A method for measuring the unit length damping of a tensile element

Abstract

The application provides a kind of cable unit length damping measurement method, belong to cable damping measurement technical field, comprising: measuring cable unit length mass, laser displacement meter is arranged in the direction of cable vibration;Initial displacement is applied to cable and released, and cable vibration is excited;The in-plane vibration displacement time history curve, velocity time history curve or acceleration time history curve of any point of cable in vibration state is measured by laser displacement meter and is filtered;The peak value of displacement time history curve, velocity time history curve or acceleration time history curve after filtering processing and the time corresponding to the peak value are extracted;Based on the peak value of displacement time history curve, velocity time history curve or acceleration time history curve after filtering processing, the time corresponding to the peak value and cable unit length mass, cable unit length damping is obtained.

Description

Technical Field

[0001] This invention relates to the field of cable damping measurement technology, and in particular to a method for measuring cable damping per unit length. Background Technology

[0002] The cable damping ratio, the ratio of damped to critical damping, reflects the attenuation between adjacent vibration peaks. However, the damping ratio of a cable structure is affected by parameters such as cable length, tension force, cable diameter, cable density, damping magnitude, and vibration frequency. For example, two cables with identical material parameters will have completely different damping ratios under different tension forces, making the ratio less applicable. Therefore, the damping ratio is not a fundamental parameter for evaluating cable vibration attenuation. Conversely, cable damping is a relatively basic natural characteristic, primarily influenced by the cable material properties, and has better applicability. However, current research lacks a clear understanding of the relationship between damping and vibration attenuation, and there is no method for measuring cable damping per unit length. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a method for measuring the damping per unit length of a cable, which can measure the damping magnitude of actual bridge stay cables or experimental stay cables, specifically including:

[0004] A method for measuring the unit length damping of a cable, comprising:

[0005] S1. Measure the mass per unit length of the cable by arranging a laser displacement meter in the direction of cable vibration;

[0006] S2. Apply an initial displacement to the cable and release it to excite the cable to vibrate;

[0007] S3. Measure the vibration displacement time history curve, velocity time history curve or acceleration time history curve of any point in the plane of the cable under vibration using a laser displacement meter.

[0008] S4. Filter the measured vibration displacement time history curve, velocity time history curve or acceleration time history curve to obtain the filtered displacement time history curve, velocity time history curve or acceleration time history curve. The filtered displacement time history curve, velocity time history curve and acceleration time history curve include displacement time history curve, velocity time history curve or acceleration time history curve under any single mode.

[0009] S5. Extract the peak value and the corresponding time of the peak value from the filtered displacement time history curve, velocity time history curve, or acceleration time history curve.

[0010] S6. Based on the peak value of the filtered displacement time history curve, velocity time history curve, or acceleration time history curve, the time corresponding to the peak value, and the mass per unit length of the cable, the damping per unit length of the cable is obtained.

[0011] Optionally, the formula for calculating the unit length damping of the cable in S6 is formula (1):

[0012] (1)

[0013] Where c is the damping per unit length of the cable;

[0014] m is the mass per unit length of the cable; t i For the time corresponding to the first peak, t i+1 This corresponds to the moment of the second peak.

[0015] δ is a process parameter in the calculation of c, where δ satisfies formula (2):

[0016] (2)

[0017] Among them, v n (x, t) i Let x be the displacement of point x on the cable at time i under n-order vibration conditions; v n (x, t) i+1 Let x be the displacement of point x on the cable at time i+1 under n-order vibration conditions.

[0018] Optionally, v n (x, t) i ) satisfies formula (3), v n (x, t) i+1 ) satisfies formula (4):

[0019] (3)

[0020] Where n is the vibration order of the cable, l is the length of the cable, and x is the distance from any point to the anchor point;

[0021] ;(4)

[0022] Optionally, the initial displacement applied to and released in step S2 to excite cable vibration includes:

[0023] Tie the weight to the cable with a rope;

[0024] Cutting the rope causes the weight to fall naturally, which in turn excites the cable to vibrate.

