CN105117519B - Electrostatic drive step type micro cantilever structure evaluation method and system - Google Patents
Electrostatic drive step type micro cantilever structure evaluation method and system Download PDFInfo
- Publication number
- CN105117519B CN105117519B CN201510451909.3A CN201510451909A CN105117519B CN 105117519 B CN105117519 B CN 105117519B CN 201510451909 A CN201510451909 A CN 201510451909A CN 105117519 B CN105117519 B CN 105117519B
- Authority
- CN
- China
- Prior art keywords
- cantilever
- micro
- stepped
- electrostatic force
- stepped micro
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Abstract
The present invention provides a kind of electrostatic drive step type micro cantilever structure evaluation method and system, structural parameters based on stepped micro-cantilever, calculate stepped micro-cantilever dimensionless width ratio, recycle the trial function of stepped micro-cantilever dimensionless group relational expression and the deformation of electrostatic force downstairs type micro-cantilever, calculate stepped micro-cantilever non-dimensional length ratio, the final optimization length calculated value for obtaining stepped micro-cantilever non-electrostatic force active region, when the length of stepped micro-cantilever non-electrostatic force active region is equal to optimization length calculated value, stepped micro cantilever structure is optimal, show that the corresponding driving voltage of current stepped micro cantilever structure has reached minimum.In whole process, processing procedure is simple, calculation amount is small, using rigorous data processing calculating process, realizes the evaluation to electrostatic drive step type micro cantilever structure.
Description
Technical field
The present invention relates to micro-electromechanical system field, is evaluated more particularly to electrostatic drive step type micro cantilever structure
Method and system.
Background technology
Driving voltage is electrostatic drive micro electro mechanical system (Micro Electro Mechanical System, MEMS) production
One important parameter of product performance improvement, new-product development, decides the performance of MEMS product, reliability and using model
Enclose.Numerous studies show that driving voltage often reduces 5V, and MEMS product service life can increase by 10 times.Low driving voltage not only may be used
To be remarkably reinforced the performance of MEMS product, extend its service life, and the application range of MEMS product can be expanded, be electrostatic
Drive an important directions of MEMS product research and development.
Stepped micro-cantilever is a kind of resulting structure pattern for reducing MEMS product driving voltage, is had been widely used for
Radio frequency microswitch, microsensor, microactrator etc..Compared with common uniform beam, stepped micro-cantilever has more knots
Structure parameter, adds the uncertainty of structure design.Due to multi- scenarios methods such as structure present in MEMS product, electric field, temperature
So that micro-structure shows the non-linear behavior of complexity, the relation of stepped microstructure parameters and driving voltage also becomes different for effect
It is often complicated.
How electrostatic drive step type micro cantilever structure evaluates whether it is optimum structure, to make full use of step type
The advantage of structure, there is no complete scheme at present.
The content of the invention
Based on this, it is necessary to for current electrostatic force step type micro cantilever structure can not rational evaluation its whether be optimal
The problem of structure, there is provided a kind of electrostatic drive step type micro cantilever structure evaluation method and system, are realized to electrostatic drive rank
Ladder type micro cantilever structure rational evaluation.
A kind of electrostatic drive step type micro cantilever structure evaluation method, including step：
The structural parameters of stepped micro-cantilever are obtained, wherein, the structural parameters of stepped micro-cantilever include step type
The gap between electrode, ladder are fixed in micro-cantilever total length, stepped micro-cantilever thickness, stepped micro-cantilever and bottom
Micro- beam length of type micro-cantilever non-electrostatic force active region, stepped micro-cantilever non-electrostatic force active region micro- beam width and
Micro- beam width in electrostatic force area；
According to micro- beam width of stepped micro-cantilever non-electrostatic force active region and micro- beam width in electrostatic force area,
Calculate stepped micro-cantilever dimensionless width ratio；
Deformed according to stepped micro-cantilever dimensionless group relational expression and electrostatic force downstairs type micro-cantilever
Trial function, calculates stepped micro-cantilever non-dimensional length ratio；
According to stepped micro-cantilever total length and stepped micro-cantilever non-dimensional length ratio, calculate stepped micro- outstanding
The optimization length of arm beam non-electrostatic force active region；
When the length of stepped micro-cantilever non-electrostatic force active region is equal to stepped micro-cantilever non-electrostatic force active region
Optimization length when, evaluate stepped micro cantilever structure and be optimal.
