CN106644683B - The determination method of circular membrane amount of deflection under maximum defluxion constrained state - Google Patents
The determination method of circular membrane amount of deflection under maximum defluxion constrained state Download PDFInfo
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- CN106644683B CN106644683B CN201710032534.6A CN201710032534A CN106644683B CN 106644683 B CN106644683 B CN 106644683B CN 201710032534 A CN201710032534 A CN 201710032534A CN 106644683 B CN106644683 B CN 106644683B
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- circular membrane
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- smooth plates
- maximum defluxion
- deformation
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- 239000012528 membrane Substances 0.000 title claims abstract description 31
- 238000000034 method Methods 0.000 title claims abstract description 9
- 230000002093 peripheral effect Effects 0.000 description 2
Classifications
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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
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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
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
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- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Chemical & Material Sciences (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The determination method of circular membrane amount of deflection under maximum defluxion constrained state: to a thickness of h, radius is a, Young's modulus of elasticity is E, Poisson's ratio is that the circular membrane that the periphery of ν fixes to clamp is laterally applied to a uniform load q, deformed film is set to be in contact with a smooth plates, and make smooth plates parallel with the film before deformation, and keep distance H between the two constant, to limit the maximum defluxion of circular membrane after deformation, based on the standing balance analysis to this On Axisymmetric Deformation of A, utilize the measured value of film and the radius b of smooth plates contact area, it then can determine that the Membrane deflection w (r) of each point in the b < r < a of region after the circular membrane contacts smooth plates.
Description
Technical field
The circular membrane fixed to clamp the present invention relates to uniform load following peripheral film under maximum defluxion constrained state
The determination method of amount of deflection.
Background technique
Circular membrane structure has a wide range of applications in fields such as machinery, electronics, bioengineering.Capacitance pressure transducer,
Development in, needing to allow circular membrane arrangement works, noncontact mode: film is not generated with smooth electrodes plate in both modes
Contact；Contact mode: film is contacted with smooth electrodes plate.Under contact mode, periphery fixing clamp (under uniform load) under pressure
The maximum defluxion of tight circular membrane is limited by the smooth electrodes plate parallel with the film before deformation always.And from text
It offers and looks into new result and see, maximum defluxion is limited the axial symmetry of circular membrane that rear perimeter edge fixes to clamp under Uniform Loads and becomes
Shape problem, there are no resolved solutions, thus influence the development work of capacitance pressure transducer,.
Summary of the invention
Analytical Solution of the present invention maximum defluxion is limited circular membrane that rear perimeter edge fixes to clamp under the Uniform Loads
On Axisymmetric Deformation of A, and give circular membrane that uniform load following peripheral fixes to clamp on this basis in maximum defluxion
The determination method of Membrane deflection under constrained state.
The determination method of circular membrane amount of deflection under maximum defluxion constrained state: to a thickness of h, radius a, Young elasticity
The circular membrane that the periphery that modulus is E, Poisson's ratio is ν fixes to clamp is laterally applied to a uniform load q, makes deformed film
It is in contact with a smooth plates, and makes smooth plates parallel with the film before deformation, and before holding smooth plates and deformation
The distance between film H it is constant, so that the maximum defluxion of circular membrane after deformation is limited, then based on to this axial symmetry
The standing balance of problem on deformation is analyzed, which contacts the Membrane deflection w of each point in the b < r < a of region after smooth plates
(r) the parsing relationship with the radius b of contact area can be expressed as
Wherein,
β=(a+b)/(2a),
α=(a2+2ab-3b2)/(4a2), c0And c1Value by equation
With
It determines, wherein
And d0Value by equation
It determines, all parameters all use the International System of Units.
As long as in this way, measuring the value of the radius b of circular membrane and smooth plates contact area, so that it may determine the circle
After film contacts smooth plates in the b < r < a of region each point Membrane deflection w (r).
Detailed description of the invention
Fig. 1 is that the circular membrane that the restricted periphery of maximum defluxion fixes to clamp loads organigram, wherein 1- becomes
Circular membrane after shape, 2- smooth plates, 3- clamping device, the circular membrane before 4- deformation, and a indicates circular membrane
Radius, b indicate that the radius of film and smooth plates contact area, r indicate that radial coordinate, w (r) indicate the lateral coordinates at point r,
Q indicates lateral uniform load, and H indicates the distance between circular membrane and smooth plates.
