CN106644682B - The determination method of annular membrane elasticity energy under combined load with hard core - Google Patents
The determination method of annular membrane elasticity energy under combined load with hard core Download PDFInfo
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- CN106644682B CN106644682B CN201710030616.7A CN201710030616A CN106644682B CN 106644682 B CN106644682 B CN 106644682B CN 201710030616 A CN201710030616 A CN 201710030616A CN 106644682 B CN106644682 B CN 106644682B
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- 238000000034 method Methods 0.000 title claims abstract description 8
- 239000012528 membrane Substances 0.000 title abstract description 8
- 239000002131 composite material Substances 0.000 claims description 5
- 230000002093 peripheral effect Effects 0.000 claims description 4
- 230000000694 effects Effects 0.000 description 1
- 230000003068 static effect Effects 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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- 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
- G01N2203/026—Specifications of the specimen
- G01N2203/0262—Shape of the specimen
- G01N2203/0274—Tubular or ring-shaped specimens
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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
- G01N2203/026—Specifications of the specimen
- G01N2203/0262—Shape of the specimen
- G01N2203/0278—Thin specimens
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- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Chemical & Material Sciences (AREA)
- Analytical Chemistry (AREA)
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- Manufacture Of Macromolecular Shaped Articles (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The invention discloses the determination methods for the annular membrane elasticity energy that hard core is had under combined load: being laterally applied to a uniform load q to the annular membrane with hard core that the periphery for being ν with a thickness of h, outer radius a, inside radius b, Young's modulus of elasticity E, Poisson's ratio fixes to clamp, wherein the radius of hard core is also b, and apply a lateral concentrfated load F simultaneously at the center of hard core, based on the standing balance analysis to this On Axisymmetric Deformation of A, using the measured value of uniform load q and concentrfated load F, then it can determine that the deformed elasticity of the annular membrane can U.
Description
Technical Field
The invention relates to a method for determining the elastic energy of a ring-shaped film with a hard core and a periphery fixedly clamped under the action of composite load.
Background
The annular film structure has wide application in the fields of machinery, electronics, bioengineering and the like. The peripheral fixed clamped ring-shaped film structure with the hard core can be used for developing a capacitive pressure sensor, wherein the ring-shaped film and the hard core are simultaneously under the action of pressure (under the action of uniformly distributed load). In practice, however, under the action of a small pressure, the dead weight of the hard core element, which is a non-negligible acting load for the annular membrane, changes the mechanical behavior of the annular membrane structure, thus affecting the accuracy of the sensor. If the load effect of the dead weight of the hard core element on the annular membrane is considered, the problem is actually that the annular membrane with the hard core is axially symmetrical and clamped fixedly at the periphery under the action of composite load. From the results of looking up new, the problem is not solved analytically, and therefore the refinement and development of the sensor are influenced.
Disclosure of Invention
The invention solves the problem of axisymmetrical deformation of the annular film with the hard core and the periphery fixedly clamped under the combined load action by analysis, and provides a method for determining the elastic energy of the annular film with the hard core and the periphery fixedly clamped under the combined action of the combined load.
The method for determining the elastic property of the annular film with the hard core under the composite load comprises the following steps: transversely applying a uniform load q to a peripheral fixedly clamped annular film with a hard core and a thickness of h, an outer radius of a, an inner radius of b, a Young's modulus of elasticity of E and a Poisson ratio of v, wherein the radius of the hard core is also b, and simultaneously applying a transverse concentrated load F to the center of the hard core, then based on the static balance analysis of the axisymmetric deformation problem, the analytic relation of the elastic energy U of the annular film to the applied uniform load q and the applied concentrated load F can be expressed as
Wherein, pi is the circumference ratio,
β＝(a+b)/(2a)，
α＝(F-πb2q)/(πa2q)，c1and c2Is given by the equation
And
is determined, and c0Is given by the formula
And (4) determining. Wherein, all parameters adopt international system of units.
Thus, the elastic energy U of the deformed annular film can be determined by measuring the values of the uniform load q and the concentrated load F applied.
Drawings
FIG. 1 is a schematic view of a peripheral fixed clamped rigid-core annular diaphragm loading configuration wherein 1-the annular diaphragm after deformation, 2-the hard core, 3-the clamping means, and a denotes the inner radius of the clamping means and the outer radius of the annular diaphragm, b denotes the radius of the hard core and the inner radius of the annular diaphragm, q denotes a laterally uniform load, F denotes a laterally concentrated load, w denotes a lateral load, andmindicating the maximum deflection of the film.