A kind of electrostatic drive step type micro cantilever structure evaluation system, including：
Parameter acquisition module, for obtaining the structural parameters of stepped micro-cantilever, wherein, the knot of stepped micro-cantilever
Structure parameter includes stepped micro-cantilever total length, stepped micro-cantilever thickness, stepped micro-cantilever and bottom and fixes electricity
Micro- beam length, the non-electrostatic masterpiece of stepped micro-cantilever in gap, stepped micro-cantilever non-electrostatic force active region between pole
With micro- beam width in area and micro- beam width in electrostatic force area；
Width is than computing module, for the micro- beam width and electrostatic according to stepped micro-cantilever non-electrostatic force active region
Micro- beam width of power active region, calculates stepped micro-cantilever dimensionless width ratio；
Length is than computing module, for according to rank under stepped micro-cantilever dimensionless group relational expression and electrostatic force
The trial function of ladder type micro-cantilever deformation, calculates stepped micro-cantilever non-dimensional length ratio；
Optimization length computing module, for according to stepped micro-cantilever total length and stepped micro-cantilever dimensionless
Length ratio, calculates the optimization length of stepped micro-cantilever non-electrostatic force active region；
Evaluation module, it is non-equal to stepped micro-cantilever for the length when stepped micro-cantilever non-electrostatic force active region
During the optimization length in electrostatic force area, evaluate stepped micro cantilever structure and be optimal.
Electrostatic drive step type micro cantilever structure evaluation method and system of the present invention, the knot based on stepped micro-cantilever
Structure parameter, calculates stepped micro-cantilever dimensionless width ratio, recycle stepped micro-cantilever dimensionless group relational expression and
The trial function of electrostatic force downstairs type micro-cantilever deformation, calculates stepped micro-cantilever non-dimensional length ratio, finally obtains
The optimization length calculated value of stepped micro-cantilever non-electrostatic force active region is obtained, when stepped micro-cantilever non-electrostatic force active region
Micro- beam length when being equal to optimization length calculated value, evaluate stepped micro cantilever structure and be optimal, that is, show current ladder
The corresponding driving voltage of type micro cantilever structure has reached minimum, if unequal, shows current stepped micro cantilever structure
It is not up to optimal, it can also continue to optimize.In whole process, processing procedure is simple, calculation amount is small, using rigorous data processing meter
Calculation process, realizes the evaluation to electrostatic drive step type micro cantilever structure.
Brief description of the drawings
Fig. 1 is that the flow of electrostatic drive step type micro cantilever structure evaluation method one embodiment of the present invention is illustrated
Figure；
Fig. 2 is the structure diagram of the RF MEMS Switches of ladder type micro cantilever structure；
Fig. 3 is the structural representation of electrostatic drive step type micro cantilever structure evaluation system one embodiment of the present invention
Figure.
Embodiment
As shown in Figure 1, a kind of electrostatic drive step type micro cantilever structure evaluation method, including step：
S100：The values of the structural parameters of stepped micro-cantilever is obtained, wherein, the structural parameters of stepped micro-cantilever include
Between stepped micro-cantilever total length, stepped micro-cantilever thickness, stepped micro-cantilever and bottom are fixed between electrode
Gap, micro- beam length of stepped micro-cantilever non-electrostatic force active region, micro- beam of stepped micro-cantilever non-electrostatic force active region
Width and micro- beam width in electrostatic force area.
For existing stepped micro-cantilever, when evaluating it, first have to obtain its corresponding structure design ginseng
Number, specifically, as shown in Fig. 2, these parameters include stepped micro-cantilever total length L, stepped micro-cantilever thickness h,
The gap g between electrode is fixed in stepped micro-cantilever and bottom0, stepped micro-cantilever non-electrostatic force active region micro- beam length
Spend L1, width b1And micro- beam width b in electrostatic force area2。
S200：According to micro- beam width of stepped micro-cantilever non-electrostatic force active region and micro- beam in electrostatic force area
Width, calculates stepped micro-cantilever dimensionless width ratio.
Stepped micro-cantilever dimensionless width is than β=N × b1/b2, in formula, N is the non-electrostatic effect of stepped micro-cantilever
The beam number in area, b1For single micro- beam width of stepped micro-cantilever non-electrostatic force active region, b2For the micro- of electrostatic force area
Beam width.