Specific embodiment
Technical solution of the present invention is described in further detail below with reference to Fig. 1:
One uniform load q is laterally applied to the round rubber film that periphery fixes to clamp, makes deformed film and one
A smooth plates are in contact, and allow smooth plates with deformation before film it is parallel, and keep smooth plates with deform before it is thin
The distance between film H is constant, to limit the maximum defluxion of round rubber film after deformation, wherein smooth plates and deformation
The distance between preceding film H=13mm, thickness h=1mm, the radius a=50mm, Young's modulus of lasticity E of round rubber film
=7.84MPa, Poisson's ratio ν=0.47.Measure the radius b=25mm of film Yu smooth plates contact area.Using institute of the present invention
The method provided, then α=(a2+2ab-3b2)/(4a2)=0.3125, β=(a+b)/(2a)=0.75, passes through equation
With
That is, equation
With
Wherein,
Available c0=0.2907060055, c1=-0.03622260533.Then, by equation
That is, equation
Wherein,
d1=-0.7166461285,
d2=-1.286834462,
d3=0.1048118431,
d4=-0.7783728781,
d5=0.07988664578,
d6=-0.5435878967,
d7=-0.1413928502,
Available d0=0.2610548475.Finally, by formula
That is, formula
It is then available, when the radius b of deformed film and smooth plates contact area reaches 25mm, in region
The Membrane deflection (mm) of each point in 25mm < r < 50mm:
Claims (1)
1. the determination method of circular membrane amount of deflection under maximum defluxion constrained state, it is characterised in that: be to a thickness of h, radius
A, the circular membrane that the periphery that Young's modulus of elasticity is E, Poisson's ratio is ν fixes to clamp is laterally applied to a uniform load q, makes to become
Film after shape is in contact with a smooth plates, and makes smooth plates parallel with the film before deformation, and keeps smooth flat
Plate and the distance between the film H before deformation are constant, to limit the maximum defluxion of circular membrane after deformation, measure film with
The value of the radius b of smooth plates contact area, the circular membrane contact smooth plates after in the b < r < a of region each point film
Amount of deflection w (r) determines by following formula,
Wherein,
β=(a+b)/(2a),
α=(a2+2ab-3b2)/(4a2), c0And c1Value by equation
With
It determines, wherein
And d0Value by equation
It determines, all parameters all use the International System of Units.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201710032534.6A CN106644683B (en) | 2017-01-16 | 2017-01-16 | The determination method of circular membrane amount of deflection under maximum defluxion constrained state |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710032534.6A CN106644683B (en) | 2017-01-16 | 2017-01-16 | The determination method of circular membrane amount of deflection under maximum defluxion constrained state |
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| CN106644683A CN106644683A (en) | 2017-05-10 |
| CN106644683B true CN106644683B (en) | 2019-01-15 |
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| CN201710032534.6A Expired - Fee Related CN106644683B (en) | 2017-01-16 | 2017-01-16 | The determination method of circular membrane amount of deflection under maximum defluxion constrained state |
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| CN110231215B (en) * | 2019-06-05 | 2021-06-08 | 重庆大学 | Method for determining maximum deflection of prestressed circular film with deflection limited by elasticity |
Citations (6)
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|---|---|---|---|---|
| CN2613756Y (en) * | 2003-05-14 | 2004-04-28 | 西安交通大学 | Bubbling instrument for testing film mechanics |
| CN101672750A (en) * | 2009-09-27 | 2010-03-17 | 重庆大学 | Geometric measurement method of Poisson's ratio and Young's elastic modulus of thin film material |
| CN103837400A (en) * | 2014-03-24 | 2014-06-04 | 重庆大学 | Method for determining thin film deflection value of periphery-clamped circular thin film under concentrated force |
| CN103968801A (en) * | 2014-05-30 | 2014-08-06 | 重庆大学 | Method for determining maximum deflection value of pre-stressed circular thin film under uniformly distributed load |
| CN104020036A (en) * | 2014-06-19 | 2014-09-03 | 重庆大学 | Method for determining maximal deflection of annular prestress film under transverse centralized load |
| CN104792618A (en) * | 2015-04-22 | 2015-07-22 | 重庆大学 | Method for determining maximum deflection of large-deflection-angle circular membrane under uniformly distributed load |
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2017
- 2017-01-16 CN CN201710032534.6A patent/CN106644683B/en not_active Expired - Fee Related
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN2613756Y (en) * | 2003-05-14 | 2004-04-28 | 西安交通大学 | Bubbling instrument for testing film mechanics |
| CN101672750A (en) * | 2009-09-27 | 2010-03-17 | 重庆大学 | Geometric measurement method of Poisson's ratio and Young's elastic modulus of thin film material |
| CN103837400A (en) * | 2014-03-24 | 2014-06-04 | 重庆大学 | Method for determining thin film deflection value of periphery-clamped circular thin film under concentrated force |
| CN103968801A (en) * | 2014-05-30 | 2014-08-06 | 重庆大学 | Method for determining maximum deflection value of pre-stressed circular thin film under uniformly distributed load |
| CN104020036A (en) * | 2014-06-19 | 2014-09-03 | 重庆大学 | Method for determining maximal deflection of annular prestress film under transverse centralized load |
| CN104792618A (en) * | 2015-04-22 | 2015-07-22 | 重庆大学 | Method for determining maximum deflection of large-deflection-angle circular membrane under uniformly distributed load |
Non-Patent Citations (1)
| Title |
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| 受预张力薄膜的轴对称大挠度问题;吴建梁;《中国优秀硕士学位论文全文数据库 基础科学辑》;20091215(第12期);第A005-78页 |
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