CN110319947B - Temperature monitoring method of special-shaped section structure based on isothermal elastic effect - Google Patents
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Abstract
The invention discloses a temperature monitoring method of a special-shaped section structure based on an isothermal elastic effect, which comprises the following steps: carrying out finite element dispersion on the special-shaped cross-section structure, and acquiring a wave velocity dispersion curve of the special-shaped cross-section structure at room temperature by using a semi-analytic finite element; establishing a Murnaghan superelasticity model, and dividing a wave propagation process under the temperature deformation condition into a temperature deformation process and a wave propagation process; solving a temperature sensitivity curve of the special-shaped cross-section structure, and selecting an optimal excitation frequency f and a mode M through the temperature sensitivity curve and a wave velocity dispersion curve; the piezoelectric sensors are respectively installed at two ends of the special-shaped cross section structure, the guided wave signals of the special-shaped cross section structure at room temperature are used as reference signals, the guided wave signals with the temperature T are obtained, the two guided wave signals are compared, actual phase shift is measured, and the temperature value of the special-shaped cross section structure is obtained according to the fitted phase shift curve delta T, so that the temperature monitoring of the special-shaped cross section structure is realized.
Description
Technical Field
The invention relates to the technical field of isothermal monitoring, in particular to a method for monitoring the temperature of a special-shaped section structure based on isothermal elastic effect.
Background
Due to long propagation distance, high damage sensitivity, fast response and wide application of ultrasonic guided waves in the fields of Structural Health Monitoring (SHM) and non-destructive monitoring (NDE), including damage detection and damage localization. Research shows that the ultrasonic guided waves are particularly sensitive to changes of propagation environments, such as temperature, stress and the like. These environmental effects can change the guided wave propagation velocity and lead to failure of prediction of lesion localization. In addition, some researchers have also attempted to exploit the environmental sensitivity of guided wave propagation to reveal the state of the propagation environment. To develop an effective SHM/NDT system, it is important to fully understand the impact of environmental factors on guided wave propagation. The temperature change can cause the propagation sound velocity of the guided wave in the solid to change, and the phenomenon is called acoustic-elastic effect. The acoustoelastic effect caused by temperature changes is a nonlinear phenomenon. In addition, the profiled cross-sectional structure such as a rail has a complicated cross-sectional shape, and the guided wave mode propagating through the profiled cross-sectional structure is much more complicated than that of a simple structure such as a plate or a rod. Under different frequencies, different modes have different sensitivities to temperature, so that the ultrasonic guided wave frequency dispersion calculation for researching the isothermal elastic effect is particularly important. Meanwhile, when the finite element is used for calculating the influence of the temperature load on the guided wave propagation, the factor of a high-order elastic constant is often ignored, and the calculation result has errors.
Disclosure of Invention
According to the problems in the prior art, the invention discloses a temperature monitoring method of a special-shaped cross section structure based on an isothermal elastic effect, which is characterized in that the phase velocity and the group velocity of a complex special-shaped cross section structure under different temperature levels are calculated, so that the change curve of the temperature sensitivity of ultrasonic guided waves along with the frequency is obtained; the method is based on a semi-analytic finite element method and combines a temperature acoustic elasticity theory, and a Murnaghan superelasticity model is introduced into calculation. Dividing the wave propagation process under the temperature deformation condition into a temperature deformation process and a wave propagation process, wherein the temperature deformation process assumes that the material is isotropic, and the wave propagation process assumes a superelasticity model; the method specifically comprises the following steps:
carrying out finite element dispersion on the special-shaped cross-section structure, and acquiring a wave velocity dispersion curve of the special-shaped cross-section structure at room temperature by using a semi-analytic finite element;
establishing a Murnaghan superelasticity model, and dividing a wave propagation process under the temperature deformation condition into a temperature deformation process and a wave propagation process;
solving a temperature sensitivity curve of the special-shaped cross-section structure, and selecting an optimal excitation frequency f and a mode M through the temperature sensitivity curve and a wave velocity dispersion curve;
the method comprises the following steps that piezoelectric sensors are respectively installed at two ends of a special-shaped cross section structure, wherein one end of each piezoelectric sensor is an excitation end, the other end of each piezoelectric sensor is a receiving end, an electric signal is converted into a displacement signal through the force-electricity coupling effect of the piezoelectric sensors, the displacement signal is transmitted along the length direction of the special-shaped cross section structure, and the receiving ends are used for receiving the displacement signal and converting the displacement signal into the electric signal;
the method comprises the steps of taking a guided wave signal of the special-shaped cross section structure at room temperature as a reference signal, obtaining a guided wave signal with the temperature T, comparing the two guided wave signals, measuring actual phase shift, and obtaining a temperature value of the special-shaped cross section structure according to a fitted phase shift curve delta T, so that the temperature monitoring of the special-shaped cross section structure is realized.