S300：Become according to stepped micro-cantilever dimensionless group relational expression and electrostatic force downstairs type micro-cantilever
The trial function of shape, calculates stepped micro-cantilever non-dimensional length ratio.
In one of the embodiments, the dimensionless group relational expression of stepped micro-cantilever can obtain in the following way
：
Step 1：According to modified couplestress theory and Euler-Bernoulli Jacob's beam model, it is immeasurable to establish stepped micro-cantilever
The pick-up voltage prediction model of guiding principle parameter.
Step 2：Reached most according to the pick-up voltage prediction model of stepped micro-cantilever dimensionless group and pick-up voltage
The corresponding pick-up voltage first derivative of small value is zero principle, establishes the dimensionless group relational expression of stepped micro-cantilever.
It is non-essential, the trial function of electrostatic force downstairs type micro-cantilever deformationUnder being acted on for unit load
The normalized warping function of unit length step type micro-cantilever.
S400：According to stepped micro cantilever structure design parameter and stepped micro-cantilever non-dimensional length ratio, meter
Calculate the optimization length of stepped micro-cantilever non-electrostatic force active region.
Specifically calculation formula isWherein α is stepped micro-cantilever non-dimensional length ratio, and L is step type
Micro-cantilever total length,For the optimization length of stepped micro-cantilever non-electrostatic force active region.
S500：According to the length of stepped micro-cantilever non-electrostatic force active region and the non-electrostatic masterpiece of stepped micro-cantilever
During with the optimization length in area, stepped micro cantilever structure is evaluated.
Compare the optimization length of stepped micro-cantilever non-electrostatic force active regionWith stepped micro-cantilever non-electrostatic force
The length L of active region1Size, ifThen stepped micro cantilever structure is optimal, otherwise, stepped micro-cantilever
Structure is not up to optimal, and driving voltage not up to minimizes, and stepped micro cantilever structure can also further optimize.
Electrostatic drive step type micro cantilever structure evaluation method of the present invention, the structure ginseng based on stepped micro-cantilever
Number, calculates stepped micro-cantilever dimensionless width ratio, recycles stepped micro-cantilever dimensionless group relational expression and electrostatic
The trial function of power effect downstairs type micro-cantilever deformation, calculates stepped micro-cantilever non-dimensional length ratio, finally obtains rank
The optimization length calculated value of ladder type micro-cantilever non-electrostatic force active region, when the length of stepped micro-cantilever non-electrostatic force active region
When degree is equal to the optimization length of stepped micro-cantilever non-electrostatic force active region, stepped micro cantilever structure is optimal, i.e.,
Show that the corresponding driving voltage of current stepped micro cantilever structure has reached minimum, if unequal, show current step type
Micro cantilever structure is not up to optimal, can also continue to optimize.In whole process, processing procedure is simple, calculation amount is small, and use is rigorous
Data processing calculating process, realize the evaluation to electrostatic drive step type micro cantilever structure.
In one of the embodiments, the dimensionless group relational expression of the stepped micro-cantilever is specially：
In formula, β is stepped micro-cantilever dimensionless width ratio, and α is stepped micro-cantilever non-dimensional length ratio,The trial function deformed for electrostatic force downstairs type micro-cantilever,ForSecond dervative, η for examination letter
Number system number.
In one of the embodiments, the trial function of the electrostatic force downstairs type micro-cantilever deformationFor
The normalized warping function of the lower unit length step type micro-cantilever of specific loading effect.
In one of the embodiments, micro- beam width according to stepped micro-cantilever non-electrostatic force active region and
Micro- beam width in electrostatic force area, calculate stepped micro-cantilever dimensionless width is than specific formula：
In formula, β is stepped micro-cantilever dimensionless width ratio, and N is stepped micro-cantilever non-electrostatic force active region
Micro- beam number, b1For single micro- beam width of stepped micro-cantilever non-electrostatic force active region, b2For micro- beam in electrostatic force area
Width.
In order to further explain in detail the technical side of electrostatic drive step type micro cantilever structure evaluation method of the present invention
Case and its effect brought, will be analyzed using an instantiation below.
