CN108195532A - A kind of measuring method of girder construction crackle equivalent stiffness - Google Patents
A kind of measuring method of girder construction crackle equivalent stiffness Download PDFInfo
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- CN108195532A CN108195532A CN201711331415.7A CN201711331415A CN108195532A CN 108195532 A CN108195532 A CN 108195532A CN 201711331415 A CN201711331415 A CN 201711331415A CN 108195532 A CN108195532 A CN 108195532A
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- crackle
- equivalent stiffness
- girder construction
- intrinsic frequency
- rank intrinsic
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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
- G01M5/0066—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by exciting or detecting vibration or acceleration
Abstract
The invention discloses a kind of measuring methods of girder construction crackle equivalent stiffness.This method chooses a series of sample point respectively in the possibility value range of crack position and crackle equivalent stiffness, using these sample points as the input parameter of girder construction dynamic analysis, CRACKED BEAM Mishap Database is solved, and then is drawn using crack position and equivalent stiffness as the structure of input first three rank intrinsic frequency influence curved surface；Then vibration-testing is carried out to girder construction, using the structure of acquisition, first three rank intrinsic frequency goes interception intrinsic frequency to influence curved surface, first three rank intrinsic frequency influence curve is drawn out, the intersection point of three intrinsic frequency influence curves can measure equivalent stiffness and the corresponding position of crackle.This method different type and equivalent stiffness of shape crackle suitable for girder construction measure.
Description
Technical field
The invention belongs to mechanical fault diagnosis fields, and in particular to a kind of measurement side of girder construction crackle equivalent stiffness
Method.
Background technology
With the progress of science and technology and the development of modern industry, higher and higher want is proposed to the maintenance of mechanical equipment
It asks, as the important load carrying unit of large and complex structure, beam structure has a wide range of applications in engineering practice, and (such as aviation is navigated
My god, mechanical equipment, bridge structure etc.), under the action of long-term alternate stress or impact load, structure can usually crack.
The generation of crackle and continuous extension, usually make structure that fracture failure occur, eventually lead to the generation of catastrophic failure.Therefore,
The crack detection of girder construction is the important guarantee of engineering project safety.With the generation and extension of crackle, crackle equivalent stiffness
Corresponding variation can be generated, this variation can be in the degree of injury and feature for effectively reflecting structure.Therefore, it is equivalent to crackle
Rigidity is studied, and girder construction crack detection is had a very important significance.
Any structure can be regarded as the dynamic system being made of quality, damping and stiffness matrix, once in structure
Crackle equivalent stiffness changes, then can lead to the change of system vibration modal parameter (vibration shape, amplitude, intrinsic frequency etc.).Institute
With the relationship by finding modal parameter and structural damage, crackle equivalent stiffness can be identified using the variation of modal parameter.
In the modal parameters such as the vibration shape, amplitude, intrinsic frequency, intrinsic frequency is easy to measure, and with higher precision.This hair as a result,
It is bright to propose a kind of intrinsic frequency using structure to measure the method for girder construction crackle equivalent stiffness.
Invention content
The purpose of the present invention is to provide a kind of measuring methods of girder construction crackle equivalent stiffness.This method is in crack position
A series of sample point is chosen respectively with the possibility value range of crackle equivalent stiffness, using these sample points as girder construction power
The input parameter of credit analysis solves CRACKED BEAM Mishap Database, and then draws using crack position and equivalent stiffness as the knot inputted
First three rank intrinsic frequency of structure influences curved surface；Then vibration-testing is carried out to girder construction, using the intrinsic frequency of first three rank of the structure of acquisition
Rate goes interception intrinsic frequency to influence curved surface, draws out first three rank intrinsic frequency influence curve, three intrinsic frequency influence curves
Intersection point can measure equivalent stiffness and the corresponding position of crackle.This method different type and shape crackle suitable for girder construction
Equivalent stiffness measure.