Furthermore, for the special-shaped cross section structure, the material of the special-shaped cross section structure arranged in the process of deforming under the temperature is isotropic, and the special-shaped cross section structure arranged in the process of wave propagation is super-elastic.
Further, the solution method of the temperature sensitivity curve is as follows:
△cp＝cpT-cp0
wherein cpTIs the phase velocity value, cp, of the profiled cross-sectional structure at a temperature of T0Is the phase velocity value of the special-shaped section structure under the room temperature condition.
Further, the wave propagation equation of the special-shaped section structure in the temperature deformation process is as follows:
wherein, deltaijIs a function of Crohn's function, CijklIs a second order elastic constant, CijklmnIs the third order elastic constant.
Further, the effective acoustic elastic constant of the special-shaped cross section structure in the wave propagation process under the temperature deformation condition is as follows:
wherein, CijSecond order elastic constants expressed by Voight notation, CijkIs a third order elastic constant expressed by a Voight notation.
Furthermore, the wave equation of the special-shaped cross section structure is obtained by the Hamilton principle, and the ultrasonic guided wave homogeneous wave equation of the isothermal elastic effect based on the semi-analytic finite element method is as follows:
(K(ξ)-ω2Μ)U＝0
where U is a displacement vector
By adopting the technical scheme, the temperature monitoring method of the special-shaped cross section structure based on the isothermal elastic effect is characterized in that a Murnaghan superelasticity model is introduced into calculation based on a semi-analytic finite element method in combination with a temperature acoustic elasticity theory, the dispersion curve of ultrasonic guided waves of the special-shaped cross section structure at different environmental temperatures is calculated, a temperature sensitivity curve is further obtained, the optimal excitation frequency and mode of temperature monitoring are selected, and finally the temperature monitoring of the special-shaped cross section structure is completed.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of rail wave propagation selected in accordance with the present invention;
FIG. 3 is a finite element discrete meshing under axisymmetric conditions of the present invention;
FIG. 4 is a phase velocity dispersion curve of the present invention at room temperature of 20 ℃;
FIG. 5 is a group velocity dispersion curve of the present invention at room temperature 20 ℃;
FIG. 6 is a phase velocity temperature sensitivity curve for the symmetric mode of the present invention;
FIG. 7 is a phase velocity temperature sensitivity curve for the antisymmetric mode of the present invention;
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following describes the technical solutions in the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention:
as shown in fig. 1, a method for monitoring the temperature of a special-shaped cross-section structure based on an isothermal elastic effect specifically includes the following steps:
s1: selecting a special-shaped section structure I to be subjected to temperature monitoring, and carrying out finite element dispersion on the section of the special-shaped section structure I. Calculating a wave velocity dispersion curve of the structure at room temperature by using a semi-analytic finite element;
s2: the Murnaghan superelasticity model is introduced into the calculation based on a semi-analytic finite element method in combination with a temperature acoustoelastic theory. Dividing the wave propagation process under the temperature deformation condition into a temperature deformation process and a wave propagation process, solving a temperature sensitivity curve of the special-shaped section structure, and selecting an optimal excitation frequency f and a mode M according to the temperature sensitivity curve and the wave velocity dispersion curve. For the special-shaped cross section structure, the material of the special-shaped cross section structure is isotropic in the process of deforming under the temperature, and the material of the special-shaped cross section structure is super-elastic in the process of wave propagation.