As shown in Fig. 2, mems switch material is gold, its elasticity modulus is 78.5GPa, and Poisson's ratio 0.22 is normal with respect to dielectric
Number is 1, and permittivity of vacuum is 8.854 × 10-12F/m。
Step 1：The design of Structural Parameters value of stepped micro-cantilever is obtained, wherein, stepped micro-cantilever total length L
=160 μm, thickness h=7 μm, the gap g with fixed electrode0=2 μm, micro- beam length L of non-electrostatic force active region1It is=56 μm, wide
Spend b1=30 μm, micro- beam width b in electrostatic force area2=164 μm.
Step 2：Micro- beam dimensionless width is determined than β=2 × 30/164=0.3659, due to stepped micro-cantilever in Fig. 2
There are two micro- beam N=2 in beam non-electrostatic force active region, so when calculating micro- beam dimensionless width ratio here, need to be multiplied by 2.
Step 3：Trial function chooses the normalized deformation letter of the lower unit length step type micro-cantilever of specific loading effect
Number, according to formula
Following parameter value is obtained using single argument Numerical Methed for Solving Non-linear Equations method：α=0.5133
Step 4：According to formulaDetermine
Step 5：Designing scheme is non-optimal, and driving voltage not up to minimizes.
As shown in figure 3, a kind of electrostatic drive step type micro cantilever structure evaluation system, including：
Parameter acquisition module 100, for obtaining the structural parameters of stepped micro-cantilever, wherein, stepped micro-cantilever
Structural parameters include stepped micro-cantilever total length, stepped micro-cantilever thickness, stepped micro-cantilever and bottom and consolidate
Micro- beam length, the stepped micro-cantilever in gap, stepped micro-cantilever non-electrostatic force active region between fixed electrode are non-electrostatic
Micro- beam width of power active region and micro- beam width in electrostatic force area；
Width than computing module 200, for micro- beam width according to stepped micro-cantilever non-electrostatic force active region and
Micro- beam width in electrostatic force area, calculates stepped micro-cantilever dimensionless width ratio；
Length is than computing module 300, for according to stepped micro-cantilever dimensionless group relational expression and electrostatic force
The trial function of downstairs type micro-cantilever deformation, calculates stepped micro-cantilever non-dimensional length ratio；
Optimization length computing module 400, for according to stepped micro-cantilever total length, stepped micro-cantilever dimensionless
Length ratio, calculates the optimization length of stepped micro-cantilever non-electrostatic force active region；
Evaluation module 500, for being equal to stepped micro-cantilever when the length of stepped micro-cantilever non-electrostatic force active region
During the optimization length of beam non-electrostatic force active region, stepped micro cantilever structure is optimal.
Electrostatic drive step type micro cantilever structure evaluation system of the present invention, parameter acquisition module 100 obtain stepped micro-
The structural parameters of cantilever beam, width calculate stepped micro-cantilever dimensionless width ratio than computing module 200, and length is than calculating mould
Block 300 utilizes stepped micro-cantilever dimensionless group relational expression and the examination letter of electrostatic force downstairs type micro-cantilever deformation
Number, calculates stepped micro-cantilever non-dimensional length ratio, it is non-electrostatic that optimization length computing module 400 obtains stepped micro-cantilever
The optimization length calculated value of power active region, evaluation module 500 are equal to when the length of stepped micro-cantilever non-electrostatic force active region
During the optimization length of stepped micro-cantilever non-electrostatic force active region, stepped micro cantilever structure is optimal, that is, shows to work as
The corresponding driving voltage of preceding step type micro cantilever structure has reached minimum, if unequal, shows current stepped micro-cantilever
Girder construction is not up to optimal, can also continue to optimize.In whole process, processing procedure is simple, calculation amount is small, using rigorous data
Calculating process is handled, realizes the evaluation to electrostatic drive step type micro cantilever structure.
In one of the embodiments, the electrostatic drive step type micro cantilever structure evaluation system further includes：
Pick-up voltage prediction model establishes module, for according to modified couplestress theory and Euler-Bernoulli Jacob's beam model,
Establish the pick-up voltage prediction model of stepped micro-cantilever dimensionless group；
Dimensionless group relation reality module, it is pre- for the pick-up voltage according to stepped micro-cantilever dimensionless group
It is zero principle that survey model and pick-up voltage, which reach the corresponding pick-up voltage first derivative of minimum value, establishes stepped micro-cantilever
Dimensionless group relational expression.
In one of the embodiments, the dimensionless group relational expression of the stepped micro-cantilever is specially：
In formula, β is stepped micro-cantilever dimensionless width ratio, and α is stepped micro-cantilever non-dimensional length ratio,The trial function deformed for electrostatic force downstairs type micro-cantilever,ForSecond dervative, η for examination letter
Number system number.
