CN110375908A - The mechanics parameter extracting method of multilayer clamped beam material based on Newton-decline method - Google Patents
The mechanics parameter extracting method of multilayer clamped beam material based on Newton-decline method Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
- G01L5/0047—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes measuring forces due to residual stresses
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N19/00—Investigating materials by mechanical methods
Abstract
It the invention proposes the mechanics parameter extracting method of the multilayer clamped beam material based on Newton-decline method, is tested by the algorithm of CAD or analysis of material, belongs to the technical field of measurement, test and calculating, reckoning, counting.Reflect problem really without misalignment in order to simple, the present invention uses Euler-Bernoulli beam to model for model, the object of extraction is the double-deck clamped beam model of not wide polysilicon-gold, use the double-deck clamped beam as test structure, multilayered film material Young's modulus and residual stress are extracted using multilayer micro-mechanical beam resonance model, solve the extraction of the Young's modulus and residual stress in straight situation, using the convergence of Newton-decline method modified Newton method, improve the iteration precision of Newton-decline method, expand the selection range of initial value, obtain faster iteration speed, reduce the time complexity and space complexity of algorithm.
Description
Technical field
The invention discloses the mechanics parameter extracting methods of the multilayer clamped beam material based on Newton-decline method, pass through calculating
The algorithm of machine Computer Aided Design is tested or analysis of material, and the technical field of measurement, test and calculating, reckoning, counting is belonged to.
Background technique
Microelectromechanical systems (MEMS, Micro-Electro-Mechanical Systems) refers in microelectric technique
On the basis of the hard-core technology for combining the technologies such as electricity, power, heat, optical, electromagnetic and fluid that grows up.In recent years, CMOS MEMS
Technology is widely used in MEMS processing, is manufactured that diversified micro element and micro-system.It is well known that such as Young
The mechanical parameters such as modulus, residual stress have a great impact to the structure and function of MEMS device.However, for CMOS
For MEMS technology thin-film material, under different fabrication process conditions, even if identical material also tends to show obviously
Different material properties, therefore, it is necessary to accurately measure out these mechanics parameters.But on the one hand relatively due to size
Small, the material parameter of thin-film material is difficult to be utilized classical macroscopic token technology and carries out experiment measurement；On the other hand, CMOS
MEMS device often uses multi-layer film structure, and existing test single thin film mechanical parameters method is applied to multi-layer thin
It is but not easy in membrane material parameter measurement.Therefore, the multilayered film material mechanics parameter on-line testing knot of process compatible is established
Structure and test method for monitoring MEMS thin film material mechanics characteristic, prediction and optimization properties of product and then guarantee that properties of product can
It leans on, uniformity and have very important significance steadily in the long term.It is required for specific in situ rest structure and method
Standard it is as follows: test structure processing technology must be mutually compatible with monitored technique, and test construction geometry is simple, area occupied
Small, firm reusable, measurement method is simply direct.
Traditional extraction algorithm of CMOS MEMS technology thin film material mechanics parameter mostly uses greatly Newton iteration method, but ox
Iterative method of pausing has strict requirements to the selection of initial value, and Newton method only has local convergence.The application is intended to mention
It is a kind of out to improve Newton-decline method and consider that the mechanical characteristic of material in a straightened condition extracts multilayer clamped beam mechanics of materials ginseng
Number extracts Newtonian mechanics parameter closer to the truth with faster iteration speed.
Summary of the invention
Goal of the invention of the invention is the deficiency for above-mentioned background technique, and it is solid to provide the multilayer based on Newton-decline method
The mechanics parameter extracting method of strutbeam material introduces the factor, residual accuracy, the Newton method of the root limits of error and extracts mechanics
Parameter expands the range of initial value selection and remains the convergence rate of Newton method as far as possible, solves current Newton method and extract respectively
Layer Young's modulus value do not restrain or only partial region restrain the technical issues of.
The present invention adopts the following technical scheme that for achieving the above object
The present invention uses double-layer double-end clamped beam as test structure, using multilayer micro-mechanical beam resonance model to multi-layer thin
Membrane material Young's modulus and residual stress extract, including following 8 basic steps.
