CN110319947A - Based on etc. temperature buoyancy effect profiled-cross-section structure temperature monitoring method - Google Patents
Based on etc. temperature buoyancy effect profiled-cross-section structure temperature monitoring method Download PDFInfo
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- G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
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Abstract
The invention discloses it is a kind of based on etc. temperature buoyancy effect profiled-cross-section structure temperature monitoring method, include the following steps: the Dispersion of velocity curve for carrying out finite element discretization to profiled-cross-section structure, obtaining the profiled-cross-section structure at room temperature using semi-analytic finite elemen；It establishes Murnaghan superlastic model, the wave communication process under the conditions of by temperature deformation is divided by temperature deformation process and wave communication process；The temperature susceplibility curve for solving profiled-cross-section structure chooses Optimum Excitation frequency f and mode M by temperature susceplibility curve and Dispersion of velocity curve；Piezoelectric transducer is installed respectively at the both ends of profiled-cross-section structure, using the guided wave signals of profiled-cross-section structure under room temperature as reference signal, obtain the guided wave signals that temperature is T, compare two guided wave signals, measure actual phase shift, the temperature value that profiled-cross-section structure is obtained according to the phase-shift curve Δ t of fitting, to realize the temperature monitoring of profiled-cross-section structure.
Description
Technical field
The present invention relates to etc. temperature monitoring technical field more particularly to it is a kind of based on etc. temperature buoyancy effect profiled-cross-section
The temperature monitoring method of structure.
Background technique
Since propagation distance is long, damage high sensitivity, response are fast, supersonic guide-wave is in monitoring structural health conditions (SHM) and lossless
Monitoring is applied in the field (NDE) extensively, including damage check and damage reason location.Studies have shown that supersonic guide-wave is to biography
The variation for broadcasting environment is especially sensitive, such as temperature, stress etc..The influence of these environment can change guided waves propagation speed and cause to damage
Location prediction failure.In addition, some researchers are intended to disclose communication environments using the environmental sensitivity of guided waves propagation
State.In order to develop effective SHM/NDT system, it is most important to fully understand influence of the environmental factor to guided waves propagation.Temperature
Variation will lead to the guided waves propagation velocity of sound in solid and change, and this phenomenon is known as acoustoelectric effect.The sound as caused by temperature change
Buoyancy effect belongs to non-linear phenomena.In addition, cross sectional shape is very complicated for as this profiled-cross-section structure of rail, propagate
Guided wave modal it is more complicated than simple structures such as plate and bars very much.Under different frequency, different mode for temperature susceptibility not
Together, so the supersonic guide-wave frequency dispersion calculating of the temperature buoyancy effect such as research is particularly important.Meanwhile utilizing calculating temperature by FEM
When load influences guided waves propagation, the factor of higher order elastic constant is often had ignored, calculated result is caused error occur.
Summary of the invention
According to problem of the existing technology, the invention discloses it is a kind of based on etc. temperature buoyancy effect profiled-cross-section knot
The temperature monitoring method of structure, the phase velocity that this method passes through the complicated profiled-cross-section structure of calculating guided wave in the case where different temperatures is horizontal
With group velocity, and then the temperature susceplibility of supersonic guide-wave is obtained with the change curve of frequency；This method is based on semi-analytic finite elemen
Method combination temperature Vocal cord injection, Murnaghan superlastic model is introduced into calculating.It will be under the conditions of by temperature deformation
Wave communication process, which is divided into, is propagated two processes by temperature deformation process and wave, is deformed process by temperature and is assumed that material is every
The same sex, wave communication process are then assumed to be hyperelastic model；This method specifically includes the following steps:
Finite element discretization is carried out to profiled-cross-section structure, obtains the profiled-cross-section structure at room temperature using semi-analytic finite elemen
Dispersion of velocity curve；
It establishes Murnaghan superlastic model, the wave communication process under the conditions of by temperature deformation is divided by temperature deformation
Journey and wave communication process；
The temperature susceplibility curve for solving profiled-cross-section structure is chosen by temperature susceplibility curve and Dispersion of velocity curve
Optimum Excitation frequency f and mode M；
Piezoelectric transducer is installed respectively at the both ends of profiled-cross-section structure, wherein one end is excitation end, and one end is receiving end,
Displacement signal is converted electrical signals to by the stress-electric coupling effect of piezoelectric transducer, wherein displacement signal is along profiled-cross-section knot
The length direction of structure is propagated, and wherein receiving end is for receiving displacement signal and being translated into electric signal；
Using the guided wave signals of profiled-cross-section structure under room temperature as reference signal, the guided wave signals that temperature is T are obtained,
Two guided wave signals are compared, actual phase shift is measured, the temperature value of profiled-cross-section structure is obtained according to the phase-shift curve Δ t of fitting,
To realize the temperature monitoring of profiled-cross-section structure.
