CN105486933B - Device and method by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient - Google Patents
Device and method by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient Download PDFInfo
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- CN105486933B CN105486933B CN201511016534.4A CN201511016534A CN105486933B CN 105486933 B CN105486933 B CN 105486933B CN 201511016534 A CN201511016534 A CN 201511016534A CN 105486933 B CN105486933 B CN 105486933B
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- G—PHYSICS
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
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Abstract
Device and method by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient, the device includes the flexure electric material of plane mosquito-repellent incense shape, electrode positioned at the flexure inside and outside cambered surface of electric material, the reflective membrane positioned at flexure electric material end respectively, the fix bar fixed positioned at mosquito-repellent incense formula flexure electric material center with bending electric material；Signal source output control signal is simultaneously sent into high voltage power supply, electrode is electrically connected with high voltage power supply, and high voltage power supply exports high-tension electricity to electrode, and material is due to flexoelectric effect after energization, deformation is produced, the mosquito-repellent incense formula structure of material is exaggerated the amplitude of deformation and produces displacement output in flexure electric material end；Laser displacement gauge projects measurement light source and the reflective membrane positioned at flexure electric material end is staggered relatively, can measure deformation quantity during material deformation, bond material structure, power electrical parameter and deformation quantity, can calculate the inverse flexoelectric coefficient for bending electric material.
Description
Technical field
The present invention relates to the stress-electric coupling technical field in material science, and in particular to passes through mosquito-repellent incense formula displacement equations structure
The device and method of the inverse flexoelectric coefficient of measurement.
Background technology
Flexoelectric effect be a kind of stress-electric coupling characteristic for being widely present in all dielectric materials, in particular to due to strain
Gradient produces electric polarization or because electric-force gradient produces the behavior of material deformation.As the emerging of intelligence structure and intellectual material
Point is studied, flexoelectric effect has extensive potential using value in every field such as Aero-Space, military science, bio-pharmaceuticals.
The research of inverse flexoelectric effect also rests essentially within theory stage at present, studies one of main contents of inverse flexoelectric effect and is exactly
The research of inverse flexoelectric coefficient, and due to inverse flexoelectric coefficient measurement due to its output displacement it is small, uniform electric-force gradient is difficult
The presence of the problems such as to apply, it is always the emphasis and difficult point of research.
Flexure electricity is present in all dielectrics, and its principle has just been suggested early in the sixties in last century and in certain limit
Great development is inside obtained, the simplification descriptive equation of the material electrodes containing piezo-electric effect is：
Wherein Pi,eijk,σjk,εjk,μijkl,xlRespectively degree of polarization, piezoelectric constant, stress, strain, flexoelectric coefficient
And gradient direction, equation the right Section 1 is piezo-electric effect caused by stress, and Section 2 is the gradient caused by strain gradient
The flexoelectric effect in direction, due to piezo-electric effect being not present in centrosymmetrical crystal, therefore only Section 2 is present, i.e.,
And for inverse flexure electricity, then have
Wherein Tij,fijklAnd EjkIt is the electric field of equivalent stress, inverse flexoelectric coefficient and application respectively.
It can be seen from above-mentioned formula in the case where the conditions such as material, test specimen are certain, molecular symmetry crystal etc. effect
Power is directly proportional to electric-force gradient.Therefore, present invention employs by applying electric field, electric-force gradient is produced so as to produce equivalent stress
Cause material that the method for micro-strain occurs, and micro-displacement is amplified by plane mosquito-repellent incense shape structure, then by bending electric material
The inverse flexoelectric coefficient of total distortion measurement material of material, improve the feasibility and measurement accuracy of experiment.
