Material Modulus Testing Method Based on Internal Force Identification of Bow-Shaped Device
Through the self-internal force identification method based on the bow device, the elastic modulus of the sheet material is calculated using the vibration frequency, which solves the problem of measuring sheet material in the prior art, and achieves fast and inexpensive modulus testing and real-time change monitoring.
Patent Information
- Application Number
- CN202210646618.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-08
- Publication Date
- 2025-01-03
- Estimated Expiration
- 2042-06-08
AI Technical Summary
The prior art is difficult to measure the elastic modulus of sheet materials quickly and economically, and cannot test the changes in the material modulus for a long time, and it is poor in applicability to sheet materials.
The self-internal force identification method based on the bow device is used to calculate the self-internal force of the bow device by measuring the vibration frequency of the tensioned steel wire, and the elastic modulus of the sheet material is inverted by combining the principle of structural dynamics and material mechanics theory. The method includes measuring the cross-sectional dimensions of the sheet material, calculating the moment of inertia, making a curved bow frame, measuring the deformation and vibration frequency of the curved bow frame, calculating deformation parameters, and finally inverting the material modulus.
It can quickly and inexpensively measure the elastic modulus of the sheet material, and can test the changes in the material modulus in real time. It is suitable for sheet material, reducing the requirements for equipment and specimen size.
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Figure CN114894899B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a testing method, in particular to a material modulus testing method based on self-internal force identification of a bow-shaped device, and belongs to the field of building structure material parameters. Background Art
[0002] The material modulus test is usually carried out in a universal testing machine, by measuring the material's stress-strain curve to convert the material's elastic model. However, this method requires expensive experimental equipment, has strict requirements on the specimen size of the test material, is not well applicable to thin sheet materials, and cannot test the change of material modulus for a long time. Summary of the invention
[0003] In view of the above problems in the prior art, the present invention provides a material modulus testing method based on self-internal force identification of a bow-shaped device, so as to solve the problem of how to quickly measure the elastic modulus of a thin sheet material.
[0004] To achieve this technical purpose, the present invention adopts the following scheme:
[0005] A material modulus testing method based on self-internal force identification of a bow device, which adopts a material modulus testing device, the material modulus testing device comprising a bow device, an excitation device, a vibration pickup device, a control box, a computer, a data acquisition box and a signal generator; the bow device comprises a bending bow frame and a tensioned steel wire arranged thereon, and the two ends of the tensioned steel wire are arranged at the bottom of the two ends of the bending bow frame through fixing nuts; the excitation device and the vibration pickup device are arranged on one side or both sides of the bow device; the excitation device and the vibration pickup device are not in contact with the bow device, and one end of the excitation device and the vibration pickup device are both facing the tensioned steel wire; the other end of the excitation device is connected to one end of the signal generator, and the other end of the vibration pickup device is connected to one end of the control box; the other end of the signal generator and the other end of the control box are both connected to the data acquisition box, and the data acquisition box is in communication connection with the computer. The specific testing method comprises the following steps:
[0006] Step 1: Measure the cross-sectional dimensions of the sheet material and calculate its moment of inertia;
[0007] Step 2: Make a bending arch frame with the sheet material of the modulus to be measured, fix the tensile steel wire, and measure the deformation size of the bending arch frame;
[0008] Step 3: Measure the first-order vibration frequency of the tensioned steel wire in the bow device and convert it into the internal force of the bow device;
[0009] Step 4: Calculate the deformation parameter p value according to the deformation size of the bending bow frame;
[0010] Step 5: Inverse the bending bow material modulus parameters.
[0011] Furthermore, the step 1 specifically includes: measuring the cross-sectional width b and height d of the thin sheet material to be measured, and calculating its moment of inertia I.
[0012] Furthermore, the step 2 is specifically as follows: the thin sheet material to be tested is used as a bending bow frame in the bow device, combined with the tensioned steel wire and the fixing nut to form a bow device, and the effective length L of the bending bow frame and the effective length l of the tensioned steel wire in the bow device are measured.