1) this algorithm uses double-layer double-end clamped beam as test structure, using multilayer micro-mechanical beam resonance model to multilayer
Thin-film material Young's modulus and residual stress extract, and need to derive after release two-end fixed beam one in straight situation respectively
Functional relation between rank resonance frequency and size and mechanics parameter.
It is straight after release:
In formula (1), fj1sFor the one class resonant frequency of two-end fixed beam jth layer material in straight situation after release, l is double
The length of clamped beam is held,For the equivalent Young's modulus of jth layer membrane materials, IjIt is jth layer membrane materials on cross section
Area AjAbout the rotary inertia of neutral axis, ρjFor the density of material of jth layer membrane materials,For jth layer membrane materials etc.
Imitate residual stress.
2) object that this algorithm extracts is the not clamped beam form of wide polysilicon-gold (PolySilicon-Au) double-layer double-end
Type, the structure use the PolyMUMPs standard surface micro fabrication of MEMSCAP company.It is surveyed by laser doppler resonator
Measure its resonance frequency.For the multilayer two-end fixed beam being made of n-layer thin-film material, there is the 2n mechanics of materials for needing to solve special
Property parameter, at this moment needs the beam of at least 2 groups different lengths, beam identical for each group of length will at least have n multilayer both-end
Clamped beam, and the width of this group of multilayer Liangqi n-layer at least has the different types of combination of n kind.
3) by formula (1) it is known that the material parameter and construction geometry of the one class resonant frequency of multilayer two-end fixed beam and beam
Size is related, the one class resonant frequency of multilayer two-end fixed beam can be considered as determining about Young's modulus and residual stress
Implicit function.The length l and thickness h of one class resonant frequency and multilayer two-end fixed beamjIt is related, but each slice width degree b with beamjNothing
It closes, but the ratio b with each slice width degreej/b1In relation to (present invention is herein with the first layer width b of multilayer two-end fixed beam1For base
It is quasi-, it is specified that all multilayer two-end fixed beam structure first layer width all having the same), it is double in the case of straight situation after release
Hold the one class resonant frequency of clamped beam about the implicit function of Young's modulus and residual stress such as formula (2) shown in, in addition, adding practical
In work technique, the thickness of film layer is determined by process flow, and what designer can control is only to test structure planar
Geometry, and the thickness h of structurejIt can not change for designer.
fjs=fjs(E1,E2,...,En,σ1,σ2,...,σn,b2,b3,...,bn,l) (2)。
4) present invention first by Newton iterative method trial, be intended to using Newton method need to by Young's modulus in formula (1) with it is other
Anti- solution comes out the relationship of each parameter, by the form that the transformation of equation is general at Newton iteration method by its abbreviation, will survey in step 2
N class value out brings in equation the original form that can obtain Newton iteration into, i.e. the function of many variables Nonlinear System of Equations of n dimension:
5) Newton iteration method need to choose suitable iterative initial value, by the MEMSCAP data announced and other documents
The corresponding parametric values provided determine the range of iterative initial value, and initial value is then determined under this magnitude, are obtained using iterative formula (4)
To iteration result.Although by this method obtain as a result, very fast in single neighbouring convergence rate, calculate it is complicated, together
When global convergence it is very poor.
x(k+1)=x(k)-F′(x(k))-1F(x(k)) (k=0,1 ...) (4),
In formula (4), x(k)、x(k+1)For kth time, kth+1 time iterative value, F (X(k)) acquired according to kth time iterative value
Simplify the obtained solution of equations for meeting Newton iteration method common version, F ' (x by formula (2)(k)) it is F (X(k)) single order lead
Number.
6) iterative formula of above-mentioned Newton iteration method is optimized, using Newton-decline method iteration, iterative formula modification
For formula (5), it is made to obtain different the number of iterations by changing its factor of going down the hill；Secondly, by change residual precision with
And the limits of error of root, so that down-hill method is obtained higher iteration precision；Finally, in order to verify the constringency performance of down-hill method, Ke Yixuan
The iterative initial value of not same area is selected from multiple directions iteration, by relaxing initial value, whether verifying is several times by script convergence domain after iteration
Outer initial value pulls in convergence domain.
