CN110501177B - Cantilever beam damage identification method based on free end inclination angle influence line curvature - Google Patents

Cantilever beam damage identification method based on free end inclination angle influence line curvature Download PDF

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CN110501177B
CN110501177B CN201910798841.4A CN201910798841A CN110501177B CN 110501177 B CN110501177 B CN 110501177B CN 201910798841 A CN201910798841 A CN 201910798841A CN 110501177 B CN110501177 B CN 110501177B
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rigidity
damage
inclination angle
influence line
measuring point
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CN110501177A (en
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唐盛华
成鹏
张学兵
秦付倩
杨文轩
张佳奇
刘宇翔
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Xiangtan University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0008—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of bridges
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0041—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress
    • G01M5/005—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress by means of external apparatus, e.g. test benches or portable test systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M99/00—Subject matter not provided for in other groups of this subclass
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M99/00—Subject matter not provided for in other groups of this subclass
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Abstract

The invention discloses a cantilever beam damage identification method based on free end inclination angle influence line curvature, which comprises the following steps: applying a moving load to the damaged cantilever beam to obtain an actually measured inclination angle influence line of the free end measuring point; calculating the curvature of the actually measured inclination angle influence line after the beam structure is damaged; dividing the load value by the curvature of the inclination angle influence line to obtain the rigidity of each position of the beam structure, and identifying the damage position through the mutation of the rigidity curve of the damage state; eliminating the rigidity of the damaged position, and fitting the residual rigidity curve to obtain a rigidity curve in an undamaged state; and calculating the damage degree according to the rigidity curves of the damaged and undamaged states to obtain the structural rigidity of the damaged position. The method can accurately position and quantify the damage of the cantilever beam, is applied to damage assessment of the cantilever beam, and verifies the application value of the inclination angle influence line curvature index in cantilever beam damage identification through equal-section and variable-section cantilever beam calculation.

Description

Cantilever beam damage identification method based on free end inclination angle influence line curvature
Technical Field
The invention relates to the technical field of nondestructive testing of beam structures, in particular to a cantilever beam damage identification method based on free end inclination angle influence line curvature.
Background
In recent years, more and more old bridges are used in China, and the problems are increasingly obvious. Many existing bridges cannot meet functional requirements, and safety accidents such as bridge breakage and collapse occur sometimes, so that scholars in the field of civil engineering gradually realize the importance of health monitoring and safety assessment on bridge structures and research various damage identification technologies. Structural damage identification is an important component of a bridge structure health monitoring system, two major damage identification methods are mainly used at present, one is a damage identification method based on dynamic parameters, structural damage is judged mainly through changes of structural modes (vibration frequency and vibration mode), and the method has high requirements on the number of measuring points, the measurement precision of a sensor, a mode parameter identification method and the like. The other method is a damage identification method based on static parameters, the structural damage identification method based on the static parameters can effectively avoid the uncertain influences of quality, particularly damping and the like, and meanwhile, the structural damage identification technology based on the static parameters is widely researched because the existing measurement equipment and technology are advanced and mature and a quite accurate measurement value of a structure can be obtained at a lower cost.
The structural damage identification technology based on the static force parameter is mainly researched based on deflection, static force strain, support reaction force influence line indexes and the like, along with the progress of the tilt sensor technology, the change of a structural tilt angle curve before and after damage is expected to be applied to structural damage identification, and at present, relevant literature reports about tilt angle damage identification are rarely seen.
Disclosure of Invention
In order to solve the technical problems, the invention provides the cantilever beam damage identification method based on the free end inclination angle influence line curvature, which has the advantages of simple algorithm and low cost.
The technical scheme for solving the problems is as follows: a cantilever beam damage identification method based on free end inclination angle influence line curvature comprises the following steps:
(1) applying moving load to each measuring point position of the damaged cantilever beam to obtain an actually measured inclination angle influence line of the measuring point at the free end;
(2) calculating the curvature of the actually measured inclination angle influence line after the beam structure is damaged;
(3) dividing the load by the curvature of the inclination angle influence line to obtain the rigidity of each position of the beam structure, and identifying the damage position through the sudden change of the damage state rigidity curve;
(4) eliminating the rigidity of the damaged position, and fitting the residual rigidity curve to obtain a rigidity curve in an undamaged state;
(5) and calculating the damage degree according to the rigidity curves of the damaged and undamaged states to obtain the structural rigidity of the damaged position.