[0013] Furthermore, the step three is specifically as follows: the tensioned steel wire in the bow device is a string-drawing structure, and the first-order vibration frequency f thereof is obtained by combining an excitation device and a vibration pickup device; and the tension exerted on the tensioned steel wire is a manifestation of the internal force of the bow device, and the internal force of the bow device can be obtained by calculating the tension;
[0014] According to the principles of structural dynamics, the tension of the tensioned steel wire and its vibration frequency have the following relationship:
[0015]
[0016] in, is the linear density of the tensioned steel wire; l is the effective length of the tensioned steel wire; f is the first-order vibration frequency of the tensioned steel wire; T is the internal force of the bow device, that is, the tension of the tensioned steel wire.
[0017] Furthermore, the step 4 is specifically as follows: calculating the deformation parameter p value by combining the calculation formula of the effective length L of the complete bow frame and the effective length l of the tensioned steel wire;
[0018] The bending arch is simplified into a large deformation compression rod model, point O is the connection between the bow device and the tension wire, and point A is the highest point of the bending arch; from the overall force characteristics, point A is regarded as the fixed end, point O is the free end, and the bending arch is subjected to the vertical pressure T provided by the tension wire at point O, causing the bending arch to buckle; a rectangular coordinate axis xOy is established with point O as the origin, and the pressure is the internal force of the bow device, which is downward along the positive direction of the x-axis; in addition, L is the effective length of the bending arch, s is the distance from point O along the compression rod axis, α is the maximum torsion angle of the arch, that is, the torsion angle at point O, θ is the torsion angle per unit length of the bending arch, 0<θ<α, l and h are the effective length of the tension wire and the distance from the highest point of the bending arch to the tension wire, respectively;
[0019] According to the bending theory in material mechanics, the deflection curve equation of the bending bow has the following expression:
[0020]
[0021] Among them, E a I is the bending stiffness of the bending arch;
[0022] Derivative both sides of equation (2) with respect to s and multiply by dθ, and using the relationship dy / ds=sinθ, we can obtain the following relationship:
[0023]
[0024] In the formula,
[0025] Integrating formula (3) yields:
[0026]
[0027] Where C is the integral constant, which can be determined by the top condition of the rod; since the bending moment at the top of the compression rod is zero, dθ / ds=0, and θ=α, we can get C=-k 2 cosα; From the model, we know that dθ / ds is always negative, that is:
[0028]
[0029] By transposing and integrating it, the length of the curved bow is:
[0030]
[0031] Let p = sin(α / 2) and introduce a new variable Right now:
[0032]
[0033] When θ changes from 0 to α, changes from 0 to 1, and From 0 to 0.5π; differentiate both sides of equation (7) and move the terms to obtain:
[0034]
[0035] in addition:
[0036]
[0037] Substituting equations (8) and (9) into equation (6), we can obtain:
[0038]
[0039] Among them, K(p) is the first kind of complete elliptic integral, and its value is only related to p. Therefore, the value of K(p) can be obtained by referring to the numerical table of the first kind of complete elliptic integral according to the calculated p value;
[0040] Similarly, we can deduce that:
[0041]
[0042] Where E(p) is the complete elliptic integral of the second kind, which can also be obtained by referring to the numerical table of complete elliptic integral of the second kind according to the calculated p value;
[0043] Combining equation (10) and equation (11), we can get:
[0044]
[0045] Different p values are calculated using formula (12), thereby obtaining different K(p) and E(p), until the p value when the left and right sides of formula (12) are equal is the final p value.
[0046] Furthermore, the step 5 is specifically as follows: according to the deformation size and internal force of the bending frame, the modulus E of the bending frame material, that is, the sheet material, is inverted. a Size:
[0047]
[0048] Furthermore, the excitation device is a speaker, and the vibration pickup device is a laser detector.
[0049] Furthermore, the effective length L of the bending arch is the length of the bending arch between the fixing nuts, which is 25-32 cm; the effective length l of the tensioned steel wire is the length of the tensioned steel wire between the fixing nuts, which is 20-30 cm.