λ is the factor of going down the hill.
7) finally, taking various sizes of double-layer double-end cantilever beam, the robustness of the algorithm is examined, is verified under same magnitude
The convergent of other sizes has verified whether not convergent jump discontinuity.The number that the result of acquisition and MEMSCAP are announced
The corresponding parametric values comparison provided accordingly and in other documents.Then compare the operational precision deviation of Newton iteration and down-hill method
Size.
The present invention by adopting the above technical scheme, has the advantages that
(1) the invention proposes a kind of each layer Young's modulus of double-layer double-end clamped beam material and residual stress in straight situation
Under extraction algorithm, solve current Newton method and extract each layer mechanics parameter value of thin-film material not restrain or only receive in partial region
The problem of holding back, setting residual accuracy and then interception iterative value significance bit under the constant constraint of convergence rate and convergence result
Number, the iterative value of Newton-decline method meet residual accuracy institute it is constrained when approached using classical Newton method and meet the root limits of error
Convergence solution, this method maximizes favourable factors and minimizes unfavourable ones, remains the convergence rate of Newton method as far as possible but improve the convergence of Newton method,
Iteration precision by improving Newton-decline method obtains faster iteration speed, reduces the time complexity of algorithm, to obtaining height
Constringent mechanics parameter has practical meaning.
(2) present invention is talked about to after the release of multilayer beam there is a situation where straight, and is joined to mechanics in straight situation
Number extracts equation group and is improved, and the mechanics parameter of extraction is more accurate.
(3) initial value outside convergence domain is pulled in by convergence domain by multiple directions iteration, expands the range of initial value selection, changes
Classical Newton method defect of local convergence due to Initial value choice is too harsh has been apt to it, therefore, disclosed method is more suitable
The property used.
Detailed description of the invention
Fig. 1 is the extraction algorithm of each layer Young's modulus of double-layer double-end clamped beam material and residual stress in straight situation
Flow chart.
Fig. 2 is the algorithm implementation flow chart of Newton-decline method.
Specific embodiment
The technical solution of invention is described in detail with reference to the accompanying drawing.
(1) the physical quantity introduction of two-end fixed beam
When thin-film width and its thickness meet bi< 5hiI.e. narrow beam when, equivalent Young's modulusIt is exactly Young's modulus EiIts
Body；When thin-film width and its thickness meet bi≥5hiI.e. wide beam when, equivalent Young's modulusIt is one about Young's modulus and pool
Pine ratio viRelational expression, i.e.,Then equivalent Young's modulusAbout the relationship between film thickness and its width are as follows:
Equivalent residual stressForIt undergoes before release process (when i.e. deformation occurs), the length of beam
For l.The width of i-th layer membrane materials is wi, with a thickness of hi, density of material ρi, Young's modulus Ei.The bottom surface of multilayer beam is (i.e.
The top surface of substrate) position in z-axis is z0, z0=0, position of i-th layer of the top surface in z-axis is z from bottom to upi, then:
Neutral plane height zcAre as follows:
Rotary inertia I of area of i-th layer membrane materials on cross section about neutral axisiAre as follows:
Defining micromachined membrane deflection of beam rigidity isLinear density isAxial load isThat is:
Wherein, AiFor area of i-th layer membrane materials on cross section.
