band has two symmetrical counterweight grooves, and counterweight plates 11 are installed in the counterweight grooves, which can be made of aluminum plates.

[0159] The rigid test section is equipped with two sets of force sensors 9, which are located between the core beam 1 and the outer narrow strip. By using the built-in force sensors 9, the rigid outer narrow strip is connected to the core beam 1 through the force measurement system, thus avoiding the influence of the overall inertial force of the model on the accuracy of the force measurement.

[0160] The support structure includes two end supports and at least two elastic supports. The two end supports are connected to both ends of the core beam 1, respectively. The at least two elastic supports are spaced apart between the two end supports along the extension direction of the core beam 1, and are respectively located between any two rigid compensation sections. The elastic supports are connected to the core beam frame. "Elastic support 7" refers to the support condition of the elastic supports, and "end constraint 4" refers to the constraint form of the end supports. The two ends of the core beam 1 are detachably connected to the end constraints 4 via end plates, facilitating the later installation of the rigid test section outer narrow strip 5 and the verification of the core beam frame's quality. Corresponding end constraints 4 are respectively provided on the lower side of the end plates.

[0161] This invention discloses a design method for a synchronous force and vibration measurement dual-mode narrow-strip aeroelastic model capable of simulating dual vertical bending modes. Compared to traditional segmental models, which can only simultaneously perform force and vibration measurement of first-order vertical bending and torsional modes, this invention can simultaneously perform force and vibration measurement tests of two-order vertical bending modes. By employing local geometric scaling in the longitudinal and transverse directions, the span can be further reduced by a factor of n compared to conventional aeroelastic models, while the transverse dimensions are enlarged by a factor of n. This avoids the limitation of conventional aeroelastic models, which cannot measure forces due to their small transverse scaling ratio. Therefore, the model of this invention can simultaneously perform force and vibration measurement tests, making it practical for vortex-induced vibration wind tunnel tests. By directly fitting the mode shape data into mode shape functions, without simplifying the mode shapes to simple harmonic functions, it ensures that not only simple harmonic modes but also non-simple harmonic modes can be simulated. By using a built-in force measurement system, the rigid outer narrow strip is connected to the core beam 1 through the force measurement system, avoiding the influence of the overall inertial force of the model on the accuracy of the force measurement. The model's outer casing is designed with a rigid narrow band to ensure sufficient rigidity in the test section, facilitating force measurement and demonstrating good practicality in wind tunnel testing. Specific Implementation

[0163] like Figure 1 As shown, the present invention provides a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model that can simulate dual vertical bending modes, including a core beam 1, a transverse diaphragm beam 2, an end plate 3, an end constraint 4, a rigid test section outer narrow band 5, a rigid compensation section outer narrow band 6, an elastic support 7, a concentrated mass point 8, a force sensor 9, and a response measurement system 10.

[0164] The design method for this gas bullet model includes the following steps:

[0165] Step 1: Establish a finite element model of the target bridge and perform modal analysis to extract the modal masses of each order. Equivalent mass of main beam Modal frequencies and mode shape :

[0166]

[0167] Step Two: Based on wind tunnel test requirements, similarity principles, and equivalence theory, first proceed according to... Perform overall geometric scaling:

[0168] Span scaling ratio: .

[0169] Width reduction ratio: .

[0170] Equivalent mass scaling ratio: .

[0171] Modal mass scaling ratio: .

[0172] Select the wind speed ratio based on the test conditions: .

[0173] Frequency scaling ratio: .

[0174] Overall geometric scaling results:

[0175]

[0176] To meet the experimental requirements, the span was adjusted according to the overall geometric scaling.

[0177] Local geometric scaling is performed to further reduce the span of the model.

[0178] Vertical scaling ratio , , .

[0179] If the total mass remains constant, then the equivalent mass is: , , .

[0180] Maintaining consistent modal quality: .

[0181] If the lift remains constant, the scaling ratio of the model width can be derived:

[0182] , , .

[0183] Therefore, the span is shortened to .

[0184] Then increase the width. ,ensure .

[0185] Maintaining consistent frequency: The frequency is kept the same by adjusting the distributed stiffness and the support stiffness.

[0186] Maintaining consistent mode shapes: .