In the cantilever beam damage identification method based on the free end inclination angle influence line curvature, in the step (2), the inclination angle influence line curvature theta' is calculated through the central difference:
Figure BDA0002181733310000021
wherein the subscript i is the number of measurement points, thetai"is the inclination angle of the measuring point i to influence the curvature of the line,. epsilon.is the average value of the distance from the measuring point i-1 to the measuring point i and the distance from the measuring point i to the measuring point i +1, and thetaiThe inclination angle of the test position when the load acts on the point i.
In the cantilever beam damage identification method based on the free end inclination angle influence line curvature, in the step (3), the structural damage state rigidity curve BdThe calculation method comprises the following steps:
Figure BDA0002181733310000031
wherein, BdiThe rigidity of the damage state of the point is measured i, P is a moving load value thetaiThe measuring points I are the curvature of a slope influence line of the load acting on the measuring point I, n is the number of the measuring points, the measuring points 1 are arranged at the fixed end of the cantilever beam, the measuring points n are arranged at the free end of the cantilever beam, the number of the measuring points n is continuous and increases from 1 to n in sequence, and i is more than or equal to 2 and less than or equal to n-1.
In the above cantilever beam damage identification method based on the free end inclination angle influence line curvature, in step (3), if the abrupt change of the stiffness curve is not obvious, the slope of the stiffness curve is further calculated to assist in judging the damage position, and the slope calculation method of the stiffness curve is as follows:
Figure BDA0002181733310000032
wherein, B'djThe slope of the stiffness curve, ε, for the damage status of the j measurement point*The distance from the point j-1 to the point j.
In the cantilever beam damage identification method based on the free end inclination angle influence line curvature, in the step (4), linear fitting is adopted for the rigidity curve of the constant-section beam in an undamaged state, local parabolic fitting is adopted for the variable-section beam, and the fitted rigidity curve of the undamaged stateBuComprises the following steps:
Bu＝[0 Bu2 … Bui … Bu(n-1) 0]；
wherein, BuiStiffness of the undamaged state fitted to the ith measurement point.
In the cantilever beam damage identification method based on the free end inclination angle influence line curvature, in the step (5), the quantitative index D of the structural damage degreeeThe calculation method comprises the following steps:
De＝[0 De2 … Dei … De(n-1) 0]；
wherein D iseiFor the structural damage degree identified by the ith measuring point, the calculation method comprises the following steps:
Figure BDA0002181733310000033
according to the cantilever beam damage identification method based on the free end inclination angle influence line curvature, in the step (1), the number of the structure inclination angle influence line measuring points is not less than 6.
The invention has the beneficial effects that: the method comprises the steps of firstly applying a moving load to a damaged cantilever beam to obtain an inclination angle influence line of a measuring point at the free end of the damaged beam, then calculating the curvature of an actually-measured inclination angle influence line after the beam structure is damaged, then dividing the curvature of the inclination angle influence line by the load to obtain the rigidity of the damaged state of the beam structure, judging the damaged position according to the mutation of the rigidity curve of the damaged state, then eliminating the rigidity of the damaged position, fitting the rest rigidity curve to obtain the rigidity curve of the damaged front beam structure, and finally calculating the damage degree according to the rigidity curve of the damaged front beam structure and the rigidity curve of the damaged state. The invention verifies the application value of the inclination angle influence line curvature index in cantilever beam damage identification through the equal-section and variable-section cantilever beam calculation example, and provides an effective new method for cantilever beam damage positioning, quantification and rigidity identification.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention.
Figure 2 is a diagram of a cantilever beam structure model of the present invention.
FIG. 3 is a unit bending moment and action bending moment diagram of the free end of the cantilever beam.
FIG. 4 is a unit force action bending moment diagram of the cantilever i-1 measuring point of the present invention.
FIG. 5 is a unit force action bending moment diagram of the cantilever i test point of the present invention.
FIG. 6 is a bending moment diagram of unit force action at the i +1 measuring point of the cantilever beam.
FIG. 7 is a diagram of an isometric cantilever finite element model according to an embodiment of the present invention.
FIG. 8 is a schematic diagram of a slope influence line of the damage status measuring point 21 according to an embodiment of the invention.
FIG. 9 is a schematic diagram of the line curvature influenced by the inclination angle of the damage status measuring point 21 according to an embodiment of the present invention.
FIG. 10 is a schematic diagram of a stiffness curve identified at measurement point 21 in accordance with an embodiment of the present invention.
FIG. 11 shows the structural damage degree D identified by the measuring point 21 in the first embodiment of the present inventioneSchematic representation of (a).