(2) relationship of double-layer double-end clamped beam one class resonant frequency and material parameter
For keeping the double-deck micromechanics clamped beam of straightened condition, the Approximate Analytic Formula of each rank resonance frequency after release
Are as follows:
For the multilayer two-end fixed beam being made of n-layer thin-film material, there is the 2n characteristic of material mechanics for needing to solve ginseng
Number, at this moment needs the beam of at least 2 groups different lengths, beam identical for each group of length will at least have n multilayer both-end clamped
Beam, and the width of this group of multilayer Liangqi n-layer at least has the different types of combination of n kind.The single order of multilayer two-end fixed beam
Resonance frequency is related with the material parameter of beam and geometrical scale, the one class resonant frequency of multilayer two-end fixed beam can be regarded
For the determining implicit function about Young's modulus and residual stress.The length l of one class resonant frequency and multilayer two-end fixed beam and
Thickness hjIt is related, but each slice width degree b with beamjIt is unrelated, but the ratio b with each slice width degreej/b1It is related (herein the present invention with
The first layer width b of multilayer two-end fixed beam1On the basis of, it is specified that all multilayer two-end fixed beam structure first layers all have phase
Same width), in addition, the thickness of film layer is determined that designer can control only by process flow in actual processing technique
It is only the geometry of test structure planar, and the thickness h of structurejIt can not change for designer.
Assuming that the width of jth root multi-layer beam each layer from bottom to up is respectively bj1, bj2..., bjn... (1≤j≤n), separately
The width of a piece beam, that is, kth root multi-layer beam each layer from bottom to up is respectively bk1, bk2..., bkn... (1≤k≤n, k ≠ j), that
, vector (bj1, bj2..., bjn...) and vector (bk1, bk2..., bkn...) it and must linear independence.Since the present invention advises
All multilayer two-end fixed beam structure first layer width all having the same are determined, therefore, as long as the 2nd layer of guarantee is to most here
The width combination of top layer is not exactly the same.It is humorous by the above-mentioned available at least 2n single order of at least 2n multilayer cantilever beam
Vibration frequency, available one equation group being made of at least 2n linear equation, for each root multi-layer two-end fixed beam
Speech substitutes into the corresponding function of formula (1) in equation group (14):
(3) Newton-decline method iterative process
Be intended to using Newton method need to by the relationship of Young's modulus in formula (14) and other each parameters anti-solution comes out, pass through equation
Convert the form that its abbreviation is general at the Newton iteration method as shown in formula (15):
Wherein, f1,…,fnIt is (x1,x2,…xn) the function of many variables.
If being denoted as with vector mark:
X=(x1,x2,…,xn)T∈Rn, F=(f1,f2,…fn)T (16)。
For above-mentioned equation group be possible to one solution or multiple solutions, it is also possible to have it is infinite solution or without solution, unless special
Outside different equation, generally accurate solution cannot be acquired using direct method, can only be solved at present using iterative approximation, according to different thoughts
Iteration convergence is constructed in x*Sequence of iterations x(k), (k=0,1 ...).
Provide an approximation root of equationBy the component fi of function F (x)i(x) (i=
1 ... n) in x(k)Place's function of many variables Taylor expansion simultaneously takes its linear segment, can indicate are as follows: F (x) ≈ F (x(k))+F′(x(k))
(x-x(k)), it then enables above formula right end be equal to zero and obtains system of linear equations:
F′(x(k))(x-x(k))=- F (x(k)) (17),
Wherein,
F ' (x) is known as Jacobian matrix, solves formula (18), solution is denoted as x(k+1).The iterative formula of Newton method are as follows:
x(k+1)=x(k)-F′(x(k))-1F(x(k)) (k=0,1 ...) (19).
Newton-decline method is by the iterative formula modification in Newton method are as follows:
Wherein, λ is referred to as to go down the hill the factor, and the selection for the factor of going down the hill should meet | F (x(k+1)) | < | F (x(k)) | establishment, when
|F(x(k)) | < ε1Or | x(k+1)-x(k)| < ε2When just stop iteration, and take x*≈x(k), wherein ε1、ε2It is previously set
Precision, ε1For residual accuracy, ε2For the root limits of error；Otherwise, then subtract λ, continue iteration, be calculated by above-mentioned iterative process
One function value sequence declined with zero strictly monotone for lower bound, this method are known as Newton-decline method.
Newton-decline method optimizes original method, and this method is maximized favourable factors and minimized unfavourable ones, and expands the range of initial value selection, while to the greatest extent may be used
The convergent speed of Newton method can be remained.