The purpose of the present invention is realized by following technical proposals：
A kind of measuring method of girder construction crackle equivalent stiffness, this method include the following steps：
1) crackle can be described with torsionspring in girder construction, and the rigidity of torsionspring illustrates crackle equivalent stiffness；
A series of sample point is chosen respectively in the possibility value range of crack position and crackle equivalent stiffness, these sample points are substituted into
Into finite element model, the characteristic equation of crackle beam vibration is obtained；
2) solve the characteristic equation of crackle beam vibration, obtain CRACKED BEAM Mishap Database, so draw with crack position and
Crackle equivalent stiffness is the structure of input first three rank intrinsic frequency influence curved surface；
3) by carrying out vibration-testing to CRACKED BEAM, its first three rank intrinsic frequency is extracted；
4) using first three rank intrinsic frequency of actual measurement as input, intercepting first three rank intrinsic frequency influences curved surface, obtains first three
Rank intrinsic frequency influence curve goes out crackle equivalent stiffness using the intersection measurement of three influence curves.
Further, in the step 1), the characteristic equation of crackle beam vibration is obtained, is included the following steps：
1) crackle in girder construction is described with torsionspring, then structural model can be expressed as connecting by torsionspring
Get up two sections of flawless beams, and the rigidity of torsionspring is crackle equivalent stiffness；
2) a series of sample point is chosen respectively in the possibility value range of crack position and crackle equivalent stiffness, by these
Input parameter of the sample point as girder construction dynamic analysis；
3) sample point of crack position and crackle equivalent stiffness is input in finite element model, obtains crackle beam vibration
Characteristic equation is：
|K(k,β)-ωi 2M |=0
In formula：K represents system Bulk stiffness matrix, and M represents system total quality matrix, ωiRepresent circular frequency, k is represented
Crackle equivalent stiffness, β represent crackle relative position.ωi=2 π fi, i=1,2,3, fiFor system frequency.
Further, in the step 3), the method for first three rank intrinsic frequency of measurement structure is as follows：
1) test experimental bed of girder construction and test system are built, the girder construction containing crackle is clamped on experimental bench；
2) pulse excitation is carried out to girder construction, obtains vibration signal, therefrom extract first three rank intrinsic frequency f of girder constructioni,
I=1,2,3.
Further, in the step 4), the step of crackle equivalent stiffness is gone out using the intersection measurement of intrinsic frequency influence curve
It is rapid as follows：
1) to survey obtained first three rank intrinsic frequency of girder construction as input, first three rank intrinsic frequency that interception is gone to construct
Curved surface is influenced, draws out first three rank intrinsic frequency influence curve；
2) first three rank intrinsic frequency influence curve is plotted in the same coordinate system, utilizes three intrinsic frequency influence curves
Intersection point can measure crackle equivalent stiffness.
Present invention employs finite element modeling and vibration test technologies, have following features：
1. the present invention need to only test overall structure or partial structurtes, it is not required to be known in advance the position of crackle
Determine the size of crackle equivalent stiffness；
2. the present invention different type and equivalent stiffness of shape crackle suitable for girder construction measure；
3. the equivalent stiffness that the present invention can be used for crackle in different cross section shape girder construction measures, as rectangular beam, circle are cut
Face beam, hollow beam etc..
Description of the drawings
It is rectangular crack girder construction and crackle cross section that Fig. 1 (a), 1 (b), which are respectively,；
Fig. 2 is the torsionspring model of CRACKED BEAM；
Fig. 3 (a), 3 (b), 3 (c) are respectively that first three rank intrinsic frequency of rectangular beam structures influences curved surface；
Fig. 4 (a), 4 (b) are respectively the frequency influence curve graph that the crackle equivalent stiffness under two kinds of operating modes measures.
Specific embodiment
Attached drawing is used to aid in illustrating specific embodiments of the present invention.The present invention can be used in different cross section shape girder construction
The equivalent stiffness of crackle measures, such as rectangular beam, circular beam, hollow beam.Below by taking rectangular beam as an example, with reference to attached drawing to this hair
Bright content is described in further detail.
It is rectangular crack beam model with reference to shown in Fig. 1 (a), 1 (b).Fig. 1 (a) is rectangular crack girder construction, and Fig. 1 (b) is
Crackle cross section, rectangular co-ordinate of the x, y, z for three directions, a are crack depth, and b is the width of beam, and h is depth of beam.
It is the torsionspring model of CRACKED BEAM with reference to shown in Fig. 2.The crackle in girder construction is described with torsionspring, then
Structural model can be expressed as connecting two sections of flawless beams by torsionspring, and the rigidity of torsionspring is that crackle is equivalent
Rigidity.