[0050] Furthermore, the two ends of the tensioned steel wire are symmetrically fixed at the two ends of the bending arch frame; and the nut of the fixing nut is fixedly arranged on the outer side of the bending arch frame.
[0051] Furthermore, the bending bow frame is a metal or plastic bending bow frame, that is, the sheet material is metal or plastic; in addition, when the excitation device and the vibration pickup device are arranged on both sides of the bow device, the bow device to be tested is placed between the excitation device and the vibration pickup device, and the axial direction of the tensioned steel wire is perpendicular to the direction of the vibration pickup device and the direction of the excitation device; the measuring point position of the tensioned steel wire is located at the focal position of the laser emitted by the vibration pickup device, and the excitation device is 8-12cm away from the tensioned steel wire.
[0052] Compared with the prior art, the present invention has the following beneficial effects:
[0053] The present invention can quickly measure the elastic modulus of thin sheet materials through a simple and cheap tool such as an arch device, and can test the modulus change of the arch frame material in real time according to the vibration frequency of the tensioned steel wire in the arch device. BRIEF DESCRIPTION OF THE DRAWINGS
[0054] The present invention will be further described below by means of the accompanying drawings.
[0055] Figure 1 It is a schematic diagram of the structure of the bow device of the present invention;
[0056] Figure 2 It is a schematic diagram of the connection of the components of the material modulus testing device based on the self-internal force identification of the bow-shaped device of the present invention;
[0057] Figure 3 It is the large deformation compression rod model of the bow frame;
[0058] Figure 4 It is the tensile test result of elastic metal steel sheet;
[0059] Figure 5 This is the stress relaxation condition of the plastic bending bow. DETAILED DESCRIPTION
[0060] Combined with Figure 1-5 The embodiments of the present invention are described in detail.
[0061] Example 1
[0062] The present embodiment is a material modulus testing method based on the self-internal force identification of the bow device, which uses a material modulus testing device, such as Figure 1-2 As shown, the material modulus testing device includes an arch device 1, an excitation device 2, a vibration pickup device 3, a control box 4, a computer 5, a data acquisition box 6 and a signal generator 7. The arch device 1 includes a bending arch frame 11 and a tensioned steel wire 12 arranged thereon, and both ends of the tensioned steel wire 12 are arranged at the bottom of both ends of the bending arch frame 11 through fixing nuts 13. The excitation device 2 and the vibration pickup device 3 are arranged on one side of the arch device 1. The excitation device 2 and the vibration pickup device 3 are not in contact with the arch device 1, and one end of the excitation device 2 and the vibration pickup device 3 are both facing the tensioned steel wire 12. The other end of the excitation device 2 is connected to one end of the signal generator 7, and the other end of the vibration pickup device 3 is connected to one end of the control box 4. The other end of the signal generator 7 and the other end of the control box 4 are both connected to the data acquisition box 6, and the data acquisition box 6 is in communication connection with the computer 5.
[0063] like Figure 1 As shown, in this embodiment, the excitation device 2 is a sound, and the vibration pickup device 3 is a laser detector. The effective length L of the bending arch 11 is the length of the bending arch between the fixing nuts 13, and the effective length l of the tensioned steel wire 12 is the length of the tensioned steel wire between the fixing nuts 13. The two ends of the tensioned steel wire 12 are symmetrically fixed at the two ends of the bending arch 11. The nut of the fixing nut 13 is fixedly arranged on the outer side of the bending arch 11.
[0064] The specific test method includes the following steps:
[0065] Step 1: Measure the cross-sectional dimensions of the sheet material and calculate its moment of inertia.
[0066] Specifically: measure the cross-sectional width b and height d of the thin sheet material to be tested, and calculate its moment of inertia I.
[0067] Step 2: Make the sheet material of the modulus to be measured into a bending frame 11, fix the tensioned steel wire 12, and measure the deformation size of the bending frame 11.
[0068] Specifically, the thin sheet material to be tested is used as the bending bow frame 11 in the bow device 1, combined with the tensioned steel wire 12 and the fixing nut 13 to form a bow device, and the effective length L of the bending bow frame in the bow device 1 and the effective length l of the tensioned steel wire 12 are measured.