Further, for profiled-cross-section structure, the material being located at by temperature deformation process lower different type cross section structure is each
It is elastic material to the same sex, wave communication process lower different type cross section structure.
Further, the solution mode of the temperature susceplibility curve are as follows:
△ cp=cpT-cp0
Wherein, cpTBe temperature be T when profiled-cross-section structure phase velocity angle value, cp0It is profiled-cross-section structure under room temperature
Phase velocity angle value.
It is further, described by temperature deformation process lower different type cross section structure wave propagation equations are as follows:
Wherein, δijFor Kronecker function, CijklFor second order elasticity constant, CijklmnFor three rank elastic constants.
Further, under the conditions of by temperature deformation in wave communication process profiled-cross-section structure effective sonic elastic modulus are as follows:
Wherein, CijTo utilize the second order elasticity constant of Voight symbolic formulation, CijkTo utilize the three of Voight symbolic formulation
Rank elastic constant.
Further, the wave equation of profiled-cross-section structure is obtained by Hamiton's principle, based on semi-analysis finite element method
Etc. temperature buoyancy effect supersonic guide-wave homogeneous wave equation are as follows:
(K(ξ)-ω2Μ) U=0
Wherein U is motion vector
By adopting the above-described technical solution, it is provided by the invention it is a kind of based on etc. temperature buoyancy effect profiled-cross-section knot
The temperature monitoring method of structure, method combination temperature Vocal cord injection of this method based on semi-analytic finite elemen, Murnaghan is surpassed
It plays model to be introduced into calculating, calculate at different ambient temperatures, the dispersion curve of the supersonic guide-wave of profiled-cross-section structure, into
And temperature sensitivity curve is obtained, the Optimum Excitation frequency and mode of temperature monitoring are chosen, profiled-cross-section structure is finally completed
Temperature monitoring.
Detailed description of the invention
In order to illustrate the technical solutions in the embodiments of the present application or in the prior art more clearly, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
The some embodiments recorded in application, for those of ordinary skill in the art, without creative efforts,
It is also possible to obtain other drawings based on these drawings.
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is that rail wave selected by the present invention propagates figure；
Fig. 3 is the finite element discretization grid dividing under axisymmetric condition of the present invention；
Fig. 4 is the phase velocities dispersion curve at 20 DEG C of room temperature of the present invention；
Fig. 5 is the group velocity dispersion curve at 20 DEG C of room temperature of the present invention；
Fig. 6 is the phase velocity temperature susceplibility curve of the symmetrical mode of the present invention；
Fig. 7 is the phase velocity temperature susceplibility curve of antisymmetry mode of the present invention；
Specific embodiment
To keep technical solution of the present invention and advantage clearer, with reference to the attached drawing in the embodiment of the present invention, to this
Technical solution in inventive embodiments carries out clear and complete description:
It is as shown in Figure 1 it is a kind of based on etc. temperature buoyancy effect profiled-cross-section structure temperature monitoring method, it is specific to wrap
Include following steps:
S1: choosing the profiled-cross-section structure I that carry out temperature monitoring, carries out finite element discretization to its section.It is solved using half
Finite element is analysed, the Dispersion of velocity curve of the structure at room temperature is calculated；
S2: Murnaghan superlastic model is introduced by the method combination temperature Vocal cord injection based on semi-analytic finite elemen
In calculating.Wave communication process under the conditions of by temperature deformation is divided into and is propagated two processes by temperature deformation process and wave, is solved
The temperature susceplibility curve of profiled-cross-section structure chooses Optimum Excitation frequency by temperature susceplibility curve and Dispersion of velocity curve
F and mode M.For profiled-cross-section structure, being located at by the material of temperature deformation process lower different type cross section structure is isotropism, wave
Communication process lower different type cross section structure is elastic material.