It is that first three rank intrinsic frequency of rectangular beam structures influences curved surface with reference to shown in Fig. 3 (a), 3 (b), 3 (c).Fig. 3 (a),
3 (b), 3 (c) represent the intrinsic frequency curved surface of first, second and third rank respectively, and β represents crackle relative position in figure, and k represents crackle etc.
Imitate rigidity, f1、f2、f3For first three rank intrinsic frequency of structure.
With reference to shown in Fig. 4 (a), 4 (b), the frequency influence curve graph for the measurement of crackle equivalent stiffness.Fig. 4 (a), 4 (b) point
Crackle equivalent stiffness figure Wei not be measured under two kinds of operating modes, the crackle that the intersection points of three frequency influence curve graphs indicates measurement is equivalent
Rigidity and the crack position corresponding to it.β represents crackle relative position in figure, and K represents crackle equivalent stiffness.
The present invention is implemented according to the following steps:
Step 1. describes the crackle in girder construction with torsionspring, obtains the characteristic equation of crackle beam vibration.Specifically
For：
1) rectangular crack girder construction and crackle cross section such as Fig. 1 (a), 1 (b) are shown.Girder construction is described with torsionspring
In crackle, then structural model can be expressed as connecting two sections of flawless beams, the rigidity of torsionspring by torsionspring
As crackle equivalent stiffness.The torsionspring model of CRACKED BEAM is as shown in Figure 2.
2) a series of sample point is chosen respectively in the possibility value range of crack position and crackle equivalent stiffness, by these
Input parameter of the sample point as girder construction dynamic analysis.
3) sample point of crack position and crackle equivalent stiffness is input in finite element model, obtains crackle beam vibration
Characteristic equation is：
|K(k,β)-ωi 2M |=0
In formula：K represents system Bulk stiffness matrix, and M represents system total quality matrix, ωiRepresent circular frequency, k is represented
Crackle equivalent stiffness, β represent crackle relative position.ωi=2 π fi, i=1,2,3, fiFor system frequency.
According to CRACKED BEAM Mishap Database rendering architecture, first three rank intrinsic frequency influences curved surface to step 2., such as Fig. 3 (a), 3
(b), shown in 3 (c).Specially：
1) characteristic equation of crackle beam vibration is solved, obtains CRACKED BEAM Mishap Database；
2) it draws using crack position and equivalent stiffness as the structure of input first three rank intrinsic frequency influence curved surface.
Step 3. to CRACKED BEAM by carrying out vibration-testing, first three rank intrinsic frequency of measurement structure.Specially：
1) test experimental bed of girder construction and test system are built, the girder construction containing crackle is clamped on experimental bench；
2) pulse excitation is carried out to girder construction, obtains vibration signal, therefrom extract first three rank intrinsic frequency f of girder constructioni,
I=1,2,3.
Step 4. goes out crackle equivalent stiffness using the intersection measurement of intrinsic frequency influence curve, such as Fig. 4 (a), 4 (b), institute
Show.Specially：
1) to survey obtained first three rank intrinsic frequency of girder construction as input, first three rank intrinsic frequency that interception is gone to construct
Curved surface is influenced, draws out first three rank intrinsic frequency influence curve；
2) first three rank intrinsic frequency influence curve is plotted in the same coordinate system, utilizes three intrinsic frequency influence curves
Intersection point can measure crackle equivalent stiffness.
The present invention is described in further details below by specific embodiment：
Embodiment 1：
The present embodiment is by taking rectangular beam as an example, mainly for illustrating the measuring method of girder construction crackle equivalent stiffness.Rectangular beam
Both ends freely-supported, length L=0.4m, width b=0.012m, height h=0.02m, Young's modulus of lasticity E=1.7381 × 1011N/
m2, density p=7384.9kg/m3, Poisson's ratio v=0.3.β and k represents the relative position and equivalent stiffness of crackle respectively.
The present embodiment by choosing a series of sample respectively in the possibility value range of crack position and crackle equivalent stiffness
This point using these sample points as the input parameter of girder construction dynamic analysis, solves CRACKED BEAM Mishap Database, and then draw
Using crack position and equivalent stiffness as the structure of input, first three rank intrinsic frequency influences curved surface, as shown in figure 3, Fig. 3 (a), 3 (b),
3 (c) represents first, second and third rank intrinsic frequency curved surface respectively.Then vibration-testing is carried out to girder construction, is obtained under two kinds of operating modes
First three the rank intrinsic frequency f obtained1、f2、f3As shown in table 1.