[0069] Step 3: Measure the first-order vibration frequency of the tensioned steel wire 12 in the bow device 1 and convert it into the internal force of the bow device.
[0070] Specifically, the tensioned steel wire 12 in the bow device 1 is a string structure, and its first-order vibration frequency f is obtained by combining the excitation device 2 and the vibration pickup device 3. The tension on the tensioned steel wire 12 is a manifestation of the internal force of the bow device 1, and the internal force of the bow device 1 can be obtained by calculating the tension.
[0071] According to the principle of structural dynamics, the tension of the tensioned steel wire 12 and its vibration frequency have the following relationship:
[0072]
[0073] in, is the linear density of the tensioned steel wire. l is the effective length of the tensioned steel wire. f is the first-order vibration frequency of the tensioned steel wire. T is the internal force of the bow device, that is, the tension of the tensioned steel wire.
[0074] Step 4: Calculate the deformation parameter p value according to the deformation size of the bending bow frame 11.
[0075] Specifically, the deformation parameter p is calculated by combining the calculation formula of the effective length L of the complete bow frame and the effective length l of the tensioned steel wire.
[0076] like Figure 3As shown, the bending arch 11 is simplified into a large deformation compression rod model, point O is the connection point between the bow device and the tensioned steel wire, and point A is the highest point of the bending arch. From the overall force characteristics, point A is regarded as the fixed end, point O is the free end, and the bending arch is subjected to the vertical pressure T provided by the tensioned steel wire at point O, causing the bending arch to buckle. A rectangular coordinate axis xOy is established with point O as the origin, and the pressure is the internal force of the bow device, which is downward along the positive direction of the x-axis. In addition, L is the effective length of the bending arch, s is the distance from point O along the compression rod axis, α is the maximum torsion angle of the arch, that is, the torsion angle at point O, θ is the torsion angle per unit length of the bending arch, 0<θ<α, l and h are the effective length of the tensioned steel wire and the distance from the highest point of the bending arch to the tensioned steel wire, respectively.
[0077] According to the bending theory in material mechanics, the deflection curve equation of the bending bow has the following expression:
[0078]
[0079] Among them, E a I is the bending stiffness of the bending arch.
[0080] Derivative both sides of equation (2) with respect to s and multiply by dθ, and using the relationship dy / ds=sinθ, we can obtain the following relationship:
[0081]
[0082] In the formula,
[0083] Integrating formula (3) yields:
[0084]
[0085] Where C is the integral constant, which can be determined by the top condition of the rod. Since the bending moment at the top of the compression rod is zero, dθ / ds=0, and θ=α, we can get C=-k 2 cosα. From the model, we know that dθ / ds is always negative, that is:
[0086]
[0087] By transposing and integrating it, the length of the curved bow is:
[0088]
[0089] Let p = sin(α / 2) and introduce a new variable Right now:
[0090]
[0091] When θ changes from 0 to α, changes from 0 to 1, and From 0 to 0.5π. Differentiate both sides of equation (7) and move the terms to get:
[0092]
[0093] in addition:
[0094]
[0095] Substituting equations (8) and (9) into equation (6), we can obtain:
[0096]
[0097] Among them, K(p) is the first kind of complete elliptic integral, and its numerical value is only related to p. Therefore, the value of K(p) can be obtained by referring to the numerical table of the first kind of complete elliptic integral according to the calculated p value.
[0098] Similarly, we can deduce that:
[0099]
[0100] Wherein, E(p) is the complete elliptic integral of the second kind, which can also be obtained by referring to the numerical table of complete elliptic integral of the second kind according to the calculated p value.
[0101] Combining equation (10) and equation (11), we can get:
[0102]
[0103] Different p values are calculated using formula (12), thereby obtaining different K(p) and E(p), until the p value when the left and right sides of formula (12) are equal is the final p value.
[0104] Step 5: Inverse the bending bow material modulus parameters.