The content of the invention
In order to fill the blank in related experiment field, it is an object of the invention to provide pass through mosquito-repellent incense formula displacement equations structure
The device and method of the inverse flexoelectric coefficient of measurement, i.e., occur shape by bending electric material to plane mosquito-repellent incense shape in the case of energization
Become, and the reflective membrane relative displacement change of flexure electric material end is measured by laser displacement gauge, with reference to the knot of flexure electric material
The multiplication factor of structure parameter, the output signal of power electrical parameter and signal source and high voltage power supply, the inverse of material can be calculated and scratch
Bent electrostrictive coefficient；The present invention has lower equipment precision, environment vibration isolation requirement and higher measurement essence by structure displacement enlargement
Degree.
To achieve the above objectives, the present invention adopts the following technical scheme that：
Device by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient, include the flexure of plane mosquito-repellent incense shape structure
Electric material 1, positioned at the flexure extrados of electric material 1 and the electrode 2 of intrados, the reflective membrane 4 positioned at flexure electric material 1 end, Gu
Fixed pole 3 is mutually fixed with the centre for bending electric material 1 and is fixed with the external world, and electrode 2 electrically connects with the output end of high voltage power supply 6,
The input of high voltage power supply 6 electrically connects with the output end of signal source 5；Also include laser displacement gauge 7, the survey that laser displacement gauge 7 projects
Amount light source is relative with reflective membrane 4 to be changed with measuring the relative displacement of reflective membrane 4.
The structure of the flexure electric material 1 forms plane mosquito-repellent incense shape structure to ensure that generation is uniform for some is circular
Electric-force gradient, deformation is accumulated, be easy to measure；Its width is 0.1-10mm, thickness 0.1-10mm, a diameter of 1-
100mm, its structural parameters match with material parameter, to ensure that flexure electric material 1 when making alive acts on, occurs sufficiently large
Deformation.
The electrode 2 has the rigidity far below flexure electric material 1 and possesses good electric conductivity.
The measurement accuracy of the laser displacement gauge 7 disclosure satisfy that the deformation of flexure electric material 1.
Measuring method by mosquito-repellent incense formula displacement equations structure measurement against the device of flexoelectric coefficient described above：It will scratch
Bent electric material 1 is fixed by the fix bar 3 consolidated with flexure electric material 1 center, and electric signal is delivered to high voltage power supply 6 by signal source 5,
Output is to electrode 2 after high voltage power supply 6 amplifies the electric signal power, and flexure electric material 1 is produced electric field in the radial direction of material
Gradient, due to the inverse flexoelectric effect of material, small ring deformation occurs for flexure electric material 1, bends the plane mosquito of electric material 1
Fragrant shape structure can add up the miniature deformation of multiple annulus, and its cumulative ring deformation shows flexure electric material 1 end
On reflective membrane 4, and obtained by laser displacement gauge 7 measurement relative with reflective membrane 4；Output signal, the high pressure in binding signal source 5
The power amplification multiple of power supply 6 and the structural parameters and power electrical parameter for bending electric material 1, just can be calculated the inverse of material
Flexoelectric coefficient.
Piezo-electric effect is not present in assymetric crystal centered on flexure electric material (1), and material electrodes abbreviation list is described as：
Wherein Pi,εjk,μijkl,xlRespectively degree of polarization, strain, flexoelectric coefficient and gradient direction；
And for the inverse flexure electricity shown in the present invention, then have
Wherein T(ij,n),fijklAnd EjkBe respectively equivalent stress on n-th section of circular arc, material inverse flexoelectric coefficient and apply
The electric field added；
Wherein S(ij, n)It is the modulus of elasticity of equivalent strain and material respectively with E；
Displacement caused by flexure electric material (1) is：
Wherein Rn, N be respectively bend electric material (1) mean camber line radius and semicircle loop-drive sum；
There is certain relation in inverse flexoelectric coefficient, electric material is bent by measuring with displacement caused by flexure electric material (1)
Expect displacement caused by (1), inverse flexoelectric coefficient can be calculated.
Compared to the prior art the present invention, has the following advantages that：
1) structure is passed through compared to the inverse flexure electrical measurement means by laser measurement relative displacement reported, the present invention
Displacement enlargement, there is lower equipment precision, environment vibration isolation requirement and higher measurement accuracy.