[0025] Optionally, the cable is a steel cable, a CFRP cable, or a BFRP cable;

[0026] The cable is a parallel cable or a stranded cable.

[0027] Optionally, the cables can be arranged horizontally or at an angle.

[0028] Among them, the cable only bears the tension force.

[0029] Optionally, the anchoring points of the cable may be supported by lubricating oil or free-rotating bearings.

[0030] Optionally, the ratio of the sag of the cable to the span of the cable is less than 1:8.

[0031] The above technical solution has at least the following advantages compared with the existing technology:

[0032] This invention considers the relationship between damping and vibration attenuation, and measures the damping per unit length of the cable. Therefore, this invention proposes a cable damping measurement method, which can measure the damping of actual bridge stay cables or experimental cables, thus overcoming the shortcomings of existing technologies.

[0033] In practical engineering, the damping ratio is often used to predict the rate of cable attenuation. However, the damping ratio of a cable structure is affected by parameters such as cable length, tension force, cable diameter, cable density, damping magnitude, and vibration frequency, making it highly dependent on actual measurements. Unlike the damping ratio, damping is a material-related parameter. Once the damping of a cable made of a certain material is measured, it can be further generalized to cables made of the same material. However, there is currently a lack of methods for measuring cable damping. This patent addresses this deficiency. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 The experimental setup diagram for the actual measurement of cable damping;

[0036] Figure 2 The mid-span displacement time history curve was obtained from the damping test of the cable.

[0037] Figure 3 The time history curve of the mid-span displacement of a 1000m CFRP cable;

[0038] Figure 4 The time history curve of the mid-span displacement of a 1500m CFRP cable;

[0039] Figure 5 The time history curve of the mid-span displacement of a 2000m CFRP cable;

[0040] The following are the component labels in the attached diagram:

[0041] 1. Test cable, 2. Laser displacement meter, 3. Nylon rope. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0043] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms “first,” “second,” and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an,” “a,” or “the,” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising,” “including,” or “including,” and similar terms mean that the element or object preceding the word encompasses the element or object listed following the word and its equivalents, without excluding other elements or objects. The terms “connected,” “linked,” or “connected,” and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0044] It should be noted that the terms "up", "down", "left", "right", "front" and "back" used in this invention are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0045] Currently, there is a lack of research on the relationship between damping and vibration attenuation, and even more so, a method for measuring the damping per unit length of cables. Therefore, this invention proposes a method for measuring cable damping, which can measure the damping magnitude of actual bridge stay cables or experimental cables. The specific details are as follows:

[0046] A method for measuring the unit length damping of a cable, comprising:

[0047] S1. Measure the mass per unit length of the cable by arranging a laser displacement meter in the direction of cable vibration;

[0048] Displacement gauges, velocity gauges, or accelerometers can be installed to prepare for subsequent testing.

[0049] The cable is made of steel, CFRP, or BFRP; its structure is either parallel or stranded. The cable can be arranged horizontally or at an angle, and it only bears tension force. That is, the cable can be a stay cable in actual engineering projects; or a test cable arranged horizontally or at an angle in a laboratory. The cable only bears tension force and does not bear other loads.

[0050] The anchoring points of the cables are supported by lubricating oil or free-rotating bearings to reduce the impact of friction at the anchoring points on the damping test results.

[0051] The ratio of the sag of the cable to the span of the cable is less than 1:8.

[0052] S2. Apply an initial displacement to the cable and release it to excite the cable to vibrate;

[0053] Tie the weight to the cable with a rope;

[0054] Cutting the rope causes the weight to fall naturally, which in turn excites the cable to vibrate.

[0055] S3. Measure the vibration displacement time history curve, velocity time history curve or acceleration time history curve of any point in the plane of the cable under vibration using a laser displacement meter.