Detailed Description
The technical solution of the present invention is further described in detail with reference to fig. 1 below:
an evenly distributed load q is transversely applied to an annular rubber film with a hard core, wherein the annular rubber film is fixedly clamped at the periphery of the hard core, the thickness h is 0.5mm, the outer radius a is 20mm, the inner radius b is 5mm, the Young modulus E is 7.84MPa and the Poisson ratio v is 0.47, the radius of the hard core is also 5mm, a transverse concentrated load F is simultaneously applied to the center of the hard core, the measured q is 0.01MPa, and the measured F is 1.178N, and then α is (F-pi b) by adopting the method provided by the invention2q)/(πa2q) ═ 0.03125, β ═ 0.625 (a + b)/(2a), using the equation
And
namely, the equation
And
wherein,
can obtain c1＝-0.729227258，c2-0.645917810. Then, the formula is further calculated
I.e. the formula
To obtain c00.375442416. Finally, the formula
I.e. the formula
It can be obtained that the elastic energy U of the annular rubber film is 30.19N · mm or 30.19 × 10 when the uniform load q is 0.01MPa and the concentrated load F is 1.178N-3J。
Claims (1)
1. The method for determining the elastic energy of the annular film with the hard core under the composite load is characterized by comprising the following steps of: transversely applying an evenly distributed load q to a peripheral fixedly clamped annular film with a hard core and a thickness of h, an outer radius of a, an inner radius of b, a Young's modulus of elasticity of E and a Poisson ratio of v, wherein the radius of the hard core is also b, simultaneously applying a transverse concentrated load F to the center of the hard core, measuring the values of the applied evenly distributed load q and the applied concentrated load F, and determining the elastic energy U of the annular film under the combined action of the evenly distributed load q and the concentrated load F by the following formula,
wherein, pi is the circumference ratio,
β＝(a+b)/(2a)，
α＝(F-πb2q)/(πa2q)，c1and c2Is given by the equation
And
is determined, and c0Is given by the formula
All parameters are determined by adopting an international system of units.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710030616.7A CN106644682B (en) | 2017-01-16 | 2017-01-16 | The determination method of annular membrane elasticity energy under combined load with hard core |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710030616.7A CN106644682B (en) | 2017-01-16 | 2017-01-16 | The determination method of annular membrane elasticity energy under combined load with hard core |
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| Publication Number | Publication Date |
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| CN106644682A CN106644682A (en) | 2017-05-10 |
| CN106644682B true CN106644682B (en) | 2019-04-05 |
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Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113092039B (en) * | 2021-04-16 | 2022-09-27 | 重庆大学 | Method for determining elastic energy of annular film under transversely uniformly distributed load |
| CN113551977A (en) * | 2021-07-30 | 2021-10-26 | 重庆大学 | Method for determining the deflection of a ring-shaped film with a rigid inner edge |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2003320304A (en) * | 2002-04-30 | 2003-11-11 | Toyota Motor Corp | Double-layered coating film |
| CN103822822A (en) * | 2014-03-24 | 2014-05-28 | 重庆大学 | Method for measuring elastic energy of bubbled film in bubbling test on flat-bottom cylinder |
| CN104008311A (en) * | 2014-06-19 | 2014-08-27 | 重庆大学 | Method for determining elastic energy of annular prestressed film under transverse concentrated load condition |
| CN104215509A (en) * | 2014-09-25 | 2014-12-17 | 哈尔滨工业大学 | Testing device and load applying method for measuring deformation of thin film under combined load action |
| CN105675484A (en) * | 2016-04-26 | 2016-06-15 | 重庆大学 | Method for determining elastic energy of circular membrane with rigid slab in center and under uniformly distributed load |
-
2017
- 2017-01-16 CN CN201710030616.7A patent/CN106644682B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2003320304A (en) * | 2002-04-30 | 2003-11-11 | Toyota Motor Corp | Double-layered coating film |
| CN103822822A (en) * | 2014-03-24 | 2014-05-28 | 重庆大学 | Method for measuring elastic energy of bubbled film in bubbling test on flat-bottom cylinder |
| CN104008311A (en) * | 2014-06-19 | 2014-08-27 | 重庆大学 | Method for determining elastic energy of annular prestressed film under transverse concentrated load condition |
| CN104215509A (en) * | 2014-09-25 | 2014-12-17 | 哈尔滨工业大学 | Testing device and load applying method for measuring deformation of thin film under combined load action |
| CN105675484A (en) * | 2016-04-26 | 2016-06-15 | 重庆大学 | Method for determining elastic energy of circular membrane with rigid slab in center and under uniformly distributed load |
Non-Patent Citations (3)
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| 复合载荷下圆薄膜大挠度问题的一般解;蒋成立;《中国优秀硕士学位论文全文数据库 基础科学辑》;20070515;第A005-116页 |
| 薄膜材料杨氏模量测量方法的研究进展;岳义等;《微纳电子技术》;20141015;第659-665页 |
| 非线性载荷作用下圆形薄膜的有限变形分析;张忠凯等;《应用力学学报》;20130430;第147-152页 |
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