[0105] Specifically: According to the deformation size and internal force of the bending frame, the modulus E of the bending frame material, that is, the thin sheet material, is inverted. a Size:
[0106]
[0107] In the specific test, the bending arch 11 is a metal steel sheet bending arch, that is, the sheet material is an elastic metal steel sheet, and the device is used to test the elastic modulus of the elastic steel sheet material. A metal steel sheet with an unknown elastic modulus is selected and made into the bending arch 11. Figure 1 As shown, three bow-shaped devices 1 with different effective lengths L and effective lengths l of the tensioned steel wire 12 are prepared, and the bow-shaped devices 1 are used Figure 2The music excitation device + laser detector shown in the figure obtains its first-order frequency. The material, size parameters and frequency results of the bow device are shown in the following table.
[0108] Parameters related to the measurement of the bow modulus of elastic metal materials
[0109]
[0110] After calculation, the elastic moduli of the three bow devices 1 are: 168803.6MPa, 167354.4MPa, and 172299.3MPa. The elastic moduli calculated are not much different, with an average of 169485.8MPa and a maximum deviation of 2.95%. Considering the manual errors in the manufacture and measurement of the bow device 1, it can be considered that the elastic modulus values obtained by inversion are consistent.
[0111] The tensile test was carried out on the metal steel sheet using an MTS universal testing machine. The tensile test was carried out three times in total, and the results were taken as the average value of the three tests. Figure 4 As shown, the elastic modulus obtained by the tensile test is 171851.40 MPa, and the error compared with the elastic modulus result obtained by inverse calculation is 1.377%. Therefore, it is simple and effective to use the bow device 1 to calculate the elastic modulus of the bow material by inverse calculation of the internal force.
[0112] Example 2
[0113] Viscoelastic materials such as engineering plastics are widely used in various fields due to their advantages such as small weight, low price and high strength. As the use time goes by, the load capacity of viscoelastic materials such as engineering plastics changes, resulting in stress relaxation. The three-point loading method is used to study the stress relaxation characteristics of plastics. The plastic specimen is made into a three-point loading device using equipment such as a universal testing machine and the loading pressure head is kept fixed. The stress relaxation of the plastic specimen is reflected by the pressure change of the loading pressure. The test cost and equipment requirements are high. The use of a bow device can solve these problems well.
[0114] Compared with the conventional three-point loading test, the bow device does not require professional equipment and is low in cost. The following uses a plastic sheet as a bending bow to study its bending relaxation characteristics.
[0115] In order to calculate the bending modulus of the plastic bow, three types of bows with the same effective length L but different bending degrees (height h) were made. The relevant parameters are shown in the table below.
[0116] Parameters related to the measurement of the modulus of the bow device
[0117]
[0118] During the monitoring process, the bow device was continuously subjected to a vibration test to measure the basic frequency of the string, which lasted for 7 days. While measuring the basic frequency of the string, the string length l and deflection h of the bow device were also tested. The excitation device 2 and the vibration pickup device 3 are arranged on both sides of the bow device 1, and the bow device 1 to be tested is placed between the excitation device 2 and the vibration pickup device 3. The axial direction of the tensioned steel wire 12 is perpendicular to the direction of the vibration pickup device 3 and the direction of the excitation device 2. The measuring point position of the tensioned steel wire 12 is located at the focal position of the laser emitted by the vibration pickup device 3, and the excitation device 2 is 10 cm away from the tensioned steel wire 12 (not shown in the figure).
[0119] According to the measurement results, the shape of the plastic bending bow frame did not change during the bending relaxation test and was consistent with the initial value, which ruled out the change in modulus caused by the change in the bending bow frame shape. Figure 5 The relaxation of the plastic bow under three working conditions.
[0120] The stress relaxation of the bow device method and the conventional method has the same change pattern. The stress decreases to a large extent during the test and then gradually stabilizes, which is consistent with the Maxwell model's description of the stress relaxation of viscoelastic materials. Therefore, the method of using the bow device to test the stress relaxation of the bow frame material is feasible and effective. Figure 5 It can be seen that the bending relaxation characteristics of the plastic bending bow under the three working conditions are basically the same. The stress magnitude decreases linearly in the first 6 hours, and then the stress magnitude gradually stabilizes. The following stress relaxation formula is used to fit the stress relaxation data of the bow device:
[0121] E t =E1(1-mlogt) (13)
[0122] Where t is time, E t is the modulus at time t, and m is the relaxation coefficient.