2) test specimen is measured compared to the laser type reported, material shape involved in the present invention can produce more uniform
Electric-force gradient, so as to obtain more accurate theoretical description and to power electrical phenomena more accurately explain and description.
3) ring-type flexure electric material can be made compared to single ring-type flexure electric material displacement measurement design, the present invention
Miniature deformation is added up, and reduces measurement accuracy, improves the operability of experiment.
In a word, the present invention can realize the device and method by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient
The inverse flexoelectric coefficient of material is obtained, compensate for the blank and deficiency of prior art.
Brief description of the drawings
Accompanying drawing is schematic structural view of the invention.
Embodiment
Below in conjunction with drawings and the specific embodiments, the present invention is described in further detail.
As shown in drawings, device and method of the present invention by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient,
Fixed by the fix bar 3 consolidated with flexure electric material 1 center including electric material 1 will be bent, applied in the cambered surface of flexure electric material 1
Pole 2 is powered up, and electrically connects electrode 2 and the output end of high voltage power supply 6, the input of high voltage power supply 6 and the output end of signal source 5
Electrical connection, signal source 5 export electric signal and deliver to electrode 2 after amplifying by high voltage power supply 6, flexure electric material 1 is produced in radial direction
Raw electric-force gradient, due to inverse flexoelectric effect, ring deformation occurs for material, accumulates ring deformation by plane mosquito-repellent incense shape structure
And show total deformation of the accumulation, the measurement light source that laser displacement gauge 7 exports in the reflective membrane that flexure electric material 1 bottom is fixed
Relative with reflective membrane 4, when relative position change occurs for reflective membrane 4, laser displacement gauge 7 just can measure the deformation quantity, with reference to material
The structural parameters of material, power electrical parameter, the power amplification multiple of the signal parameter of signal source 5 and high voltage power supply, can be calculated
Bend the inverse flexoelectric coefficient of electric material 1.
The computational methods of the inverse flexoelectric coefficient of the flexure electric material 1 are as follows：
Piezo-electric effect is not present in assymetric crystal centered on flexure electric material (1), and material electrodes abbreviation list is described as：
Wherein Pi,εjk,μijkl,xlRespectively degree of polarization, strain, flexoelectric coefficient and gradient direction；
And for inverse flexure electricity, then have
Wherein T(ij,n),fijklAnd EjkBe respectively equivalent stress on n-th section of circular arc, material inverse flexoelectric coefficient and apply
The electric field added；
Wherein Tij,SijklIt is the modulus of elasticity of equivalent stress, equivalent strain and material respectively with E.
Displacement caused by flexure electric material (1) is：
Wherein R, N are respectively the mean camber line radius and semicircle loop-drive sum for bending electric material (1).
There is certain relation in inverse flexoelectric coefficient, electric material is bent by measuring with displacement caused by flexure electric material (1)
Expect displacement caused by (1), inverse flexoelectric coefficient can be calculated.
As the preferred embodiment of the present invention, the flexure electric material 1 has higher dielectric constant, positive flexure electricity system
Number and breakdown voltage.
As the preferred embodiment of the present invention, the electrode 2 has good electric conductivity and relatively low attachment rigidity.
Claims (5)
1. by mosquito-repellent incense formula displacement equations structure measurement against the device of flexoelectric coefficient, it is characterised in that：Including plane mosquito-repellent incense shape
The flexure electric material (1) of structure, positioned at flexure electric material (1) extrados and the electrode (2) of intrados, positioned at flexure electric material
(1) centre of the reflective membrane (4) of end, fix bar (3) and flexure electric material (1) is mutually fixed and fixed with the external world, electrode
(2) electrically connected with high voltage power supply (6) output end, high voltage power supply (6) input electrically connects with the output end of signal source (5)；Also wrap
Include laser displacement gauge (7), the measurement light source that laser displacement gauge (7) projects and reflective membrane (4) are with respect to measure the phase of reflective membrane (4)
To change in displacement.