FIG. 12 is a finite element model diagram of a cantilever beam with a variable cross-section according to an embodiment of the present invention.
FIG. 13 is a schematic diagram of the influence line of the inclination angle of the damage status measuring point 21 in the second embodiment of the present invention.
FIG. 14 is a diagram illustrating the line curvature influenced by the inclination angle of the damage status measuring point 21 according to the second embodiment of the present invention.
FIG. 15 is a schematic diagram of a stiffness curve identified at measurement point 21 in example two of the present invention.
FIG. 16 is a graph showing the slope of the stiffness curve identified at measurement point 21 in the second embodiment of the present invention.
FIG. 17 is a schematic diagram of the fitting of stiffness curves at measuring points 3-5 in the second embodiment of the invention.
FIG. 18 is a schematic diagram of the stiffness curve fitting at the measuring points 8, 9, 12 and 13 in the second embodiment of the invention.
FIG. 19 is a schematic diagram of the fitting of stiffness curves at the measuring points 17-19 in the second embodiment of the invention.
FIG. 20 shows the structural damage degree D identified by the measuring point 21 in the second embodiment of the present inventioneSchematic representation of (a).
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
As shown in fig. 1, a cantilever beam damage identification method based on free end inclination angle influence line curvature specifically includes the following steps:
step 1: and applying moving load to each measuring point position of the damaged cantilever beam to obtain an actually measured inclination angle influence line of the measuring point at the free end.
In step 1, the cantilever beam structure model is shown in fig. 2, the span of the cantilever beam is L, a is the left end point of the cantilever beam, the distance from the damaged position to the left end a is a, the distances between the measuring points are epsilon, the rigidity of the undamaged structure is EI, and the rigidity of the damaged unit is EId. The unit bending moment M is 1, and the bending moment acting on the free end position is (as shown in fig. 3):
Figure BDA0002181733310000051
bending moment M when load P acts on the positions of the measuring points i-1, i and i +1 respectively1、M2、M3(see fig. 4-6) are:
M1＝P(a-x) (2)
M2＝P(a+ε-x) (3)
M3＝P(a+2ε-x) (4)
in the formula, x represents the distance from the left end point A of the cantilever beam.
Therefore, when the structural damage is obtained, the inclination angles of the measuring points are respectively as follows:
Figure BDA0002181733310000061
Figure BDA0002181733310000062
Figure BDA0002181733310000063
in the formula, thetaidIndicates the tilt angle of the point i at which the structure is damaged, and the subscript "d" indicates the state of structural damage.
Step 2: and (4) calculating the curvature of the actually measured inclination angle influence line after the beam structure is damaged.
In step 2, calculating by adopting a center difference method to obtain the curvature theta of the dip angle influence line of the i measuring point on the right side of the damage positionidComprises the following steps:
Figure BDA0002181733310000064
and step 3: and (3) dividing the load by the curvature of the inclination angle influence line to obtain the rigidity of each position of the structure, and identifying the damage position through the sudden change of the damage state rigidity curve.
In step 3, a structural damage state stiffness curve BdThe calculation method comprises the following steps:
Figure BDA0002181733310000065
wherein, BdiThe rigidity of the damage state of the point is measured, i, and P is a moving load value, theta ″)idThe curvature of a slope angle influence line of a load acting on the ith measuring point is shown, n is the number of the measuring points, the No. 1 measuring point is arranged at the fixed end of the cantilever beam, the No. n measuring points are arranged at the free end of the cantilever beam, the number of the measuring points is continuous and increases from 1 to n, and i is more than or equal to 2 and less than or equal to n-1.
When the damage position is identified through the sudden change of the rigidity curve in the damage state, if the sudden change of the rigidity curve is not obvious, the calculation method for the slope of the rigidity curve to assist in judging the slope of the rigidity curve in the damage position can be further calculated as follows:
Figure BDA0002181733310000071
wherein, B'djThe slope of the stiffness curve, ε, for the damage status of the j measurement point*The distance from the point j-1 to the point j.
And 4, step 4: and eliminating the rigidity of the damaged position, and fitting the residual rigidity curve to obtain the rigidity curve in the undamaged state.
In step 4, linear fitting is adopted for the rigidity curve of the constant-section beam in the undamaged state, local parabolic fitting is adopted for the variable-section beam, and the fitted rigidity curve B of the undamaged stateuComprises the following steps:
Bu＝[0 Bu2 … Bui … Bu(n-1) 0] (11)
wherein, BuiStiffness of the undamaged state fitted to the ith measurement point.