S3: solving a temperature sensitivity curve, wherein the solving method comprises the following steps:
△cp＝cpT-cp0
wherein cpTIs the phase velocity value, cp, of structure I at temperature T0Is the phase velocity value of structure I under room temperature;
s4: selecting a frequency and a mode with small frequency dispersion and sensitive temperature as an optimal excitation frequency f and a mode M for temperature monitoring through a wave velocity dispersion curve obtained by combining a temperature sensitivity curve and a semi-analytic finite element solution in S1;
s5: and piezoelectric sensors are respectively arranged at two ends of the structure I, one end of the structure I is an excitation end, the other end of the structure I is a receiving end, the sensors at the excitation end and the receiving end are respectively arranged, and the sensors are coupled with the surface of the structure I.
S6: the excitation signal of the excitation end sensor is an n-period and f-frequency electric signal modulated by a Hanning window, the electric signal is converted into a displacement signal through the force-electricity coupling effect of the piezoelectric sensor, the displacement signal is transmitted along the length direction of the structure I, received by the receiving sensor and finally converted into the electric signal.
S7: and obtaining a guided wave signal of the structure I at room temperature, taking the guided wave signal as a reference signal, obtaining a guided wave signal at the temperature of T, comparing the two signals, and measuring the actual phase shift, so that the temperature of the structure I is obtained according to the fitted phase shift curve delta T, and the temperature monitoring of the structure I is realized.
Further, S2 introduces a Murnaghan superelasticity model into the calculation based on a semi-analytic finite element method in combination with the temperature acoustoelastic theory. The wave propagation process under the temperature deformation condition is divided into a temperature deformation process and a wave propagation process, the temperature deformation process assumes that the material is isotropic, and the wave propagation process assumes that the material is super-elastic.
S21, obtaining a wave propagation equation of deformation generated under the influence of temperature by adopting a Murnaghan theoretical model as follows:
wherein, deltaijIs a function of Crohn's function, CijklIs a second order elastic constant, CijklmnIs a third order elastic constant
S22: based on the temperature acoustoelastic theory, it can be deduced that the effective acoustoelastic constant in isotropic media for semi-analytic finite element calculation is:
wherein, CijSecond order elastic constants expressed by Voight notation, CijkIs a third order elastic constant expressed by a Voight notation.
S23: the wave equation of the special-shaped cross section structure is given by the Hamilton principle, and the general homogeneous wave equation of the ultrasonic guided wave based on the isothermal elastic effect of the semi-analytic finite element method is as follows:
(K(ξ)-ω2Μ)U＝0
where U is a displacement vector
Example (b): in this embodiment, the specific steps for selecting the rail with the special-shaped cross section structure are as follows:
1.1, solving by using a semi-analytic finite element method, wherein the rail is of a symmetrical structure, carrying out finite element dispersion on half of the section of the rail in order to save calculation time, and completing the calculation of a symmetrical mode and an anti-symmetrical mode through setting boundary conditions. And obtaining the phase velocity and group velocity dispersion curve of the rail under the room temperature condition.
1.2 solving the phase velocity and group velocity dispersion curves at different temperatures by using a method based on the combination of the temperature elastic effect and a semi-analytic finite element.
1.3 obtaining a wave control equation under the temperature elastic effect theory:
1.4 wherein the content of the amino acid sequence,
1.5Cijklis a second order elastic constant, CijklmnIs a third order elastic constant;
1.6 the wave equation is that,
1.7 obtaining the general homogeneous wave equation of the acoustoelastic ultrasonic guided wave in the stringer by the semi-analytic finite element method
(K(ξ)-ω2Μ)U＝0 (12)
1.8 wherein K ([ xi ]) - [ K ]1+iξK2+ξ2K3
1.9 when isotropic materials are subjected to a uniform temperature change, the material is isotropic in a sense.