[0123] In the three bow-shaped devices, the relaxation coefficients of the hard plastic materials are 0.082, 0.064, and 0.048, respectively. The greater the degree of curvature of the plastic bow, the greater its relaxation coefficient.
[0124] The other structures and testing methods are the same as those in Example 1 and will not be described in detail here.
[0125] In summary, although the embodiments of the present invention have been described, it can be understood that the above embodiments are exemplary and cannot be understood as limitations of the present invention. Ordinary technicians in the field can change, modify, replace and modify the above embodiments without departing from the principles and purpose of the present invention.
Claims
1. A material modulus testing method based on self-internal force identification of a bow-shaped device, which uses a material modulus testing device, wherein the material modulus testing device comprises a bow-shaped device (1), an excitation device (2), a vibration pickup device (3), a control box (4), a computer (5), a data acquisition box (6) and a signal generator (7); the bow-shaped device (1) comprises a bending bow frame (11) and a tensioned steel wire (12) arranged thereon, wherein both ends of the tensioned steel wire (12) are arranged at the bottom of both ends of the bending bow frame (11) through fixing nuts (13); the excitation device (2) and the vibration pickup device (3) are arranged on the bow-shaped device (1) on one side or both sides; the excitation device (2) and the vibration pickup device (3) are not in contact with the bow device (1), and one end of the excitation device (2) and the vibration pickup device (3) are both facing the tensioned steel wire (12); the other end of the excitation device (2) is connected to one end of the signal generator (7), and the other end of the vibration pickup device (3) is connected to one end of the control box (4); the other end of the signal generator (7) and the other end of the control box (4) are both connected to the data acquisition box (6), and the data acquisition box (6) is in communication connection with the computer (5), characterized in that The specific test method includes the following steps: Step 1: Measure the cross-sectional dimensions of the sheet material and calculate its moment of inertia; Step 2: Making a bending frame (11) from a sheet material of a modulus to be measured, fixing a tensioned steel wire (12), and measuring the deformation size of the bending frame (11); Step three: measuring the first-order vibration frequency of the tensioned steel wire (12) in the bow device (1), and converting it into the internal force of the bow device; the specific step three is: the tensioned steel wire (12) in the bow device (1) is a string-drawn structure, and the first-order vibration frequency f thereof is obtained by combining an excitation device (2) and a vibration pickup device (3); and the tension exerted on the tensioned steel wire (12) is a manifestation of the internal force of the bow device (1), and the internal force of the bow device (1) can be obtained by calculating the tension; According to the principle of structural dynamics, the tension of the tensioned steel wire (12) and its vibration frequency have the following relationship: in, is the linear density of the tensioned steel wire; l is the effective length of the tensioned steel wire; f is the first-order vibration frequency of the tensioned steel wire; T is the internal force of the bow device, that is, the tension of the tensioned steel wire; Step 4: calculating the value of the deformation parameter p according to the deformation size of the bending bow frame (11); the step 4 specifically comprises: calculating the value of the deformation parameter p by combining the calculation formula of the effective length L of the complete bow frame and the effective length l of the tensioned steel wire; The bending arch (11) is simplified into a large deformation compression rod model, where point O is the connection between the arch device and the tensioned steel wire, and point A is the highest point of the bending arch; from the overall force characteristics, point A is regarded as the fixed end, and point O is the free end. The bending arch bears the vertical pressure T provided by the tensioned steel wire at point O, causing the bending arch to buckle; a rectangular coordinate axis xOy is established with point O as the origin, and the pressure is the internal force of the arch device, which is downward along the positive direction of the x-axis; in addition, L is the effective length of the bending arch, s is the distance from point O along the compression rod axis, α is the maximum torsion angle of the arch, that is, the torsion angle at point O, θ is the torsion angle per unit length of the bending arch, 0<θ<α, l and h are the effective length of the tensioned steel wire and the distance from the highest point of the bending arch to the tensioned steel