And 5: and calculating the damage degree according to the rigidity curves of the damaged and undamaged states to obtain the structural rigidity of the damaged position.
In step 5, when the cell between the measuring points i-1, i is not damaged, EI is equal to Bui。
When damage occurs to the cell between the measurement points i-1, i:
Figure BDA0002181733310000072
by substituting formula (12) for formula (8):
Figure BDA0002181733310000073
therefore, the damage level of the cell can be obtained as follows:
Figure BDA0002181733310000081
in the step 1, the number of the structural dip angle influence line measuring points is not less than 6.
The first embodiment is as follows: referring to fig. 7, the span of the cantilever beam with the uniform cross section is 100cm, 5cm is divided into a unit, 20 units and 21 measuring points (in the figure, the numbers in the circle at the upper row are the unit numbers, and the numbers at the lower row are the measuring point numbers). The cross-sectional dimension of the plate isb × h is 4.5cm × 1.5cm, and the elastic modulus of the material is 2.7 × 103MPa, Poisson's ratio of 0.37, density of 1200kg/m3。
Damage in an actual engineered structure, such as crack initiation, material corrosion, or a decrease in elastic modulus, typically only causes a large change in the stiffness of the structure, with little effect on the mass of the structure. Therefore, in finite element calculations, it is assumed that structural element damage only causes a decrease in element stiffness, and not a change in element mass. Damage to the cell is simulated by a decrease in the modulus of elasticity. Beam structure models were built using ANSYS software beam3 beam cells. Taking a multi-unit damage condition as an example, consider that damage occurs to different degrees at three positions of the fixed branch end unit 1, the midspan unit 10 and the free end unit 20, and the damage condition is shown in table 1.
TABLE 1 cantilever Multi-Damage Condition
Figure BDA0002181733310000082
The specific implementation steps are as follows:
step 1: and applying a moving load of 1kN to obtain actual measurement inclination angle influence lines of the free end measuring point 21 after the cantilever beam is damaged, wherein the actual measurement inclination angle influence lines are respectively shown in the graph 8.
Step 2: the curvature of the inclination angle influence line after the beam structure is damaged is calculated, as shown in fig. 9, the result shows that obvious peak values appear at the units 1, 10 and 20, and the damage of the units 1, 10 and 20 can be preliminarily judged.
And step 3: the load value is divided by the inclination angle influence line curvature value to obtain a structural rigidity curve in a damaged state, as shown in fig. 10, it can be seen that the rigidity of the units 1, 10 and 20 is obviously reduced and the units are damaged.
And 4, step 4: eliminating rigidity values of the left and right measuring points of the units 1, 10 and 20, and performing linear fitting on the residual rigidity curve to obtain the rigidity of the beam structure without damage as a constant, wherein the rigidity is about 34.172N m2。
And 5: calculating damage degree from the stiffness curves of damaged and undamaged states, as shown in FIG. 11, the identified damage degree is substantially the same as the theoretical value, and further calculating the actual damage unitRigidity EIdWhen the degree of damage is 0.3, the rigidity of the damaged cell is EId＝EI(1-0.3)＝34.172*0.7＝23.92N·m2And is less rigid than that shown in fig. 10.
Example two: referring to fig. 12, the span of the cantilever beam with variable cross section is 100cm, the division of the unit and the node is the same as that of the first embodiment, the free end of the cross section dimension of the plate is b × h which is 4.5cm × 1.5cm, the fixed end is b × h which is 22.5cm × 3.0cm, and the elastic modulus of the material is 2.7 × 103MPa, Poisson's ratio of 0.37, density of 1200kg/m3。
The damage condition is the same as that of the first embodiment.
The specific implementation steps are as follows:
step 1: and applying a moving load of 1kN to obtain actual measurement inclination angle influence lines of the free end measuring point 21 after the cantilever beam is damaged, wherein the actual measurement inclination angle influence lines are respectively shown in the graph 13.
Step 2: the curvature of the inclination angle influence line after the beam structure is damaged is calculated, as shown in fig. 14, the result shows that an obvious peak appears at the unit 10, the unit 10 can be preliminarily judged to be damaged, and mutation at other positions is not obvious.