1.10 this study is limited to changes in guided wave propagation at equal temperature changes, and each of the elastic constants can be obtained from equation (2), where,
1.11 solving a frequency dispersion curve and a temperature sensitivity curve, wherein the temperature sensitivity solving method comprises the following steps:
△cp＝cpT-cp0
wherein cpTIs the phase velocity value, cp, of structure I at temperature T0Is the phase velocity value of the rail under the condition of room temperature;
1.12, selecting a frequency and a mode with small frequency dispersion and sensitive temperature as an optimal excitation frequency f and a mode for monitoring the temperature by combining a temperature sensitivity curve with a wave velocity dispersion curve obtained by solving a semi-analytic finite element in S1;
1.13 calculating theoretical phase shift delta t under different temperature conditions, and fitting a temperature-phase shift curve.
Wherein x is0For the distance from the excitation end to the receiving end, Δ x is x0Multiplied by the strain.
1.14 installing a piezoelectric sensor on the rail, wherein one end of the piezoelectric sensor is an excitation end, the other end of the piezoelectric sensor is a receiving end, the sensors of the excitation end and the receiving end are respectively installed, and the sensors are coupled with the surface of the structure I.
1.15 the excitation signal of the excitation end sensor is an n-period and f-frequency electrical signal modulated by a Hanning window, the electrical signal is converted into a displacement signal through the force-electricity coupling effect of the piezoelectric sensor, and the displacement signal is transmitted along the length direction of the rail, received by the receiving sensor and finally converted into the electrical signal.
1.16 the guided wave signal of rail under the room temperature condition is obtained, and as the reference signal, the guided wave signal when obtaining the temperature and being T compares two signals, surveys the phase shift to obtain the temperature of rail according to the phase shift curve of fitting, thereby realize the temperature monitoring of rail.
Example 2 the specific procedure was as follows:
1.1 the example selects the CHN60 type rail, the material properties are shown in tables 1 and 2, and the propagation diagram of guided waves in the rail is shown in FIG. 2;
TABLE 1
TABLE 2
1.2, as shown in fig. 3, the grid division of the rail section is performed, the propagation of guided waves in the rail is solved by using a semi-analytic finite element, and the wave propagation direction motion is simplified into simple harmonic motion, so that a three-dimensional model is simplified into a two-dimensional model, and only the grid division is performed on the rail section.
1.3 the cell type as used in the example of fig. 3 is a three-node triangle cell.
1.3 the rail is symmetrical in section, and in order to save calculation time, only half of the grid needs to be drawn, and boundary conditions are set to obtain phase velocity and group velocity dispersion curves of the symmetrical mode and the anti-symmetrical mode of the rail.
1.4, wherein the boundary conditions of the symmetric and anti-symmetric modes are set, if the horizontal displacement of the left boundary node in FIG. 3 is set to 0, the symmetric mode is solved; the left boundary node vertical and along-wave propagation displacement is set to 0, and the antisymmetric mode is solved under the boundary condition.
1.5 solving the guided wave propagation in the rail at room temperature by using the semi-analytic finite element, and solving the phase velocity Cp of the guided wave propagation in the rail at 20 ℃ at room temperature0And group velocity Cg0. The frequency range is selected to be 0-60kHz, as shown in FIG. 4 for medium velocity dispersion plots at room temperature in the rail, and as shown in FIG. 5 for group velocity dispersion plots at room temperature in the rail.
1.6 phase velocity Cp of guided wave propagation in railway at 100 deg.C, obtained by temperature elastic effect combined with semi-analytic finite element methodTAnd group velocity value CgT。
1.7 solving for phase velocity temperature sensitivity, KCp＝(CpT-Cp0) V Δ T, fig. 6 is a phase velocity temperature sensitivity curve of the symmetric mode, and fig. 7 is a phase velocity temperature sensitivity curve of the anti-symmetric mode.
1.9 for the temperature monitoring of the rail, selecting a mode with smaller frequency dispersion according to the graph 5, selecting a mode with higher temperature sensitivity according to the graphs 6-7, and selecting a guided wave mode and a frequency suitable for the temperature monitoring by combining the graphs 5-7.
1.10 calculating the theoretical phase shift delta t under different temperature conditions and fitting a temperature-phase shift curve.
Wherein x is0For the distance from the excitation end to the receiving end, Δ x is x0Multiplied by the strain.
1.11 installing piezoelectric sensors on the rail, one end being an excitation end and the other end being a receiving end, installing sensors of the excitation end and the receiving end respectively, as shown in fig. 2, the sensors are respectively the positions of the excitation end and the receiving end, and the sensors are coupled with the surface of the rail.
1.12 the excitation signal of the excitation end sensor is an n-period and f-frequency electrical signal modulated by a Hanning window, the electrical signal is converted into a displacement signal through the force-electricity coupling effect of the piezoelectric sensor, and the displacement signal is transmitted along the length direction of the rail, received by the receiving sensor and finally converted into the electrical signal.
1.13 the guided wave signal of rail under the room temperature condition is obtained, and as reference signal, the guided wave signal when obtaining the temperature and being T compares two signals, surveys the phase shift to obtain the temperature of rail according to the phase shift curve of fitting, thereby realize the temperature monitoring of rail.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (3)
1. A temperature monitoring method of a special-shaped cross section structure based on an isothermal elastic effect is characterized by comprising the following steps:
carrying out finite element dispersion on the special-shaped cross-section structure, and acquiring a wave velocity dispersion curve of the special-shaped cross-section structure at room temperature by using a semi-analytic finite element;
establishing a Murnaghan superelasticity model, and dividing a wave propagation process under the temperature deformation condition into a temperature deformation process and a wave propagation process;
solving a temperature sensitivity curve of the special-shaped cross-section structure, and selecting an optimal excitation frequency f and a mode M through the temperature sensitivity curve and a wave velocity dispersion curve;
the method comprises the following steps that piezoelectric sensors are respectively installed at two ends of a special-shaped cross section structure, wherein one end of each piezoelectric sensor is an excitation end, the other end of each piezoelectric sensor is a receiving end, an electric signal is converted into a displacement signal through the force-electricity coupling effect of the piezoelectric sensors, the displacement signal is transmitted along the length direction of the special-shaped cross section structure, and the receiving ends are used for receiving the displacement signal and converting the displacement signal into the electric signal;
the method comprises the steps of taking a guided wave signal of the special-shaped cross-section structure at room temperature as a reference signal to obtain a guided wave signal with the temperature T, comparing the two guided wave signals to measure actual phase shift, and obtaining a temperature value of the special-shaped cross-section structure according to a fitted phase shift curve delta T, so that the temperature monitoring of the special-shaped cross-section structure is realized;
the wave propagation equation of the special-shaped section structure in the deformation process under the temperature is as follows:
wherein, deltaikIs a function of Crohn's function, CijklIs a second order elastic constant, CijklmnIs a third order elastic constant;
the wave equation of the special-shaped cross section structure is obtained by the Hamilton principle, and the ultrasonic guided wave homogeneous wave equation of the isothermal elastic effect based on the semi-analytic finite element method is as follows:
(K(ξ)-ω2Μ)U＝0
where U is a displacement vector
2. The method of claim 1, wherein: for the special-shaped cross section structure, the material of the special-shaped cross section structure is isotropic in the process of deforming under the temperature, and the material of the special-shaped cross section structure is super-elastic in the process of wave propagation.
3. The method of claim 2, wherein: the solving mode of the temperature sensitivity curve is as follows:
△cp＝cpT-cp0
wherein cpTIs the phase velocity value, cp, of the profiled cross-sectional structure at a temperature of T0Is the phase velocity value of the special-shaped section structure under the room temperature condition.
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