wire, respectively; According to the bending theory in material mechanics, the deflection curve equation of the bending bow has the following expression: Among them, E a I is the bending stiffness of the bending arch; Derivative both sides of equation (2) with respect to s and multiply by dθ, and using the relationship dy / ds=sinθ, we can obtain the following relationship: In the formula, Integrating formula (3) yields: Where C is the integral constant, which can be determined by the top condition of the rod; since the bending moment at the top of the compression rod is zero, dθ / ds=0, and θ=α, we can get C=-k 2 cosα; From the model, we know that dθ / ds is always negative, that is: By transposing and integrating it, the length of the curved bow is: Let p = sin(α / 2) and introduce a new variable Right now: When θ changes from 0 to α, changes from 0 to 1, and From 0 to 0.5π; differentiate both sides of equation (7) and move the terms to obtain: in addition: Substituting equations (8) and (9) into equation (6), we can obtain: Among them, K(p) is the first kind of complete elliptic integral, and its value is only related to p. Therefore, the value of K(p) can be obtained by referring to the numerical table of the first kind of complete elliptic integral according to the calculated p value; Similarly, by differentiating the effective length l of the tensioned steel wire along the longitudinal axis x, we can derive: Where E(p) is the complete elliptic integral of the second kind, which can also be obtained by referring to the numerical table of complete elliptic integral of the second kind according to the calculated p value; Combining equation (10) and equation (11), we can get: Use formula (12) to calculate different p values, and thus find different K(p) and E(p), until the p value when the left and right sides of formula (12) are equal is the final p value; Step 5: Inverse the bending bow material modulus parameters.
2. A material modulus testing method based on self-internal force identification of a bow device according to claim 1, characterized in that: The step 1 specifically includes: measuring the cross-sectional width b and height d of the thin sheet material to be tested, and calculating its moment of inertia I.
3. A material modulus testing method based on self-internal force identification of a bow device according to claim 2, characterized in that: The second step specifically comprises: using the thin sheet material to be tested as a bending bow frame (11) in the bow device (1), combining it with a tensioned steel wire (12) and a fixing nut (13) to form a bow device, and measuring the effective length L of the bending bow frame and the effective length l of the tensioned steel wire (12) in the bow device (1).
4. A material modulus testing method based on bow device self-internal force identification according to claim 3, characterized in that: The step 5 is specifically as follows: according to the deformation size of the bending frame and the internal force, the modulus E of the bending frame material, i.e. the sheet material, is inverted. a Size:
5. A material modulus testing method based on bow device self-internal force identification according to claim 1, characterized in that: The excitation device (2) is a speaker, and the vibration pickup device (3) is a laser detector.
6. A material modulus testing method based on bow device self-internal force identification according to claim 1, characterized in that: The effective length L of the bending arch (11) is the length of the bending arch between the fixing nuts (13), which is 25-32 cm; the effective length l of the tensioned steel wire (12) is the length of the tensioned steel wire between the fixing nuts (13), which is 20-30 cm.
7. A material modulus testing method based on bow device self-internal force identification according to claim 1, characterized in that: The two ends of the tensioned steel wire (12) are symmetrically fixed to the two ends of the bending arch frame (11); and the nut of the fixing nut (13) is fixedly arranged on the outer side surface of the bending arch frame (11).
8. A material modulus testing method based on bow device self-internal force identification according to claim 1, characterized in that: The bending bow frame (11) is a metal or plastic bending bow frame, that is, the sheet material is metal or plastic; in addition, when the excitation device (2) and the vibration pickup device (3) are arranged on both sides of the bow device (1), the bow device (1) to be tested is placed between the excitation device (2) and the vibration pickup device (3), and the axial direction of the tensioned steel wire (12) is perpendicular to the direction of the vibration pickup device (3) and the direction of the excitation device (2); the measuring point position of the tensioned steel wire (12) is located at the focal position of the laser emitted by the vibration pickup device (3), and the excitation device (2) is 8-12 cm away from the tensioned steel wire (12).