S3: temperature susceplibility curve, method for solving are solved are as follows:
△ cp=cpT-cp0
Wherein, cpTBe temperature be T when structure I phase velocity angle value, cp0It is the phase velocity angle value of room temperature condition flowering structure I；
S4: the Dispersion of velocity curve solved by semi-analytic finite elemen in temperature sensitivity curve combination S1 is chosen
Frequency dispersion is smaller and Optimum Excitation frequency f and mode M to the more sensitive frequency of temperature and mode as temperature monitoring；
S5: piezoelectric transducer is installed at the both ends in structure I respectively, and one end is excitation end, and one end is receiving end, is pacified respectively
The sensor at dress excitation end and receiving end, sensor are coupled with structure I surface.
S6: the electric signal that excitation end sensor pumping signal is the n period of Hanning window modulation, frequency is f is passed by piezoelectricity
The stress-electric coupling effect of sensor converts electrical signals to displacement signal, and displacement signal is propagated along the length direction of structure I, and by
Receiving sensor receives, and is finally translated into electric signal.
S7: obtaining the guided wave signals of structure I under room temperature, as reference signal, obtains guided wave letter when temperature is T
Number, two signals are compared, actual phase shift is measured, so that the temperature of structure I is obtained according to the phase-shift curve Δ t of fitting, thus real
The temperature monitoring of existing structure I.
Further, method combination temperature Vocal cord injection of the S2 based on semi-analytic finite elemen, by Murnaghan superlastic mould
Type is introduced into calculating.Wave communication process under the conditions of by temperature deformation is divided into and is propagated two mistakes by temperature deformation process and wave
Journey is deformed process by temperature and assumes that material is isotropic, and wave communication process is then assumed to be elastic material.
S21 obtains the wave propagation equations of the deformation generated under the influence of temperature using Murnaghan theoretical model are as follows:
Wherein, δijFor Kronecker function, CijklFor second order elasticity constant, CijklmnFor three rank elastic constants
S22: being based on temperature Vocal cord injection, can derive for semi-analytic finite elemen calculating in isotropic medium
In effective sonic elastic modulus are as follows:
Wherein, CijTo utilize the second order elasticity constant of Voight symbolic formulation, CijkTo utilize the three of Voight symbolic formulation
Rank elastic constant.
S23: the wave equation of profiled-cross-section structure is provided by Hamiton's principle, based on semi-analysis finite element method etc. temperature
The general homogeneous wave equation of the supersonic guide-wave of buoyancy effect are as follows:
(K(ξ)-ω2Μ) U=0
Wherein U is motion vector
Embodiment: profiled-cross-section structure chooses rail in the present embodiment, the specific steps are as follows:
1.1 are solved using semi-analysis finite element method, and rail is symmetrical structure, the time are calculated in order to save, to rail
Section half carry out finite element discretization, the calculating of symmetrical mode and antisymmetry mode is completed by boundary condition setting.
Obtain the phase velocity of rail under room temperature and group velocity dispersion curve.
1.2 solve the phase velocity under different temperatures using based on method of the Temperature Elastic effect in conjunction with semi-analytic finite elemen
With group velocity dispersion curve.
Undulated control equation is obtained under 1.3 Temperature Elastic effect theories:
1.4 wherein,
1.5CijklFor second order elasticity constant, CijklmnFor three rank elastic constants；
1.6 wave equations are,
1.7 obtain the general homogeneous wave equation of acoustic elasticity supersonic guide-wave in stringer by semi-analysis finite element method
(K(ξ)-ω2Μ) (12) U=0
1.8 wherein, K (ξ)=K1+iξK2+ξ2K3
1.9 when isotropic material is changed by uniform temperature, and material is isotropic in some sense.
The variation of guided waves propagation, can be obtained elastic constant according to formula (2) when 1.10 researchs such as shall be limited only to the extent at the temperature changes
In each single item, wherein
1.11 solve dispersion curve and temperature susceplibility curve, temperature susceplibility method for solving are as follows:
△ cp=cpT-cp0
Wherein, cpTBe temperature be T when structure I phase velocity angle value, cp0It is the phase velocity angle value of rail under room temperature；
The 1.12 Dispersion of velocity curves solved by semi-analytic finite elemen in temperature sensitivity curve combination S1 are chosen
Frequency dispersion is smaller and Optimum Excitation frequency f and mode to the more sensitive frequency of temperature and mode as temperature monitoring；
1.13 calculate the theoretical phase shift △ t under condition of different temperatures, temperature-phase-shift curve of fitting.