2. the device according to claim 1 by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient, its feature
It is：The structure of the flexure electric material (1) forms plane mosquito-repellent incense shape structure to ensure that generation is uniform for some is circular
Electric-force gradient, deformation is accumulated, be easy to measure；Its width is 0.1-10mm, thickness 0.1-10mm, a diameter of 1-
100mm, its structural parameters match with material parameter, to ensure that flexure electric material (1) when making alive acts on, occurs sufficiently large
Deformation.
3. the device according to claim 1 by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient, its feature
It is：The electrode (2) has the rigidity far below flexure electric material (1) and possesses good electric conductivity.
4. the device according to claim 1 by mosquito-repellent incense formula displacement equations structure measurement against flexoelectric coefficient, its feature
It is：The measurement accuracy of the laser displacement gauge (7) disclosure satisfy that the deformation of flexure electric material (1).
5. the measuring method by mosquito-repellent incense formula displacement equations structure measurement against the device of flexoelectric coefficient described in claim 1,
It is characterized in that：It is fixed by the fix bar (3) consolidated with flexure electric material (1) center that electric material (1) will be bent, signal source
(5) electric signal is delivered into high voltage power supply (6), output is to electrode (2) after high voltage power supply (6) amplifies the electric signal power, and makes
The radial direction that electric material (1) is bent in material produces electric-force gradient, due to the inverse flexoelectric effect of material, flexure electric material (1) hair
Raw small ring deformation, the plane mosquito-repellent incense shape structure of flexure electric material (1) can add up the miniature deformation of multiple annulus,
Its cumulative ring deformation is shown on the reflective membrane (4) of flexure electric material (1) end, and is swashed by relative with reflective membrane (4)
Light displacement meter (7) measurement obtains；The output signal in binding signal source (5), the power amplification multiple of high voltage power supply (6) and flexure
The structural parameters and power electrical parameter of electric material (1), the inverse flexoelectric coefficient of flexure electric material (1) is calculated；
The method of the inverse flexoelectric coefficient for calculating flexure electric material (1) is as follows：
It is displaced through to add up caused by flexure electric material (1) and has the function that amplification；
Piezo-electric effect is not present in assymetric crystal centered on flexure electric material (1), and material electrodes abbreviation list is described as：
<mrow>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>&mu;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mi>k</mi>
<mi>l</mi>
</mrow>
</msub>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>&epsiv;</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>x</mi>
<mi>l</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein Pi,εjk,μijkl,xlRespectively degree of polarization, strain, flexoelectric coefficient and gradient direction；
And for inverse flexure electricity, then have
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>f</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mi>k</mi>
<mi>l</mi>
</mrow>
</msub>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>E</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>x</mi>
<mi>l</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein T(ij,n),fijklAnd EjkIt is equivalent stress on n-th section of circular arc, the inverse flexoelectric coefficient of material and application respectively
Electric field；
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>T</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</msub>
<mi>E</mi>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein S(ij, n)It is the modulus of elasticity of equivalent strain and material respectively with E；
Displacement caused by flexure electric material (1) is：
<mrow>
<mi>&Delta;</mi>
<mi>d</mi>
<mo>=</mo>
<mn>2</mn>
<munderover>
<mo>&Sigma;</mo>
<mn>1</mn>
<mi>N</mi>
</munderover>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mi>&pi;</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msubsup>
<msub>
<mi>R</mi>
<mi>n</mi>
</msub>
<msub>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</msub>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mi>&theta;</mi>
<mi>d</mi>
<mi>&theta;</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein Rn, N be respectively bend electric material (1) mean camber line radius and semicircle loop-drive sum；θ bends electric material (1) to form
The radian of annulus；
There is certain relation in inverse flexoelectric coefficient, with displacement caused by flexure electric material (1) by measuring flexure electric material (1)
Caused displacement, inverse flexoelectric coefficient can be calculated.
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