And step 3: the load value is divided by the inclination angle influence line curvature value to obtain a structural rigidity curve of a damaged state as shown in fig. 15, it can be seen that the rigidity of the units 1 and 10 is obviously reduced, the units are damaged units, in order to further judge whether other damaged units exist, the slope of the rigidity curve is calculated, as shown in fig. 16, it can also be seen that the free end unit 20 is damaged, and therefore, the units 1, 10 and 20 are judged to be damaged.
And 4, step 4: the stiffness curve is fitted by adopting a piecewise parabola, the stiffness values of the measuring points 3-5 are fitted as shown in figure 17, the serial number is 0, and the stiffness fitting value of the measuring point 2 in an undamaged state is 1216.5N m2And fitting the rigidity values of the measuring points 8, 9, 12 and 13 to obtain undamaged rigidity values of the measuring points 10 and 11, as shown in FIG. 18, fitting the rigidity values of the measuring points 17-19 to obtain an undamaged rigidity value of the measuring point 20, as shown in FIG. 19, and finally obtaining a rigidity curve of the beam structure when the beam structure is undamaged.
And 5: and calculating the damage degree according to the rigidity curves of the damaged state and the undamaged state, as shown in figure 20, wherein the recognized damage degree is close to a theoretical value, the damage degree recognized by the free end is slightly larger than the theoretical value, is 0.330 and is larger than the theoretical value by 10 percent, and the error is acceptable in engineering application.
The above description is only 2 embodiments of the present invention, and all equivalent changes and modifications made according to the claims of the present invention are included in the scope of the present invention.

Claims (2)

1. A cantilever beam damage identification method based on free end inclination angle influence line curvature is characterized by comprising the following steps:
(1) applying moving load to each measuring point position of the damaged cantilever beam to obtain an actually measured inclination angle influence line of the measuring point at the free end;
(2) calculating the curvature of the actually measured inclination angle influence line after the beam structure is damaged;
in the step (2), the inclination angle influence line curvature theta' is calculated through the central difference:
Figure FDA0002825048940000011
wherein, the subscript i is a measuring point number, theta ″)iThe curvature of a dip angle influence line of a measuring point i is shown, epsilon is the average value of the distance between the measuring point i-1 and the measuring point i and the distance between the measuring point i and a measuring point i +1, and theta isiThe inclination angle of the test position when the load acts on the i test point is shown;
(3) dividing the load by the curvature of the inclination angle influence line to obtain the rigidity of each position of the beam structure, and identifying the damage position through the sudden change of the damage state rigidity curve;
in the step (3), the structural damage state rigidity curve BdThe calculation method comprises the following steps:
Figure FDA0002825048940000012
wherein, BdiThe rigidity of the damage state of the point is measured, i, and P is a moving load value, theta ″)iThe curvature of a dip angle influence line acting on the ith measuring point for load, n is the number of the measuring points, the No. 1 measuring point is arranged at the fixed supporting end of the cantilever beam, and the No. n measuring point is arranged at the fixed supporting end of the cantilever beamThe number of the measuring points at the free end of the cantilever beam is continuous and is increased from 1 to n in sequence, and i is more than or equal to 2 and less than or equal to n-1;
in the step (3), if the abrupt change of the stiffness curve is not obvious, the slope of the stiffness curve is further calculated to assist in judging the damage position, and the slope calculation method of the stiffness curve is as follows:
Figure FDA0002825048940000021
wherein, B'djThe slope of the stiffness curve, ε, for the damage status of the j measurement point*The distance from the measuring point j-1 to the measuring point j;
(4) eliminating the rigidity of the damaged position, and fitting the residual rigidity curve to obtain a rigidity curve in an undamaged state;
in the step (4), linear fitting is adopted for the rigidity curve of the constant-section beam in an undamaged state, local parabolic fitting is adopted for the variable-section beam, and the fitted rigidity curve B of the undamaged stateuComprises the following steps:
Bu＝[0 Bu2…Bui…Bu(n-1) 0]；
wherein, BuiThe stiffness of the undamaged state fitted for the ith measurement point;
(5) calculating the damage degree according to the rigidity curves of the damaged and undamaged states to obtain the structural rigidity of the damaged position;
in the step (5), the quantitative index D of the structural damage degreeeThe calculation method comprises the following steps:
De＝[0 De2…Dei…De(n-1) 0]；
wherein D iseiFor the structural damage degree identified by the ith measuring point, the calculation method comprises the following steps:
Figure FDA0002825048940000022
2. the cantilever damage identification method based on the free end inclination angle influence line curvature as claimed in claim 1, wherein: in the step (1), the number of the structural dip angle influence line measuring points is not less than 6.
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