Wherein, x0For excitation end to receiving end distance, △ x is x0It is multiplied by strain.
1.14 install piezoelectric transducer on rail, and one end is excitation end, and one end is receiving end, respectively installation excitation end and
The sensor of receiving end, sensor are coupled with structure I surface.
1.15 electric signals that excitation end sensor pumping signal is the n period of Hanning window modulation, frequency is f, pass through piezoelectricity
The stress-electric coupling effect of sensor converts electrical signals to displacement signal, and displacement signal is propagated along the length direction of rail, and
It is received by receiving sensor, is finally translated into electric signal.
1.16 obtain the guided wave signals of rail under room temperature, as reference signal, obtain guided wave letter when temperature is T
Number, two signals are compared, phase shift is measured, so that the temperature of rail is obtained according to the phase-shift curve of fitting, to realize rail
Temperature monitoring.
Embodiment 2: specific step is as follows:
What 1.1 this example were chosen is CHN60 sections rail, and material properties are as shown in Table 1 and Table 2, the propagation of guided wave in rail
Figure is as shown in Figure 2；
Table 1
Table 2
1.2 such as Fig. 3 are the grid dividing in rail section, the propagation of guided wave in rail are asked using semi-analytic finite elemen, by wave
Direction of propagation movement is reduced to simple harmonic motion, so three-dimensional model simplifying is two dimensional model, it is only necessary to carry out to the section of rail
Grid dividing.
The 1.3 such as cell types used in Fig. 3 this example is three node triangular elements.
1.3 rails are that section is symmetrically, to calculate the time to save, it is only necessary to draw the grid of half, perimeter strip is arranged
Part in the hope of the symmetrical mode of rail and antisymmetry mode phase velocity and group velocity dispersion curve.
1.4 wherein, and the boundary condition of symmetric and anti-symmetric mode is set as, as the left margin knee level direction Fig. 3 is displaced
It is set as 0, corresponding solution is symmetrical mode；Left margin node vertical direction and along direction of wave travel displacement be set as 0, the side
What is solved under the conditions of boundary is antisymmetry mode.
1.5 solve the guided waves propagation in rail under room temperature using semi-analytic finite elemen, solve 20 DEG C under room temperature
Rail in guided waves propagation phase velocity Cp0With group velocity Cg0.Frequency range is selected as 0-60kHz, if Fig. 4 is iron under room temperature
Phase velocities dispersion curve figure in rail, if Fig. 5 is group velocity dispersion curve graph in rail under room temperature.
1.6 temperature that are acquired using Temperature Elastic effect combination semi-analytic finite elemen method are guided wave in rail at 100 DEG C
The phase velocity Cp of propagationTWith group velocity angle value CgT。
1.7 solve phase velocity temperature sensitivity, KCp=(CpT-Cp0)/△ T, Fig. 6 are the phase velocity temperature spirit of symmetrical mode
Acuity curve, Fig. 7 are the phase velocity temperature sensitivity curve of antisymmetry mode.
1.9 choose temperature sensitive according to Fig. 6-7 according to Fig. 5 selection lesser mode of frequency dispersion for the temperature monitoring of rail
Higher mode is spent, complex chart 5-7 chooses the guided wave modal and frequency for being suitble to temperature monitoring.
1.10 calculating the theoretical phase shift △ t under condition of different temperatures, temperature-phase-shift curve of fitting.
Wherein, x0For excitation end to receiving end distance, △ x is x0It is multiplied by strain.
1.11 install piezoelectric transducer on rail, and one end is excitation end, and one end is receiving end, respectively installation excitation end and
The sensor of receiving end, if Fig. 2 is respectively that end and receiving end sensor position, sensor is motivated to couple with rail surface.
1.12 electric signals that excitation end sensor pumping signal is the n period of Hanning window modulation, frequency is f, pass through piezoelectricity
The stress-electric coupling effect of sensor converts electrical signals to displacement signal, and displacement signal is propagated along the length direction of rail, and
It is received by receiving sensor, is finally translated into electric signal.
