CN106769394B - The determination method of axis load lower prestress circular membrane maximum defluxion - Google Patents
The determination method of axis load lower prestress circular membrane maximum defluxion Download PDFInfo
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- CN106769394B CN106769394B CN201710032393.8A CN201710032393A CN106769394B CN 106769394 B CN106769394 B CN 106769394B CN 201710032393 A CN201710032393 A CN 201710032393A CN 106769394 B CN106769394 B CN 106769394B
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- circular membrane
- prestressing force
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- 239000012528 membrane Substances 0.000 title claims abstract description 26
- 238000000034 method Methods 0.000 title claims abstract description 9
- 239000010408 film Substances 0.000 description 7
- 230000002093 peripheral effect Effects 0.000 description 4
- 238000005259 measurement Methods 0.000 description 2
- 235000013399 edible fruits Nutrition 0.000 description 1
- 238000011835 investigation Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000000465 moulding Methods 0.000 description 1
- 239000010409 thin film Substances 0.000 description 1
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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- 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 invention discloses the determination methods of axis load lower prestress circular membrane maximum defluxion: at the prestressing force circular membrane center that periphery fixes to clamp, one transverse load F is applied to prestressing force circular membrane by a smooth flat cylindrical body loading axis, wherein, the Young's modulus of elasticity of prestressing force circular membrane be E, Poisson's ratio ν, prestressing force σ0, with a thickness of h, radius a, the radius of smooth flat cylindrical body loading axis is b, standing balance analysis based on this On Axisymmetric Deformation of A then can determine that maximum defluxion w of the prestressing force circular membrane under transverse load F effect using the measured value of transverse load Fm。
Description
Technical field
The present invention relates to the determination methods for the prestressing force circular membrane maximum defluxion that axis load following peripheral fixes to clamp.
Background technique
Circular membrane structure has a wide range of applications in fields such as machinery, electronics, bioengineering.In fact, due to temperature,
The influence of the factors such as the variation of humidity and manufacture craft makes in circular membrane structure after molding, in most cases
Can be there is certain prestressing force in film, prestressed presence will change the mechanical behavior of circular membrane structure.In general, adopting
Apply load at circular membrane center with loading axis, load, measurement work can be made more convenient, however from the knot of document Investigation
Fruit sees that axis loads the analytic solutions of the On Axisymmetric Deformation of A for the prestressing force circular membrane that following peripheral fixes to clamp, there is presently no
It is presented, thus influences the work for determining prestressing force circular membrane maximum defluxion based on load measurement value.
Summary of the invention
This invention address that the analysis research of film problem, prestressing force that Analytical Solution axis load following peripheral fixes to clamp
The On Axisymmetric Deformation of A of circular membrane, and the analytic solutions of the problem are obtained, and then give axis load following peripheral fixing clamp
The determination method of the maximum defluxion of tight prestressing force circular membrane.
The determination method of axis load lower prestress circular membrane maximum defluxion: thin in the prestressing force circle that periphery fixes to clamp
At center membrane, a transverse load F is applied to prestressing force circular membrane by a smooth flat cylindrical body loading axis,
In, the Young's modulus of elasticity of prestressing force circular membrane is E, Poisson's ratio ν, prestressing force σ0, with a thickness of h, radius a, it is smooth
The radius of flat cylindrical body loading axis be b, the standing balance analysis based on this On Axisymmetric Deformation of A, the prestressing force is round
The maximum defluxion w of filmmIt can be expressed as with the parsing relationship of transverse load F
Wherein, π is pi,
c0And c1Value by equation
With
It determines, wherein
And d0Value by formula
It determines, all parameters all use the International System of Units.
As long as in this way, measuring the value of transverse load F, so that it may determine the prestressing force circular membrane in transverse load F
Maximum defluxion w under effectm。
Detailed description of the invention
Fig. 1 is that the prestressing force circular membrane that periphery fixes to clamp loads organigram, wherein 1- prestressing force circle is thin
Film, 2- smooth flat cylindrical body loading axis, 3- clamping device, and a indicates that the inside radius of clamping device and prestressing force are round
The radius of film, b indicate that the radius of smooth flat cylindrical body loading axis, F indicate that loading axis applies prestressing force circular membrane
The transverse load added, wmIndicate the maximum defluxion of prestressing force circular membrane.