(4) Newton-decline method of application enhancements extracts the mechanics parameter of multilayer clamped beam material
The mechanics parameter of multilayer clamped beam material disclosed in the present application based on Newton-decline method in a straightened condition extracts
Method is as shown in Figure 1, include following 5 big steps.
Step 1, for n-layer thin-film material constitute two-end fixed beam for, for extract its each layer film Young's modulus and
Residual stress, needs to measure the one class resonant frequency of at least two groups n-layer two-end fixed beam, and every group of n-layer two-end fixed beam includes n
N-layer two-end fixed beam, the length of n n-layer two-end fixed beam and the of same size of the first layer film but the 2nd layer thin to top
The width of film combines different, the measured value of n n-layer two-end fixed beam one class resonant frequency of record and the dimensional parameters of film.
Step 2, for release preload after all measurement objects all in straightened condition situation simultaneous it is all measurement pair
As one class resonant frequency obtains Nonlinear System of Equations, inverting nonlinear equation about the equation of film dimensions parameter and mechanics parameter
Young's modulus and residual stress and the relationship of one class resonant frequency obtain nonlinear multivariable equation group in group, by nonlinear multivariable
Equation group abbreviation is the equation group of Newton iteration form.
Step 3 introduces satisfaction | F (x(k+1)) | < | F (x(k)) | this constraint (F (x(k)) in each F (x(k)) all full
Foot this constraint) factor lambda of going down the hill, residual accuracy ε1, root limits of error ε2, for the side for the Newton iteration form that step 2 obtains
Journey group carries out iterative solution process as shown in Figure 2:
According to kth time iterative solution x(k)Single order of the equation group F (x) of Newton iteration form in current iteration Xie Chu is acquired to lead
Number F ' (x(k)) ,+1 iterative solution x of kth is solved further according to the iterative formula for introducing the factor(k+1)；
|F(x(k+1)) | < | F (x(k)) | when, using kth time iterative solution as+1 iterative solution of kth, otherwise, reduce the factor of going down the hill
Value after according to introduce the factor iterative formula solve+1 iterative solution x of kth(k+1), by+1 iterative solution assignment of kth
Kth time iterative solution is given, | F (x(k)) | < ε1When terminate iteration, and in | F (x(k))|≥ε1When adjust residual accuracy ε1Take
Value in turn intercepts the number of significant digit of iterative solution, rejudges whether+1 iterative solution of kth, kth time iterative solution meet | F
(x(k+1)) | < | F (x(k)) | this constraint；
Meet in+1 iterative solution of kth, kth time iterative solution | F (x(k+1)) | < | F (x(k)) | when this constraint, using classics
Newton iteration formula continue iterative solution until | x(k+1)-x(k)| < ε2When stop iteration.
Step 4, it chooses not after the iterative initial value of same area respectively from upper and lower both direction convergence of approximation solution, if upper and lower two sides
To the fixed value for meeting the root limits of error is all converged in, the initial value outside convergence domain is pulled in convergence domain, if upper and lower both direction
Iterative solution fluctuation or jump, reset residual accuracy.
Step 5, various sizes of double-layer double-end clamped beam is taken, the robustness of the algorithm is examined, is verified under same magnitude
The convergent of other size double-layer double-end clamped beam film Young's modulus and residual stress extraction of values, has verified whether not receive
The jump discontinuity held back resets residual accuracy when having not convergent jump discontinuity, without not convergent jump discontinuity
The corresponding parametric values provided in the data for result and the MEMSCAP announcement that comparison obtains when point and other documents, then compare
The size of Newton iteration and Newton-decline method operational precision deviation.
Applicant is successfully completed using multilayer micro-mechanical beam resonance model using Matlab to double-layer double-end clamped beam
The programming of the extraction algorithm of each layer membrane materials Young's modulus of material and residual stress in straight situation, simulation result and classics
The value of Newton method, which compares, shows that the application significantly improves the convergence problem of classical Newton method, substantially increases Young's modulus
With the extraction accuracy of residual stress, algorithm has lower time complexity and space complexity, and the optimization algorithm is for obtaining
The mechanics parameter of better utility has practical meaning.