[0187] Based on the scaling ratios determined in step two, calculate the equivalent masses of each order for a synchronous force and vibration measurement dual-mode narrowband aeroelastic model capable of simulating dual vertical bending modes. Modal quality Modal frequencies Mode shape Modal stiffness :

[0188]

[0189] Based on the principles of continuous vibration dynamics and the modal parameters of the first and second order vertical bending modes obtained above, the mode shape is fitted into a mode shape function. By adjusting the distance from the elastic support 7 to the end to 1.36m, the target stiffness of the core beam in a synchronous force and vibration measurement dual-mode narrow-band aeroelastic model that can simulate dual vertical bending modes is calculated. Elastic support target stiffness Core beam target distribution mass and target focus quality :

[0190]

[0191] F

[0192] Based on the target stiffness of the core beam Elastic support target stiffness Core beam target distribution mass and target focus quality Given the scaling ratio, aluminum was chosen as the material for core beam 1. Since the density and elastic modulus of the material are fixed once determined, it is impossible to simultaneously satisfy the target stiffness and target distributed mass. Therefore, the target stiffness of the core beam was optimized based on the model's target frequency, equivalent mass, and mode shape. Elastic support target stiffness If the deviation of the key vibration characteristic parameters of the final model from the target value is less than 5% of the threshold, then the model can proceed according to step S600 support model:

[0193]

[0194] Further, based on the model parameters, the cross-sectional dimensions of the core beam (1) are obtained as follows: concave cross-section, thickness 3mm, width 50mm, length 4.44m, height 14mm, and cross-sectional area 2.16e-4m².2 .

[0195] Further based on the model parameters and the core beam 1 parameters, the crossbeam 2 is determined to be a hollow thin-walled aluminum square tube with a height of 25mm, a width of 25mm, a thickness of 3mm, and a length of 0.35m. The model is designed with a total of 27 outer garment narrow strips, ensuring that a crossbeam 2 is set in the middle of each outer garment narrow strip, for a total of 27 crossbeams 2. In order to maintain stability, a crossbeam 2 is also set at the suspension point of the elastic support 7, so 2 more crossbeams 2 are added, for a total of 29 crossbeams 2.

[0196] A total of 8 suspension elastic supports 7 are installed, and the stiffness of the elastic support 7 is 2812 N / m.

[0197] Based on the determined geometric and material parameters of each component of the model, a finite element model of the scaled-down model was established, and modal analysis was performed. The mode shapes of the model were consistent with the target mode shapes. The deviation of the first-order vertical bending frequency of the model from the target value was 1.84%, the deviation of the second-order vertical bending frequency of the model from the target value was -1.82%, the deviation of the first-order equivalent mass of the model from the target value was 1.49%, and the deviation of the second-order equivalent mass of the model from the target value was -0.84%.

[0198] The suspension point of the elastic support 7 coincides with the location of the concentrated mass point 8. A concentrated mass is set at this location, and the suspension connector of the elastic support 7 is also part of the concentrated mass.

[0199] In this embodiment, when scaling down the aeroelastic model, the conventional approach is to perform geometric scaling. This results in a cross-sectional scaling ratio that is too small, leading to insufficient aerodynamic force and making it inconvenient to conduct force measurement tests. In this embodiment, different scaling ratios are used in the longitudinal and transverse directions, while simultaneously satisfying the equivalence of vibration characteristics.