1 structural natural frequencies of table and crackle equivalent stiffness measurement result
Using the structure under two kinds of operating modes in table 1, first three rank intrinsic frequency goes interception intrinsic frequency to influence curved surface, Ke Yihui
Make first three rank intrinsic frequency influence curve.First three rank intrinsic frequency influence curve is plotted in same coordinate system, is handed over
Point can measure crackle equivalent stiffness k and corresponding crack position β, as shown in Figure 4.Fig. 4 (a) is the frequency shadow in operating mode I
Curve graph is rung, Fig. 4 (b) is the frequency influence curve graph of operating mode II.The measurement result such as table 1 obtained from Fig. 4 (a) and Fig. 4 (b)
It is shown, the result verification validity of girder construction crackle equivalent stiffness measuring method.
Although the present invention is made that detailed description with above-described embodiment to the present invention, above-described embodiment is not used to limit
The fixed present invention.In the case where not departing from technical characteristic and the range of structures given by technical solution of the present invention, to technical characteristic
Increase, deformation or the replacement with the similary content in this field made, should all belong to protection scope of the present invention.
Claims (4)
1. a kind of measuring method of girder construction crackle equivalent stiffness, it is characterised in that：This method includes the following steps：
1) crackle can be described with torsionspring in girder construction, and the rigidity of torsionspring illustrates crackle equivalent stiffness；It is splitting
The possibility value range of line position and crackle equivalent stiffness chooses a series of sample point respectively, these sample points have been updated to
It limits in meta-model, obtains the characteristic equation of crackle beam vibration；
2) characteristic equation of crackle beam vibration is solved, obtains CRACKED BEAM Mishap Database, and then draw with crack position and crackle
Equivalent stiffness is the structure of input first three rank intrinsic frequency influence curved surface；
3) by carrying out vibration-testing to CRACKED BEAM, its first three rank intrinsic frequency is extracted；
4) using first three rank intrinsic frequency of actual measurement as input, intercepting first three rank intrinsic frequency influences curved surface, obtains first three rank and consolidates
There is frequency influence curve, go out crackle equivalent stiffness using the intersection measurement of three influence curves.
A kind of 2. measuring method of girder construction crackle equivalent stiffness according to claim 1, which is characterized in that the step
1) in, the characteristic equation of crackle beam vibration is obtained, is included the following steps：
1) crackle in girder construction is described with torsionspring, then structural model can be expressed as connecting by torsionspring
Two sections of flawless beams, the rigidity of torsionspring is crackle equivalent stiffness；
2) a series of sample point is chosen respectively in the possibility value range of crack position and crackle equivalent stiffness, by these samples
Input parameter of the point as girder construction dynamic analysis；
3) sample point of crack position and crackle equivalent stiffness is input in finite element model, obtains the feature of crackle beam vibration
Equation is：
|K(k,β)-ωi 2M |=0
In formula：K represents system Bulk stiffness matrix, and M represents system total quality matrix, and k represents crackle equivalent stiffness, and β is represented
Crackle relative position, ωiRepresent circular frequency, ωi=2 π fi, i=1,2,3, fiFor system frequency.
A kind of 3. measuring method of girder construction crackle equivalent stiffness according to claim 1, which is characterized in that the step
3) in, the method for first three rank intrinsic frequency of measurement structure is as follows：
1) test experimental bed of girder construction and test system are built, the girder construction containing crackle is clamped on experimental bench；
2) pulse excitation is carried out to girder construction, obtains vibration signal, therefrom extract first three rank intrinsic frequency f of girder constructioni, i=1,
2,3。
A kind of 4. measuring method of girder construction crackle equivalent stiffness according to claim 1, which is characterized in that the step
4) in, the step of going out crackle equivalent stiffness using the intersection measurement of three influence curves, is as follows：
1) to survey obtained first three rank intrinsic frequency of girder construction as input, first three rank intrinsic frequency that interception constructs is gone to influence
Curved surface draws out first three rank intrinsic frequency influence curve；
2) first three rank intrinsic frequency influence curve is plotted in the same coordinate system, utilizes the friendship of three intrinsic frequency influence curves
Point can measure crackle equivalent stiffness.
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