It should be noted that above-described embodiment is only presently preferred embodiments of the present invention, there is no be used to limit the present invention
Protection scope, the equivalent substitution or substitution made based on the above technical solution belongs to protection model of the invention
It encloses.
Claims (7)
1. the mechanics parameter extracting method of the multilayer clamped beam material based on Newton-decline method, which is characterized in that for thin by n-layer
The multilayer clamped beam that membrane material is constituted, choosing at least 2 groups of n-layer two-end fixed beams is measurement object, and every group of n-layer two-end fixed beam is extremely
Less comprising n length is identical and first layer thin-film width is identical but the width of the second layer to top film combines different n-layers
Two-end fixed beam measures the one class resonant frequency of each n-layer two-end fixed beam in every group of n-layer two-end fixed beam and records single order resonance
Film dimensions parameter corresponding to frequency, situation simultaneous of all measurement objects all in straightened condition after being preloaded for release
All measurement object one class resonant frequencies obtain Nonlinear System of Equations, inverting about the equation of film dimensions parameter and mechanics parameter
The relationship of mechanics parameter and one class resonant frequency obtains nonlinear multivariable equation group in the Nonlinear System of Equations, will be polynary non-thread
Property equation group abbreviation be Newton iteration form equation group, setting meet Newton iteration form equation group letter at next iteration solution
The absolute value of numerical value is less than the residual essence of this constraint of the absolute value of Newton iteration form equation group functional value at current iteration solution
Exactness sets the root limits of error, and the convergence solution for meeting the root limits of error is approached using the newton iteration formula for introducing the factor.
2. the mechanics parameter extracting method of the multilayer clamped beam material based on Newton-decline method according to claim 1, special
Sign is, sets the root limits of error, and the convergence solution for meeting the root limits of error is approached using the newton iteration formula for introducing the factor
Method particularly includes:
At iterative solution twice in succession Newton iteration form equation group functional value be unsatisfactory for residual accuracy institute it is constrained when, amendment
Iteration functional value of Newton iteration form equation group at current iteration solution reaches residual essence again after the value for the factor of going down the hill
Exactness；
At iterative solution twice in succession Newton iteration form equation group functional value meet residual accuracy institute it is constrained when, using warp
Allusion quotation newton iteration formula approaches the convergence solution for meeting the root limits of error.
3. the mechanics parameter extracting method of the multilayer clamped beam material based on Newton-decline method according to claim 2, special
Sign is, at iterative solution twice in succession Newton iteration form equation group functional value be unsatisfactory for residual accuracy institute it is constrained when,
Amendment go down the hill the factor value after again iteration until the functional value of Newton iteration form equation group reaches residual at current iteration solution
Measure accuracy method particularly includes: | F (x(k+1))|≥|F(x(k)) | when, reduce by half go down the hill the factor value after according to introducing
The iterative formula of the factor solves+1 iterative solution of kth, and+1 iterative solution of kth is assigned to kth time iterative solution, | F (x(k)) | <
ε1When terminate iteration, and in | F (x(k))|≥ε1When adjustment residual accuracy value after judged at iterative solution twice in succession again
It is constrained that Newton iteration form equation group functional value meets residual accuracy institute | F (x(k+1)) | < | F (x(k)) | whether, x(k)、x(k +1)Respectively+1 kth time, kth iterative solution, F (x(k))、F(x(k+1)) it is respectively kth time, Newton iteration at+1 iterative solution of kth
The functional value of form equation group, ε1For residual accuracy.
4. the mechanics parameter extracting method of the multilayer clamped beam material based on Newton-decline method according to claim 1, special
Sign is, at iterative solution twice in succession Newton iteration form equation group functional value meet residual accuracy institute it is constrained when use
Classical newton iteration formula approaches the convergence solution for meeting the root limits of error method particularly includes: in+1 iterative solution x of kth(k+1), kth
Secondary iterative solution x(k)Meet | F (x(k+1)) | < | F (x(k)) | when this constraint, continue to iteratively solve using classical newton iteration formula
Until | x(k+1)-x(k)| < ε2When stop iteration, ε2For the root limits of error.