[0056] S4. Filter the measured vibration displacement time history curve, velocity time history curve or acceleration time history curve to obtain the filtered displacement time history curve, velocity time history curve or acceleration time history curve. The filtered displacement time history curve, velocity time history curve and acceleration time history curve include displacement time history curve, velocity time history curve or acceleration time history curve under any single mode.

[0057] S5. Extract the peak value and the corresponding time of the peak value from the filtered displacement time history curve, velocity time history curve, or acceleration time history curve.

[0058] In this step, peak values ​​with longer time intervals are used to reduce the discreteness of the test damping.

[0059] S6. Based on the peak value of the filtered displacement time history curve, velocity time history curve, or acceleration time history curve, the time corresponding to the peak value, and the mass per unit length of the cable, the damping per unit length of the cable is obtained.

[0060] The formula for calculating the unit length damping of the cable is formula (1):

[0061] (1)

[0062] Where c is the damping per unit length of the cable;

[0063] m is the mass per unit length of the cable; ti For the time corresponding to the first peak, t i+1 This corresponds to the moment of the second peak.

[0064] δ is a process parameter in the calculation of c, where δ satisfies formula (2):

[0065] (2)

[0066] Among them, v n (x, t) i Let x be the displacement of point x on the cable at time i under n-order vibration conditions; v n (x, t) i+1 Let x be the displacement of point x on the cable at time i+1 under n-order vibration conditions.

[0067] Among them, v n (x, t) i ) satisfies formula (3), v n (x, t) i+1 ) satisfies formula (4):

[0068] (3)

[0069] Where n is the vibration order of the cable, l is the length of the cable, and x is the distance from any point to the anchor point;

[0070] ;(4)

[0071] Additionally, it supports repeated execution of S1-S6 multiple times to verify the reliability of the results.

[0072] This invention is based on the theory of cable vibration and the law of energy decay, and further proposes a method for measuring cable damping.

[0073] For any infinitesimal element of a cable (this application focuses on cables), its total energy E changes from its potential energy E in an extremely short time. S and kinetic energy E D Composition, in which potential energy E S Satisfying formula (5):

[0074] (5)

[0075] Where H is the equal component of the cable force; h is the additional horizontal component of the cable force.

[0076] A1 is the initial amplitude corresponding to the first-order mode; l is the length of the cable; t is the vibration time; φ1 is the phase difference corresponding to the first-order mode.

[0077] Kinetic energy E D Satisfying formula (6):

[0078] (6)

[0079] Potential energy E S and kinetic energy E D Adding them together gives the total energy E of the Lasso infinitesimal element at any instant:

[0080] (7)

[0081] Based on formula (7), it can be concluded that the magnitude of the pretension does not affect the energy decay of the cable, but only affects the potential energy E. S and kinetic energy E D The conversion between these two states. That is, for the same cable, the location of the peak displacement point will differ under different tension magnitudes, but the peak points all exhibit the same exponential decay. When the cable amplitude is at adjacent peak values ​​t... i and t i+1 At that time, kinetic energy E D The energy in the cable system is zero, expressed as potential energy E. S The data is stored in the form of [data]. Based on this principle, it can be deduced that the cable amplitude is at adjacent peak values ​​t. i and t i+1 The amplitude formulas (3) and (4) are given. Substituting formulas (3) and (4) into formula (2) and simplifying, we get formula (1). Formula (1) can be used for damping measurement.

[0082] In one specific implementation, this embodiment also provides finite element simulation data of CFRP cables at lengths of 1000m, 1500m, and 2000m to verify the accuracy of the cable damping test method. Specific cable material parameters are shown in Table 1.

[0083] Table 1 CFRP Cable Material Parameters

[0084]

[0085] Sine function excitations with an amplitude of 5m were applied to the 1000m, 1500m, and 2000m cables, respectively. The corresponding excitation functions were 5sin(πx / 576), 3sin(πx / 576), and sin(πx / 576). After release, the mid-span displacement time history data of the CFRP cables were extracted, as shown below. Figure 3 , 4 As shown in Figures 5 and 6. The first and second vibration peak values ​​and corresponding times were extracted and substituted into formulas (1) and (2) to obtain the test cable damping c, and the corresponding error analysis results are shown in Table 2. It can be seen that this damping measurement method has a high testing efficiency.