In one of the embodiments, the trial function of the electrostatic force downstairs type micro-cantilever deformationFor
The normalized warping function of the lower unit length step type micro-cantilever of specific loading effect.
In one of the embodiments, the width than computing module 200 according to the non-electrostatic masterpiece of stepped micro-cantilever
With micro- beam width in area and micro- beam width in electrostatic force area, it is more public than specific to calculate stepped micro-cantilever dimensionless width
Formula is：
In formula, β is stepped micro-cantilever dimensionless width ratio, and N is stepped micro-cantilever non-electrostatic force active region
Micro- beam number, b1For single micro- beam width of stepped micro-cantilever non-electrostatic force active region, b2For micro- beam in electrostatic force area
Width.
Embodiment described above only expresses the several embodiments of the present invention, its description is more specific and detailed, but simultaneously
Cannot therefore it be construed as limiting the scope of the patent.It should be pointed out that come for those of ordinary skill in the art
Say, without departing from the inventive concept of the premise, various modifications and improvements can be made, these belong to the protection of the present invention
Scope.Therefore, the protection domain of patent of the present invention should be determined by the appended claims.
Claims (6)
1. a kind of electrostatic drive step type micro cantilever structure evaluation method, it is characterised in that including step：
The structural parameters of stepped micro-cantilever are obtained, wherein, the structural parameters of stepped micro-cantilever are including stepped micro- outstanding
Gap, step type between arm beam total length, stepped micro-cantilever thickness, stepped micro-cantilever and bottom fixation electrode is micro-
Micro- beam length of cantilever beam non-electrostatic force active region, the micro- beam width and electrostatic of stepped micro-cantilever non-electrostatic force active region
Micro- beam width of power active region；
According to micro- beam width of stepped micro-cantilever non-electrostatic force active region and micro- beam width in electrostatic force area, calculate
Stepped micro-cantilever dimensionless width ratio；
The examination letter deformed according to stepped micro-cantilever dimensionless group relational expression and electrostatic force downstairs type micro-cantilever
Number, calculates stepped micro-cantilever non-dimensional length ratio；
According to stepped micro-cantilever total length and stepped micro-cantilever non-dimensional length ratio, stepped micro-cantilever is calculated
The optimization length of non-electrostatic force active region；
When micro- beam length of stepped micro-cantilever non-electrostatic force active region is equal to stepped micro-cantilever non-electrostatic force active region
Optimization length when, stepped micro cantilever structure is optimal；
It is described step type micro-cantilever dimensionless group relational expression be specially：
In formula, β is stepped micro-cantilever dimensionless width ratio, and α is stepped micro-cantilever non-dimensional length ratio,To be quiet
The trial function of electric power effect downstairs type micro-cantilever deformation,ForSecond dervative, η is trial function coefficient；
The trial function of the electrostatic force downstairs type micro-cantilever deformationLower unit length rank is acted on for unit load
The normalized warping function of ladder type micro-cantilever.
2. electrostatic drive step type micro cantilever structure evaluation method according to claim 1, it is characterised in that described
The trial function deformed according to stepped micro-cantilever dimensionless group relational expression and electrostatic force downstairs type micro-cantilever, calculates
There is step before stepped micro-cantilever non-dimensional length ratio：
According to modified couplestress theory and Euler-Bernoulli Jacob's beam model, the suction of the stepped micro-cantilever dimensionless group of foundation
Close voltage-prediction model；
It is corresponding that minimum value is reached according to the pick-up voltage prediction model of stepped micro-cantilever dimensionless group and pick-up voltage
Pick-up voltage first derivative is zero principle, establishes the dimensionless group relational expression of stepped micro-cantilever.
3. electrostatic drive step type micro cantilever structure evaluation method according to claim 1 or 2, it is characterised in that institute
Micro- beam width according to stepped micro-cantilever non-electrostatic force active region and micro- beam width in electrostatic force area are stated, calculates rank
Ladder type micro-cantilever dimensionless width is than specific formula：
<mrow>
<mi>&beta;</mi>
<mo>=</mo>
<mi>N</mi>
<mo>&times;</mo>
<mfrac>
<msub>
<mi>b</mi>
<mn>1</mn>
</msub>
<msub>
<mi>b</mi>
<mn>2</mn>
</msub>
</mfrac>
</mrow>
In formula, β is stepped micro-cantilever dimensionless width ratio, and N is micro- beam of stepped micro-cantilever non-electrostatic force active region
Number, b1For single micro- beam width of stepped micro-cantilever non-electrostatic force active region, b2For micro- deck-siding in electrostatic force area
Degree.