5. according to claim 1 to the mechanics parameter of the multilayer clamped beam material described in any one of 4 based on Newton-decline method
Extracting method, which is characterized in that choose not after the iterative initial value of same area respectively from upper and lower both direction convergence of approximation solution, if up and down
Both direction is all converged in the fixed value for meeting the root limits of error, and the iterative initial value outside convergence domain is pulled in convergence domain, if up and down
The iterative solution of both direction fluctuates or jump, resets residual accuracy until the iterative solution of upper and lower both direction is without wave
It moves, without jump.
6. according to claim 1 to the mechanics parameter of the multilayer clamped beam material described in any one of 4 based on Newton-decline method
Extracting method, which is characterized in that the convergence feelings of verifying other size multilayer clamped beam mechanics parameter extraction of values under same magnitude
Condition resets residual accuracy up to other size multilayer clamped beam power under same magnitude when having not convergent jump discontinuity
Learn parameter extraction value convergent jump discontinuity invariably.
7. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that the program is held by processor
The method in claim 1 is realized when row.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112129347A (en) * | 2020-09-18 | 2020-12-25 | 东南大学 | Multilayer film residual stress and Young modulus online test structure for micro-manufacturing and online extraction method |
| CN113589337A (en) * | 2021-08-16 | 2021-11-02 | 重庆两江卫星移动通信有限公司 | Single-satellite positioning method and system for communication and navigation integrated low-orbit satellite |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE19601239A1 (en) * | 1995-01-13 | 1996-07-18 | Fraunhofer Ges Forschung | Thin adhesive layer property measuring method for microsystem or microoptic technology |
| CN102607935A (en) * | 2011-12-27 | 2012-07-25 | 中国飞机强度研究所 | Measurement method of residual compression strength of composite material laminated board containing impact damages |
| CN106932263A (en) * | 2017-04-07 | 2017-07-07 | 东南大学 | Two-end fixed beam mechanics parameter measuring method and device based on resonant frequency |
| CN106996893A (en) * | 2017-04-11 | 2017-08-01 | 东南大学 | The mechanics parameter measuring method and device of a kind of double-layer double-end clamped beam |
| CN107014536A (en) * | 2017-04-28 | 2017-08-04 | 东南大学 | The mechanics parameter measuring method and device of a kind of double-layer double-end clamped beam |
-
2019
- 2019-07-02 CN CN201910589341.XA patent/CN110375908A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE19601239A1 (en) * | 1995-01-13 | 1996-07-18 | Fraunhofer Ges Forschung | Thin adhesive layer property measuring method for microsystem or microoptic technology |
| CN102607935A (en) * | 2011-12-27 | 2012-07-25 | 中国飞机强度研究所 | Measurement method of residual compression strength of composite material laminated board containing impact damages |
| CN106932263A (en) * | 2017-04-07 | 2017-07-07 | 东南大学 | Two-end fixed beam mechanics parameter measuring method and device based on resonant frequency |
| CN106996893A (en) * | 2017-04-11 | 2017-08-01 | 东南大学 | The mechanics parameter measuring method and device of a kind of double-layer double-end clamped beam |
| CN107014536A (en) * | 2017-04-28 | 2017-08-04 | 东南大学 | The mechanics parameter measuring method and device of a kind of double-layer double-end clamped beam |
Non-Patent Citations (1)
| Title |
|---|
| 李慧敏: "对牛顿迭代法及改进的总结", 《科技信息》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112129347A (en) * | 2020-09-18 | 2020-12-25 | 东南大学 | Multilayer film residual stress and Young modulus online test structure for micro-manufacturing and online extraction method |
| CN112129347B (en) * | 2020-09-18 | 2023-05-16 | 东南大学 | Multi-layer film residual stress and Young modulus on-line test structure for microfabrication and on-line extraction method |
| CN113589337A (en) * | 2021-08-16 | 2021-11-02 | 重庆两江卫星移动通信有限公司 | Single-satellite positioning method and system for communication and navigation integrated low-orbit satellite |
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