[0200] The preferred embodiments of the present invention have been described in detail above, but the present invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A method for designing a synchronous force and vibration measuring dual-mode narrow-band aeroelastic model, characterized in that, The method comprises the following steps: Step one: analyzing the characteristics of the target structure, equivalent to a two-point elastic support structure, including a core beam, a concentrated mass point, an elastic support and an end constraint, determining the constraint form and the relative position of the elastic support according to the test conditions and the characteristics of the target structure; Step two: Establish finite element model according to the characteristics of target structure and carry out modal analysis, extract the modal mass of each order of target structure , equivalent mass of core beam , modal frequency and modal shape , wherein p denotes the target structure, r denotes the order number; Step three: according to the wind tunnel test requirements, similarity principle and equivalent theory, the finite element model of the target structure is firstly scaled down in whole geometry, and then scaled down in local geometry in longitudinal direction and lateral direction on the basis of the whole geometry scaling down to determine the final scaling ratio, which includes the longitudinal geometric scaling ratio, the lateral geometric scaling ratio, the frequency scaling ratio, the equivalent mass scaling ratio, the modal mass scaling ratio, the wind speed ratio and the modal shape scaling ratio. ;​​​​​​​​​ Step four: extract the modal mass of each order from the finite element model of the target structure , the core beam equivalent mass , the modal frequency and the modal shape , and the final scale ratio, calculate the equivalent mass , the modal mass , the modal frequency , the modal shape , the modal stiffness of each order of the narrow-band aeroelastic model, where the modal stiffness is determined by the modal frequency and the modal mass: ; Step five: calculate the target design parameters of the synchronous force and vibration dual-mode narrow-band aero-elastic model according to the continuous vibration mechanics principle, the equivalent mass of each order of the narrow-band aero-elastic model , the modal mass , the modal frequency , the modal vibration mode , the modal stiffness , the relative position of the constraint form and the elastic support, the target design parameters including the core beam target stiffness , the elastic support target stiffness , the core beam target distributed mass and the target lumped mass , if there is a negative number in the four target design parameters, the relative position of the elastic support needs to be adjusted so that all the calculated values are positive numbers; Step six: designing the geometric and material parameters of each component of the synchronous force and vibration measuring double-mode narrow-band aeroelastic model according to the target design parameters, including the core beam, the cross beam, the end plate, the end constraint, the rigid test section outer clothing narrow band, the rigid compensation section outer clothing narrow band, the elastic support, the concentrated mass point, the force sensor, the response measurement system material parameters and the structure form.

2. The method of claim 1, wherein, The step six further comprises: selecting the material of the core beam frame according to the target design parameters determined in step five and the final scale ratio, and determining the elastic modulus and density of the selected material; calculating the theoretical value of the sectional moment of inertia and the theoretical value of the area of the core beam according to the target design parameters determined in step five; selecting the corresponding cross section form according to the theoretical value of the sectional moment of inertia, the theoretical value of the area and the test structure requirements, and determining the design value of the sectional moment of inertia and the design value of the area; According to the determined elastic modulus and density, model parameters, section inertia moment design value, area design value, a finite element model is established to perform modal analysis and calculate the actual equivalent mass, modal mass, modal frequency, modal shape and modal stiffness of each order of the target model, and compare with the equivalent mass, modal mass, modal frequency, modal shape and modal stiffness of each order of the narrow-band aeroelastic model obtained in step five to determine whether the model is designed. ​​​​​ 3. The design method of the synchronous force and vibration measuring double-mode narrow-band aeroelastic model according to claim 2, wherein: The finite element model is established according to the determined elastic modulus and density, model parameters, design value of sectional inertia moment and area design value, modal analysis is carried out, and actual each order equivalent mass, modal mass, modal frequency, modal mode and modal stiffness of the target model are calculated, and each order equivalent mass , modal mass , modal frequency , modal mode and modal stiffness of the narrow-band aeroelastic model obtained in step five are compared and judged to determine whether the model is designed. The step of judging whether the model is designed also includes: determine whether the frequency deviation is less than the threshold value, whether the equivalent mass deviation is less than the threshold value, and whether the vibration mode is consistent according to three judgment criteria; if the deviations of the three judgment criteria are less than the threshold value, the model design is completed; if the deviations are greater than the threshold value, the following five adjustment schemes are used to adjust and verify the deviation situation in turn:

1. adjust the design value of the sectional moment of inertia while keeping the design value of the area unchanged; 2. adjust the design value of the area while keeping the design value of the sectional moment of inertia unchanged; 3. adjust the concentrated mass value while keeping the elastic support value unchanged; 4. adjust the elastic support value while keeping the concentrated mass value unchanged; 5. select the material again; After each adjustment, modal analysis is performed to obtain the actual equivalent mass, modal mass, modal frequency, modal shape and modal stiffness of each order of the adjusted target model, and compare them with the equivalent mass, modal mass, modal frequency, modal shape and modal stiffness of each order of the narrow-band aeroelastic model obtained in step five , modal mass , modal frequency , modal shape , modal stiffness , according to three judgment criteria: whether the frequency deviation is less than the threshold, whether the equivalent mass deviation is less than the threshold, and whether the mode shape is consistent. adjust according to the adjustment scheme and the deviation evaluation method until the deviations of the three judgment criteria are less than the threshold value, and then the model design is completed.