A kind of 4. electrostatic drive step type micro cantilever structure evaluation system, it is characterised in that including：
Parameter acquisition module, for obtaining the structural parameters of stepped micro-cantilever, wherein, the structure ginseng of stepped micro-cantilever
Number include stepped micro-cantilever total length, stepped micro-cantilever thickness, stepped micro-cantilever and bottom fixation electrode it
Between gap, micro- beam length of stepped micro-cantilever non-electrostatic force active region, stepped micro-cantilever non-electrostatic force active region
Micro- beam width and electrostatic force area micro- beam width；
Width is than computing module, for the micro- beam width and electrostatic masterpiece according to stepped micro-cantilever non-electrostatic force active region
With micro- beam width in area, stepped micro-cantilever dimensionless width ratio is calculated；
Length is than computing module, for according to stepped micro-cantilever dimensionless group relational expression and electrostatic force downstairs type
The trial function of micro-cantilever deformation, calculates stepped micro-cantilever non-dimensional length ratio；
Optimization length computing module, for according to stepped micro-cantilever total length and stepped micro-cantilever non-dimensional length
Than the optimization length of the stepped micro-cantilever non-electrostatic force active region of calculating；
Evaluation module, it is non-electrostatic equal to stepped micro-cantilever for the length when stepped micro-cantilever non-electrostatic force active region
During the optimization length of power active region, evaluate stepped micro cantilever structure and be optimal；
It is described step type micro-cantilever dimensionless group relational expression be specially：
In formula, β is stepped micro-cantilever dimensionless width ratio, and α is stepped micro-cantilever non-dimensional length ratio,To be quiet
The trial function of electric power effect downstairs type micro-cantilever deformation,ForSecond dervative, η is trial function coefficient；
The trial function of the electrostatic force downstairs type micro-cantilever deformationLower unit length rank is acted on for unit load
The normalized warping function of ladder type micro-cantilever.
5. electrostatic drive step type micro cantilever structure evaluation system according to claim 4, it is characterised in that also wrap
Include：
Pick-up voltage prediction model establishes module, for according to modified couplestress theory and Euler-Bernoulli Jacob's beam model, establishing
The pick-up voltage prediction model of stepped micro-cantilever dimensionless group；
Dimensionless group relation reality module, for predicting mould according to the pick-up voltage of stepped micro-cantilever dimensionless group
It is zero principle that type and pick-up voltage, which reach the corresponding pick-up voltage first derivative of minimum value, establishes the immeasurable of stepped micro-cantilever
Guiding principle parameter relationship formula.
6. electrostatic drive step type micro cantilever structure evaluation system according to claim 4 or 5, it is characterised in that institute
Width is stated than computing module according to micro- beam width of stepped micro-cantilever non-electrostatic force active region and electrostatic force area
Micro- beam width, calculate stepped micro-cantilever dimensionless width is than specific formula：
<mrow>
<mi>&beta;</mi>
<mo>=</mo>
<mi>N</mi>
<mo>&times;</mo>
<mfrac>
<msub>
<mi>b</mi>
<mn>1</mn>
</msub>
<msub>
<mi>b</mi>
<mn>2</mn>
</msub>
</mfrac>
</mrow>
In formula, β is stepped micro-cantilever dimensionless width ratio, and N is micro- beam of stepped micro-cantilever non-electrostatic force active region
Number, b1For single micro- beam width of stepped micro-cantilever non-electrostatic force active region, b2For micro- deck-siding in electrostatic force area
Degree.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510451909.3A CN105117519B (en) | 2015-07-28 | 2015-07-28 | Electrostatic drive step type micro cantilever structure evaluation method and system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510451909.3A CN105117519B (en) | 2015-07-28 | 2015-07-28 | Electrostatic drive step type micro cantilever structure evaluation method and system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105117519A CN105117519A (en) | 2015-12-02 |
| CN105117519B true CN105117519B (en) | 2018-05-08 |
Family
ID=54665507