[0086] Table 2 Analysis of Measurement Damping Error

[0087]

[0088] This invention considers the relationship between damping and vibration attenuation, and measures the damping per unit length of the cable. Therefore, this invention proposes a cable damping measurement method, which can measure the damping of actual bridge stay cables or experimental cables, thus overcoming the shortcomings of existing technologies.

[0089] The following points need to be explained:

[0090] (1) The accompanying drawings of the embodiments of the present invention only involve the structures involved in the embodiments of the present invention. Other structures can refer to the general design.

[0091] (2) For clarity, the thickness of layers or regions is enlarged or reduced in the drawings used to describe embodiments of the invention, i.e., these drawings are not drawn to scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being “above” or “below” another element, the element may be “directly” located “above” or “below” the other element or there may be intermediate elements.

[0092] (3) Where there is no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0093] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for measuring the damping per unit length of a cable, characterized in that, include: S1. Measure the mass per unit length of the cable by arranging a laser displacement meter in the direction of cable vibration; S2. Apply an initial displacement to the cable and release it to excite the cable to vibrate; S3. Measure the vibration displacement time history curve, velocity time history curve or acceleration time history curve of any point in the plane of the cable under vibration using a laser displacement meter. S4. Filter the measured vibration displacement time history curve, velocity time history curve or acceleration time history curve to obtain the filtered displacement time history curve, velocity time history curve or acceleration time history curve. The filtered displacement time history curve, velocity time history curve and acceleration time history curve include displacement time history curve, velocity time history curve or acceleration time history curve under any single mode. S5. Extract the peak value and the corresponding time of the peak value from the filtered displacement time history curve, velocity time history curve, or acceleration time history curve. S6. Based on the peak value of the filtered displacement time history curve, velocity time history curve, or acceleration time history curve, the time corresponding to the peak value, and the mass per unit length of the cable, the damping per unit length of the cable is obtained.

2. The method for measuring the unit length damping of a cable according to claim 1, characterized in that, The formula for calculating the unit length damping of the cable of S6 is formula (1): ；（1） Where c is the damping per unit length of the cable; m is the mass per unit length of the cable; t i t represents the time corresponding to the first peak. i+1 This refers to the moment corresponding to the second peak. δ is a process parameter in the calculation of c, where δ satisfies formula (2): ；（2） Among them, v n (x, t) i Let x be the displacement of point x on the cable at time i under n-order vibration conditions; v n (x, t) i+1 Let x be the displacement of point x on the cable at time i+1 under n-order vibration conditions.

3. The method for measuring the unit length damping of a cable according to claim 2, characterized in that, v n (x, t) i ) satisfies formula (3), v n (x, t) i+1 ) satisfies formula (4): ；（3） Where n is the vibration order of the cable, l is the length of the cable, and x is the distance from any point to the anchor point; ；（4）。 4. The method for measuring the unit length damping of a cable according to claim 1, characterized in that, The process of applying an initial displacement to the cable and then releasing it in step S2, thereby exciting the cable to vibrate, includes: Tie the weight to the cable with a nylon rope; Cutting the nylon rope causes the weight to fall naturally, exciting the cable to vibrate.

5. The method for measuring the unit length damping of a cable according to claim 1, characterized in that, The cable is a steel cable, a CFRP cable, or a BFRP cable; The cable is a parallel cable or a stranded cable.

6. The method for measuring the unit length damping of a cable according to claim 1, characterized in that, The cables can be arranged horizontally or at an angle. Among them, the cable only bears the tension force.

7. The method for measuring the unit length damping of a cable according to claim 5, characterized in that, The anchor points of the cables are supported by lubricating oil or free-rotating bearings.

8. The method for measuring the unit length damping of a cable according to claim 6, characterized in that, The ratio of the sag of the cable to the span of the cable is less than 1:8.

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