4. The design method of the synchronous force and vibration measuring double-mode narrow-band aeroelastic model according to claim 1, wherein: in step one, the target structure is equivalent to a two-point elastic support structure, the end constraint form of the model corresponds to the target structure, the mass of the target structure includes the core beam distributed mass and the concentrated mass point simulation of the two-point elastic support structure, and the stiffness is simulated by the core beam stiffness and the elastic support.

5. The design method of the synchronous force and vibration measuring double-mode narrow-band aeroelastic model according to claim 1, wherein, In the third step, two scale reductions are made according to the similarity principle, the equivalent theory and the test requirements. The first is the overall geometric scale reduction, and the second is the local geometric scale reduction in the longitudinal and transverse directions to meet the test requirements. Note that the subscript m1 represents the model parameters after the first overall geometric scale reduction, the subscript m2 represents the model parameters after the second local geometric scale reduction, and the subscript P represents the parameters of the actual bridge. The overall geometric scale reduction ratio 1 is determined as follows: The appropriate wind speed ratio 1 is selected as follows: The overall geometric scale reduction process is as follows: (1) geometric similarity: (2) equivalent mass similarity: (3) modal mass similarity: (4) select the wind speed ratio according to the test conditions: (5) frequency similarity: (6) vibration mode similarity: overall geometric scale result: In order to meet the test requirements, on the basis of the overall geometric scale, according to the longitudinal , transverse partial geometric scale, the purpose of the partial geometric scale is to further reduce the longitudinal length of the model: (1) longitudinal scale: (2) the total mass remains unchanged, so the equivalent mass scale ratio is: (3) the modal mass remains unchanged: (4) according to the lift similarity, the lateral scale is: (5) the longitudinal scale ratio is then the horizontal scale is (6) Frequency similarity: , , frequency is ensured to be the same by adjusting distribution stiffness and support stiffness; (7) wind speed similarity: (8) vibration mode similarity: local geometric scale result: 。 6. The method of claim 1, wherein, in step five, The target stiffness of the core beam in the aeroelastic model is calculated according to the principle of continuous vibration mechanics , the target stiffness of the elastic support , the target distributed mass of the core beam , and the target concentrated mass , the mode shape function is fitted by fitting the mode shape data in the calculation, and the parameters of the aeroelastic model are calculated as follows: 。 7. The method of claim 1, wherein, In the step six, a force sensor for measuring inertial force of the rigid test section cover narrow band is further included, and the force sensor is installed between the core beam and the rigid test section cover narrow band.

8. The method of claim 1, wherein, In the step six, a cross beam is arranged at the center position of each rigid test section cover narrow band and the elastic support point position of the rigid compensation section cover narrow band.

9. The method of claim 1, wherein, In the step six, the concentrated mass is arranged at the elastic support point position.

10. A synchronous force and vibration measurement bimodal narrowband aeroelastic model, characterized in that, The synchronous force and vibration measurement double-mode narrow band aeroelastic model is designed by using the design method of any one of claims 1 to 9, and the synchronous force and vibration measurement double-mode narrow band aeroelastic model comprises: The core beam frame comprises two core beams arranged side by side and a plurality of cross beams connected between the two core beams in the direction in which the core beams extend, and the core beam frame is provided with a plurality of cover narrow band sections arranged at intervals in the direction in which the core beams extend, and the outer sides of the cover narrow band sections are wrapped with cover narrow bands, and the plurality of cover narrow band sections comprise a plurality of rigid compensation sections and a plurality of rigid test sections, and the rigid test sections are distributed between any two adjacent rigid compensation sections; The support structure comprises two end support members and at least two elastic support members, the two end support members are connected with the two ends of the core beam respectively, the at least two elastic support members are arranged at intervals between the two end support members in the direction in which the core beam extends, and the at least two elastic support members are arranged between any two adjacent rigid compensation sections, and the elastic support members are connected with the core beam frame.

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