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510451909.3A Active CN105117519B (en) | 2015-07-28 | 2015-07-28 | Electrostatic drive step type micro cantilever structure evaluation method and system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105117519B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107346355B (en) * | 2017-06-21 | 2020-10-30 | 中国电子产品可靠性与环境试验研究所 | Electrostatic driving step type micro-clamped beam structure detection method and system |
| CN107292028B (en) * | 2017-06-21 | 2020-08-04 | 中国电子产品可靠性与环境试验研究所 | Method and system for determining design scheme of stepped micro-clamped beam structure |
| CN109255178A (en) * | 2018-09-04 | 2019-01-22 | 东南大学 | A kind of MEMS cantilever beam structure mechanical analyzing method under the bending condition based on flexible base board |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104462680A (en) * | 2014-11-26 | 2015-03-25 | 工业和信息化部电子第五研究所 | Method and system for predicating pull-in voltage of electrostatic drive stepped micro-cantilever beam |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2006047156A2 (en) * | 2004-10-21 | 2006-05-04 | The Regents Of The University Of California | Bi-material cantilevers with flipped over material sections and structures formed therefrom |
| CN104684841A (en) * | 2012-06-13 | 2015-06-03 | 普渡研究基金会 | Microelectromechanical system and methods of use |
-
2015
- 2015-07-28 CN CN201510451909.3A patent/CN105117519B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104462680A (en) * | 2014-11-26 | 2015-03-25 | 工业和信息化部电子第五研究所 | Method and system for predicating pull-in voltage of electrostatic drive stepped micro-cantilever beam |
Non-Patent Citations (2)
| Title |
|---|
| PZT压电式微传感器的结构优化;田开云 等;《机电工程技术》;20130930;第42卷(第09期);第91-95页 * |
| 表面应力敏感型压阻微悬臂梁传感器的模拟;汪超男 等;《清华大学学报（自然科学版）》;20091130;第49卷(第11期);第1876-1879、1885页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105117519A (en) | 2015-12-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105117521B (en) | Low driving voltage step type micro cantilever structure Optimization Design and system | |
| Pan et al. | A novel method of vibration modes selection for improving accuracy of frequency-based damage detection | |
| CN104462680B (en) | The Forecasting Methodology and system of electrostatic drive step type micro-cantilever pick-up voltage | |
| Ryu et al. | Flapping dynamics of an inverted flag in a uniform flow | |
| CN105117519B (en) | Electrostatic drive step type micro cantilever structure evaluation method and system | |
| KR101065502B1 (en) | Breaking prediction method | |
| Karami et al. | Parametric study of zigzag microstructure for vibrational energy harvesting | |
| CN105930616B (en) | A kind of aircraft moves the load distribution method of aerofoil statically indeterminate structure | |
| Fu et al. | Electromechanical dynamic buckling phenomenon in symmetric electric fields actuated microbeams considering material damping | |
| Mo et al. | Energy harvesting with piezoelectric circular membrane under pressure loading | |
| Hu et al. | A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface | |
| Dung et al. | Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory | |
| CN107292028A (en) | It is determined that the method and system of stepped micro- fixed beam structure design | |
| Liu et al. | Nonlinear dynamics of two-directional functionally graded microbeam with geometrical imperfection using unified shear deformable beam theory | |
| Chaubey et al. | Biaxial and shear buckling of laminated composite elliptic paraboloids with cutouts and concentrated mass | |
| Mieczkowski | Static electromechanical characteristics of piezoelectric converters with various thickness and length of piezoelectric layers | |
| Fu et al. | Asymmetric Bouc-Wen hysteresis modeling for MFC actuator via hybrid APSO-TRR identification algorithm | |
| Li et al. | Crack growth in homogeneous media using an adaptive isogeometric fourth-order phase-field model | |
| Khiem et al. | Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material | |
| CN112052615B (en) | Micro fatigue performance prediction method based on artificial neural network | |
| Jiang et al. | Establishment and optimization of sensor fault identification model based on classification and regression tree and particle swarm optimization | |
| Liu et al. | The effect of wear on short crack propagation under fretting conditions | |
| CN108716959B (en) | Method for effectively predicting interface stress distribution of piezoelectric film and gradient non-uniform substrate | |
| Tummala et al. | Design optimization of a compliant spine for dynamic applications | |
| Dutta et al. | Exploring isospectral cantilever beams using electromagnetism inspired optimization technique |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |