CN107271301B - It is a kind of based on direct wave extract viscoelastic material answer Young's modulus measurement method - Google Patents
It is a kind of based on direct wave extract viscoelastic material answer Young's modulus measurement method Download PDFInfo
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- CN107271301B CN107271301B CN201710413324.1A CN201710413324A CN107271301B CN 107271301 B CN107271301 B CN 107271301B CN 201710413324 A CN201710413324 A CN 201710413324A CN 107271301 B CN107271301 B CN 107271301B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/32—Investigating strength properties of solid materials by application of mechanical stress by applying repeated or pulsating forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0001—Type of application of the stress
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/0202—Control of the test
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Abstract
The present invention proposes that a kind of viscoelastic material extracted based on direct wave answers Young's modulus measurement method, the impulse response function H (ω) of measuring system is obtained first, secondly obtains when requiring the Fourier transformation result of vibration excitor exciting end pumping signal being H according to H (ω)3When (ω), signal generator needs the signal S (t) exported, then time-domain signal S (t) is sent vibration excitor by signal generator, the extensional vibration signal for measuring sample fixing end and sample free end respectively, finally calculates the storage modulus E ' and fissipation factor tan (δ) of material according to formula.Multiple Young's modulus is calculated by the characteristic that direct wave is propagated in thin stick in the present invention, explicit physical meaning and easy to operate, pass through the extraction to direct wave in the thin stick of viscoplasticity, avoid the influence of both ends back wave, the direct measurement frequency wider range of its parameter, it is not limited to sample resonant frequency, and measurement result is continuous in wide frequency range.
Description
Technical field
It is specially a kind of to be glued based on what direct wave extracted the present invention relates to viscoelastic material dynamic mechanics parameter fields of measurement
Elastic material answers the direct measuring method in the continuous wide frequency range of Young's modulus.
Background technique
In viscoelastic material dynamic mechanics parameter fields of measurement, viscoelastic material answers Young's modulus and commonly measures skill at present
Art mainly has forced non-resonance method, forced resonance method, wave velocity method and inverse finite element method.
Wherein, it forces non-resonance method to motivate sample using sinusoidal stress, so that it is made forced vibration and generate corresponding deformation,
The multiple Young's modulus of material is obtained by the measurement to the phase difference being applied between the stress and strain on sample, it is typical
Direct measurement frequency range is 0.01~100Hz, and the parameter of high-frequency range need to be calculated by time temperature equivalence principle.Its advantage
It is that low frequency measurement precision is high, disadvantage is the high-frequency data indirectly measurement expanded by time temperature equivalence as a result, error can not
Estimate.
Forced resonance method mainly motivates rod-like samples using a broadband signal, to the freedom of extensional vibration sample
The extensional vibration response of end and fixing end measures, thus obtain the Oscillation Amplitude of its free end and fixing end than curve,
Amplitude Ration obtains the multiple Young's modulus at resonant frequency when then passing through resonance.Its advantage is that signal-to-noise ratio is high, the disadvantage is that measurement knot
Fruit is confined to discrete resonant frequency point.
Wave velocity method mainly carries out longitudinal pumping to rod-like samples using simple signal, using two laser vibration measurers to sample
The oscillation crosswise of two sides measures respectively at product position, and the influence of bending vibration can be eliminated after measured result superposition, is obtained
To the oscillation crosswise caused due to there are Poisson's ratio by extensional vibration, the oscillation crosswise of sample another position is measured,
Then the multiple Young's modulus of sample is obtained by the time delay and decay calculation of two o'clock vibratory response.Its advantage is that principle is simple, lack
Point is that oscillation crosswise is not easy to measure, and the influence due to reflecting signal in sample, and measurement frequency is not easy too low, and the method essence
Upper is single-frequency measurement method.
For inverse finite element method mainly by carrying out finite element modeling to viscoelastic material, input parameter is the springform of material
Amount is compared by the material surface vibratory response for obtaining FEM calculation and experimental measurements, continues to optimize input parameter
So that the two deviation meets error condition, to obtain the multiple Young's modulus of material, the method advantage is not limited to be surveyed parameter
At the resonant frequency of sample, disadvantage is under certain conditions that Inversion Calculation model can not restrain.