Specific embodiment
Technical solution of the present invention is described in further detail below with reference to Fig. 1:
At the prestressing force round rubber thin film center that periphery fixes to clamp, loaded by a smooth flat cylindrical body
Axis applies a transverse load F to prestressing force round rubber film, wherein the Young's modulus of elasticity of prestressing force round rubber film
E=7.84MPa, Poisson's ratio ν=0.47, prestressing force σ0=0.1MPa, thickness h=1mm, radius a=50mm, smooth flat circle
The radius b=5mm of cylinder loading axis.Measure transverse load F=10N.Using method given by the present invention, pass through equation
With
Wherein,
Then available c0=1.250852495, c1=2.043648304.Then, then by formula
Wherein,
Available d0=0.2789877714.Finally, by formula
It is then available, as transverse load F=10N, the maximum defluxion w of the prestressing force round rubber filmm=
9.154mm。
Claims (1)
1. the determination method of axis load lower prestress circular membrane maximum defluxion, it is characterised in that: fixed to clamp on periphery pre-
A transverse direction is applied to prestressing force circular membrane by a smooth flat cylindrical body loading axis at stress circle thin film center
Load F, wherein the Young's modulus of elasticity of prestressing force circular membrane is E, Poisson's ratio ν, prestressing force σ0, with a thickness of h, radius
Radius for a, smooth flat cylindrical body loading axis is b, measures the value of transverse load F, determines the prestressing force by following formula
Maximum defluxion w of the circular membrane under transverse load F effectm:
Wherein, π is pi,
c0And c1Value by equation
With
It determines, wherein
And d0Value by formula
It determines, all parameters all use the International System of Units.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710032393.8A CN106769394B (en) | 2017-01-16 | 2017-01-16 | The determination method of axis load lower prestress circular membrane maximum defluxion |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710032393.8A CN106769394B (en) | 2017-01-16 | 2017-01-16 | The determination method of axis load lower prestress circular membrane maximum defluxion |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106769394A CN106769394A (en) | 2017-05-31 |
| CN106769394B true CN106769394B (en) | 2019-03-29 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710032393.8A Expired - Fee Related CN106769394B (en) | 2017-01-16 | 2017-01-16 | The determination method of axis load lower prestress circular membrane maximum defluxion |
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Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111442985A (en) * | 2020-03-25 | 2020-07-24 | 重庆大学 | Method for determining maximum deflection of circular film under transversely uniformly distributed load |
| CN114136775B (en) * | 2021-11-18 | 2023-12-12 | 安徽科技学院 | Performance test device for low-dimensional photoelectric material |
Citations (8)
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|---|---|---|---|---|
| JPS6239743A (en) * | 1985-08-15 | 1987-02-20 | Nec Corp | Bending tester for measuring modulus of longitudinal elasticity of membrane |
| 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 |
| CN105890970A (en) * | 2016-04-26 | 2016-08-24 | 重庆大学 | Method for determining maximum deflection of annular films of central zone rigid plates under uniformly distributed load |
| CN106248474A (en) * | 2016-09-05 | 2016-12-21 | 重庆大学 | The laterally determination method of uniform load lower prestress circular membrane maximum defluxion |
| CN106323735A (en) * | 2016-09-05 | 2017-01-11 | 重庆大学 | Method for determining maximum deflection of pre-stressed annular film with hard core under uniformly distributed load |
-
2017
- 2017-01-16 CN CN201710032393.8A patent/CN106769394B/en not_active Expired - Fee Related
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS6239743A (en) * | 1985-08-15 | 1987-02-20 | Nec Corp | Bending tester for measuring modulus of longitudinal elasticity of membrane |
| 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 |
| CN105890970A (en) * | 2016-04-26 | 2016-08-24 | 重庆大学 | Method for determining maximum deflection of annular films of central zone rigid plates under uniformly distributed load |
| CN106248474A (en) * | 2016-09-05 | 2016-12-21 | 重庆大学 | The laterally determination method of uniform load lower prestress circular membrane maximum defluxion |
| CN106323735A (en) * | 2016-09-05 | 2017-01-11 | 重庆大学 | Method for determining maximum deflection of pre-stressed annular film with hard core under uniformly distributed load |
Non-Patent Citations (2)
| Title |
|---|
| "关于薄膜大挠度方程的极限解及其特性";袁驷;《数值计算与计算机应用》;19960630(第2期);第120-127页 |
| "大挠度储能橡胶圆板的受载挠曲特性分析";段浩 等;《机械强度》;20021231;第24卷(第4期);第531-534页 |
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| CN106769394A (en) | 2017-05-31 |
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