1.13 obtain the guided wave signals of rail under room temperature, as reference signal, obtain guided wave letter when temperature is T
Number, two signals are compared, phase shift is measured, so that the temperature of rail is obtained according to the phase-shift curve of fitting, to realize rail
Temperature monitoring.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Anyone skilled in the art in the technical scope disclosed by the present invention, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (6)
1. it is a kind of based on etc. temperature buoyancy effect profiled-cross-section structure temperature monitoring method characterized by comprising
Finite element discretization is carried out to profiled-cross-section structure, obtains the wave of the profiled-cross-section structure at room temperature using semi-analytic finite elemen
Fast dispersion curve；
Establish Murnaghan superlastic model, the wave communication process under the conditions of by temperature deformation is divided by temperature deformation process and
Wave communication process；
The temperature susceplibility curve for solving profiled-cross-section structure is chosen best by temperature susceplibility curve and Dispersion of velocity curve
Driving frequency f and mode M；
Piezoelectric transducer is installed respectively at the both ends of profiled-cross-section structure, wherein one end is excitation end, and one end is receiving end, is passed through
The stress-electric coupling effect of piezoelectric transducer converts electrical signals to displacement signal, and wherein displacement signal is along profiled-cross-section structure
Length direction is propagated, and wherein receiving end is for receiving displacement signal and being translated into electric signal；
Using the guided wave signals of profiled-cross-section structure under room temperature as reference signal, the guided wave signals that temperature is T, comparison are obtained
Two guided wave signals, measure actual phase shift, and the temperature value of profiled-cross-section structure is obtained according to the phase-shift curve Δ t of fitting, thus
Realize the temperature monitoring of profiled-cross-section structure.
2. according to the method described in claim 1, it is characterized by: being located at profiled-cross-section structure by temperature deformation process
The material of lower different type cross section structure is isotropism, wave communication process lower different type cross section structure is elastic material.
3. according to the method described in claim 2, it is characterized by: the solution mode of the temperature susceplibility curve are as follows:
Δ cp=cpT-cp0
Wherein, cpTBe temperature be T when profiled-cross-section structure phase velocity angle value, cp0It is the phase of profiled-cross-section structure under room temperature
Velocity amplitude.
4. according to the method described in claim 1, it is characterized by: described passed by temperature deformation process lower different type cross section structure wave
Broadcast equation are as follows:
Wherein, δijFor Kronecker function, CijklFor second order elasticity constant, CijklmnFor three rank elastic constants.
5. according to the method described in claim 1, it is characterized by: profiled-cross-section in wave communication process under the conditions of by temperature deformation
Effective sonic elastic modulus of structure are as follows:
Wherein, CijTo utilize the second order elasticity constant of Voight symbolic formulation, CijkTo utilize three rank bullets of Voight symbolic formulation
Property constant.
6. according to the method described in claim 1, it is characterized by: the wave equation of profiled-cross-section structure is obtained by Hamiton's principle
, based on semi-analysis finite element method etc. temperature buoyancy effect supersonic guide-wave homogeneous wave equation are as follows:
(K(ξ)-ω2M) U=0
Wherein U is motion vector
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| CN112464524A (en) * | 2020-11-07 | 2021-03-09 | 西南交通大学 | Method for determining guided wave propagation characteristics of turnout variable cross-section steel rail |
| CN112560320A (en) * | 2020-12-24 | 2021-03-26 | 华东交通大学 | Calculation method of bending vibration band gap of track structure |
| CN112818579A (en) * | 2021-02-05 | 2021-05-18 | 重庆科技学院 | Multi-parameter coupling-based efficient detection method for thermal stress field of equipment |
| CN113566124A (en) * | 2021-06-11 | 2021-10-29 | 东莞理工学院 | Method, device and equipment for selecting optimal excitation frequency of ultrasonic guided wave and storage medium |
| CN113987880A (en) * | 2021-10-28 | 2022-01-28 | 中国石油大学(华东) | Prestressed waveguide structure analysis method and system based on wave finite element method |
| CN114235971A (en) * | 2021-12-22 | 2022-03-25 | 大连海事大学 | Ultrasonic guided wave-based method for identifying damaged shape of woven composite material plate |
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