Summary of the invention
Due to forcing the direct measurement frequency range of non-resonance method lower, the survey of forced resonance method in existing measuring technique
Amount frequency be limited at discrete Frequency point, the measurement frequency range of wave velocity method is higher, inverse finite element method there are model without
The case where method restrains.The invention proposes a kind of viscoelastic materials extracted based on direct wave to answer the measurement method of Young's modulus,
Multiple Young's modulus is calculated by the characteristic that direct wave is propagated in thin stick, explicit physical meaning and easy to operate.By right
The extraction of direct wave in the thin stick of viscoplasticity, avoids the influence of both ends back wave, the direct measurement frequency wider range of parameter, no
It is limited to sample resonant frequency, and measurement result is continuous in wide frequency range.
To achieve the above object, the present invention proposes that a kind of viscoelastic material extracted based on direct wave answers Young's modulus measurement
Method, using including measuring instruments such as vibration excitor, laser vibration measurer, power amplifier, signal generation apparatus, data acquisition devices
Device, signal generator provide excitation by power amplifier for vibration excitor, by laser vibration measurer to vibration excitor exciting end and sample
The vibration velocity signal of product free end measures and passes to data acquisition device.Specific measuring process is as follows:
Step 1: the impulse response function H (ω) of measuring system is obtained by following procedure:
Signal generator sends wideband pulse signal to vibration excitor, and the Fourier transformation result of the wideband pulse signal is
H1Extensional vibration is made at (ω), the exciting end of vibration excitor, measures the extensional vibration signal at exciting end, obtains Fu of extensional vibration signal
In leaf transformation result be H2(ω)；The impulse response function for obtaining measuring system is H (ω)=H2(ω)/H1(ω)；
Step 2: according to the impulse response function H (ω) for the measuring system that step 1 obtains, obtaining that vibration excitor exciting ought be required
The Fourier transformation result for holding pumping signal is H3When (ω), the Fourier transformation result for the signal that signal generator needs to export
For H0(ω)=H3(ω)/H (ω), to H0(ω) carries out inversefouriertransform and obtains time-domain signal S (t)；
Step 3: sample will be measured and be processed as the club shaped structure that cross section is rectangle；It is free to measure sample one end, the other end
The exciting end of vibration excitor is sticked in vertically；Time-domain signal S (t) is sent vibration excitor by signal generator, and it is solid to measure sample respectively
The extensional vibration signal of fixed end and sample free end；The Fourier transformation result for obtaining sample fixing end extensional vibration signal is Vg
(ω), the Fourier transformation result of sample free end extensional vibration signal are Vz(ω)；
Step 4: the Fourier transformation result for obtaining direct wave at sample fixing end is Vg(ω), sample free end are through
The Fourier transformation result of wave is VT(ω):
Select amplitude in above-mentioned calculated result straight as sample free end less than the solution of the through wave amplitude of sample fixing end
Up to the Fourier transformation result V of waveT(ω)；
Step 5: at the sample fixing end obtained according to step 4 and the Fourier transformation knot of sample free end direct wave
The longitudinal wave velocity c (ω) and attenuation coefficient α (ω) of rod-like samples is calculated in fruit are as follows:
Wherein l is rod-like samples length, and ω is frequency,Indicate the phase of direct wave at sample fixing end；
Indicate the phase of sample free end direct wave, unwrap is phase unwrapping around function；
Step 6: according to the longitudinal wave velocity c (ω) and attenuation coefficient α (ω) of the rod-like samples that step 5 obtains, calculating
To the storage modulus E ' and fissipation factor tan (δ) of material:
Wherein ρ is density of material, and δ indicates the phase of multiple Young's modulus.
Beneficial effect
The present invention has the effect that
1, the influence for eliminating sample stick both ends reflection signal, extracts the direct wave in extensional vibration sample stick.
2, due to extracting calculating of the direct wave for multiple Young's modulus, the shadow of back wave in traditional wave velocity method is overcome
It rings, has widened the test frequency range of multiple Young's modulus.
3, the measurement result of multiple Young's modulus is not limited at resonant frequency, can be measured to obtain in continuous wide frequency range and be glued
The multiple Young's modulus of elastic material.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures
Obviously and it is readily appreciated that, in which:
Fig. 1: experimental provision schematic diagram used in the present invention；
Fig. 2: the measurement result of rubber material storage modulus and fissipation factor.
Specific embodiment
The embodiment of the present invention is described below in detail, the embodiment is exemplary, it is intended to it is used to explain the present invention, and
It is not considered as limiting the invention.
The measurement of multiple Young's modulus has been carried out in this example to viscoelastic rubber material:
The measuring device used in this example include laser vibration measurer, vibration excitor, power amplifier, signal generation apparatus and
Data acquisition device.Signal generator provides excitation by power amplifier for vibration excitor, is swashed by laser vibration measurer to vibration excitor
The vibration velocity signal of vibration end and sample free end measures and passes to data acquisition device.
Using above-mentioned apparatus, viscoelastic material is answered Young's modulus measurement method and is comprised the steps of:
Step 1: the impulse response function H (ω) of measuring system is obtained by following procedure:
Signal generator sends wideband pulse signal to vibration excitor, and the Fourier transformation result of the wideband pulse signal is
H1Extensional vibration is made at the exciting end of (ω), vibration excitor, using the extensional vibration speed signal at laser vibration measurer measurement exciting end, obtains
Fourier transformation result to extensional vibration speed signal is H2(ω)；The impulse response function for obtaining measuring system is H (ω)
=H2(ω)/H1(ω)；
Step 2: according to the impulse response function H (ω) for the measuring system that step 1 obtains, obtaining that vibration excitor exciting ought be required
The Fourier transformation result for holding pumping signal is H3When (ω), the Fourier transformation result for the signal that signal generator needs to export
For H0(ω)=H3(ω)/H (ω), to H0(ω) carries out inversefouriertransform and obtains time-domain signal S (t)；By obtained time domain
Signal S (t) is sent to vibration excitor by signal generator, can generate the ideal wideband pulse signal of waveform at vibration excitor exciting end
For subsequent measurement；
Step 3: sample will be measured and be processed as the club shaped structure that cross section is 5mm × 5mm rectangle, length 150mm；Measurement
Sample one end is free, and the other end sticks in the exciting end of vibration excitor vertically；Signal generator sends time-domain signal S (t) to sharp
Shake device, measures the extensional vibration speed signal of sample fixing end and sample free end respectively；Obtain sample fixing end extensional vibration
The Fourier transformation result of speed signal is VgThe Fourier transformation result of (ω), sample free end extensional vibration speed signal is
Vz(ω)；
Step 4: the Fourier transformation result for obtaining direct wave at sample fixing end is Vg(ω), sample free end are through
The Fourier transformation result of wave is VT(ω):
Since direct wave is constantly decayed in the sample, select amplitude in above-mentioned calculated result straight less than sample fixing end
Up to the Fourier transformation result V of wave amplitude solved as sample free end direct waveT(ω)；
Step 5: at the sample fixing end obtained according to step 4 and the Fourier transformation knot of sample free end direct wave
The longitudinal wave velocity c (ω) and attenuation coefficient α (ω) of rod-like samples is calculated in fruit are as follows:
Wherein l is rod-like samples length, and ω is frequency,Indicate the phase of direct wave at sample fixing end；Indicate sample free end direct wave phase, unwrap be matlab software in phase unwrapping around function, to
Eliminate bigger phase hit；
Step 6: according to the longitudinal wave velocity c (ω) and attenuation coefficient α (ω) of the rod-like samples that step 5 obtains, calculating
To the storage modulus E ' and fissipation factor tan (δ) of material:
Wherein ρ is density of material, and δ indicates the phase of multiple Young's modulus.
In this example, the broadband Butterworth short pulse is generated on vibration excitor as pumping signal, then according to survey
Amount principle is measured, and is compared with viscoelastic instrument test result and traditional wave velocity method test result, measurement result
As shown in Fig. 2, for the storage modulus and fissipation factor of the rubber material measured in example, it can be seen that this method measurement gained
As a result it coincide preferably with viscoelastic instrument measurement result, demonstrates the validity of this method；Compared to traditional wave velocity method, this method is low
Frequency measures more accurate, that is, has widened viscoelastic material and answered Young's modulus low-frequency range measured directly.
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective
In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.
Claims (1)
1. a kind of viscoelastic material extracted based on direct wave answers Young's modulus measurement method, it is characterised in that: including following step
It is rapid:
Step 1: the impulse response function H (ω) of measuring system is obtained by following procedure:
Signal generator sends wideband pulse signal to vibration excitor, and the Fourier transformation result of the wideband pulse signal is H1
Extensional vibration is made at (ω), the exciting end of vibration excitor, measures the extensional vibration signal at exciting end, obtains in Fu of extensional vibration signal
Leaf transformation result is H2(ω)；The impulse response function for obtaining measuring system is H (ω)=H2(ω)/H1(ω)；
Step 2: according to the impulse response function H (ω) for the measuring system that step 1 obtains, believing when requiring vibration excitor exciting end to motivate
Number Fourier transformation result be H3When (ω), the Fourier transformation result for the signal that signal generator needs to export is H0(ω)
=H3(ω)/H (ω), to H0(ω) carries out inversefouriertransform and obtains time-domain signal S (t)；
Step 3: sample will be measured and be processed as the club shaped structure that cross section is rectangle；It is free to measure sample one end, the other end is vertical
Stick in the exciting end of vibration excitor；Time-domain signal S (t) is sent vibration excitor by signal generator, measures sample fixing end respectively
With the extensional vibration signal of sample free end；The Fourier transformation result for obtaining sample fixing end extensional vibration signal is Vg
(ω), the Fourier transformation result of sample free end extensional vibration signal are Vz(ω)；
Step 4: the Fourier transformation result for obtaining direct wave at sample fixing end is Vg(ω), sample free end direct wave
Fourier transformation result is VT(ω):
Amplitude in above-mentioned calculated result is selected to be less than the solution of the through wave amplitude of sample fixing end as sample free end direct wave
Fourier transformation result VT(ω)；
Step 5: at the sample fixing end obtained according to step 4 and the Fourier transformation of sample free end direct wave as a result,
The longitudinal wave velocity c (ω) and attenuation coefficient α (ω) of rod-like samples is calculated are as follows:
Wherein l is rod-like samples length, and ω is frequency,Indicate the phase of direct wave at sample fixing end；It indicates
The phase of sample free end direct wave, unwrap are phase unwrapping around function；
Step 6: according to the longitudinal wave velocity c (ω) and attenuation coefficient α (ω) of the rod-like samples that step 5 obtains, material is calculated
The storage modulus E ' and fissipation factor tan (δ) of material:
Wherein ρ is density of material, and δ indicates the phase of multiple Young's modulus.
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Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102184332A (en) * | 2011-05-17 | 2011-09-14 | 中国船舶重工集团公司第七二五研究所 | Method for expanding dynamic mechanical test data of viscous-elastic material out of test frequency |
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Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102184332A (en) * | 2011-05-17 | 2011-09-14 | 中国船舶重工集团公司第七二五研究所 | Method for expanding dynamic mechanical test data of viscous-elastic material out of test frequency |
Non-Patent Citations (4)
| Title |
|---|
| Measurement of characteristic impedance and wave number of porous material using;Liang Sun, etc.;《Journal of the Acoustical Society of America》;20091231;全文 |
| Using boundary conditions for estimation of complex modulus from flexural wave experiments;K. Mahata, etc.;《IEEE Transactions on Control Systems Technology》;20051130;全文 |
| 基于共振法的黏弹性细棒力学参数宽频测试;侯宏等;《振动与冲击》;20150930;全文 |
| 强迫振动方法确定粘弹性细棒的复杨氏模量;贺西平等;《声学学报》;20120331;全文 |
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