CN104697882A - Mass sensor for ambient air PM (particulate matter)2.5 based on ZnO nanowire array and preparation method for mass sensor - Google Patents
Mass sensor for ambient air PM (particulate matter)2.5 based on ZnO nanowire array and preparation method for mass sensor Download PDFInfo
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Abstract
The invention discloses a mass sensor for ambient air PM (particulate matter)2.5s based on a ZnO nanowire array and a preparation method for the mass sensor, and relates to the nano technology and environment monitoring field. When ambient air flows through the ZnO nanowire array, the PM2.5 is adhered on a nanowire, the mass of the PM2.5 is detected by detecting changes of the vibration frequency of the ZnO nanowire and a quantitative relationship between the vibration frequency of the ZnO nanowire and the PM2.5 mass. The mass sensor is simple and effective, and suitable for detecting the mass of PM2.5 in various ambient air in daily life.
Description
Technical field
The present invention relates to nanometer technology and environmental monitoring field, the Apparatus and method for of specifically a kind of change and testing environment air PM2.5 particle quality by detecting ZnO nano-wire vibration frequency.
Background technology
" haze " is one of focus of paying close attention in a hurry of people instantly, because haze weather not only makes the visibility of air reduce the normal trip affecting people, and causes very important injury to the healthy of people.Wherein mist belongs to natural weather phenomenon, is totally nontoxic.The materials such as aerial cigarette and dust but haze mainly suspends, can be entered by gas and can stick in human body lower respiratory tract and the lobe of the lung, damage the health of human body, especially diameter is less than or equal to the fine particle (i.e. PM2.5) of 2.5 microns.Although PM2.5 is the component that in earth atmosphere composition, content is little, it has important impact to air quality and visibility etc., greatly affects health and atmosphere quality.Therefore, the monitoring and governance for surrounding air PM2.5 is now very urgent.
At present, the monitoring method of particle concentration in environmental gas is mainly contained: weight method, β rays method, micro-oscillating balance method etc.
Weight method is the sampling environment air device by there being certain Cutting feature, the surrounding air of a certain amount of volume is extracted with constant rate of speed, make the PM2.5 in surrounding air stay on the filter membrane of known quality, according to difference and the sampling volume of the quality before and after filter membrane sampling, the concentration of PM2.5 can be drawn.But the weight method sampling time is longer, need manual step more, cost is high, and automaticity is very low and can not realize real-time on-line monitoring.
β rays method is that the particle in air is stayed on filter membrane when surrounding air is through filter membrane, and with the filter membrane of β ray by depositing particle, the damping capacity measuring β ray energy just can calculate the concentration of particle.Although the dynamic range that β rays method is measured is wider, and measurement result is only relevant with the quality of particle, and depositing of β ray radiation source easily radiation leakage problem occurs, and this safety of health of human body for survey crew is greatly unfavorable.
Trace oscillating balance method is based on conical component vibration microbalance principle, vibration hollow conical pipe places removable filter membrane, the particle in surrounding air is allowed to be deposited on filter membrane, by measuring the oscillation frequency change of filter membrane thus calculating the quality being deposited on particle on filter membrane, then calculate the concentration of particle according to sampling flow etc.Trace oscillating balance method can realize more and more in the instrument of real-time continuous monitoring in recent particle monitoring being used, such as Thermo Scientific TEOM 1405 because of it.But such monitoring equipment volume is comparatively large, and comparatively large by temperature humidity interference, limit environmental baseline and the spatial dimension of equipment Inspection.And at present China does not also occur at the integrated system for various Conventional pollution comprehensive monitoring analysis integration of independent research, thus tool more small size, more convenient, more accurate microparticle measuring element are each expert and present pursuing a goal of scientific research personage in this respect at present.
Therefore, need forwardly at present a kind ofly not amass little, convenient, accurate, real-time, economic, health in the appearance to ambient air particulate matter (PM2.5) mass sensitivity device integrally, to realize the accurately real-time monitoring of surrounding air by the collective of environmental influence.
Summary of the invention
In order to overcome prior art Problems existing, provide a kind of mass sensitivity device, to realize carrying out in real time surrounding air PM2.5 particle quality, accurately, the monitoring of efficient, low cost, Low Damage.
For achieving the above object, the present invention proposes a kind of mass sensitivity device of the surrounding air PM2.5 particle based on ZnO nanowire array, when environmental gas flows through nano-wire array, PM2.5 particle is attached on nano wire, by detecting the change of ZnO nano-wire vibration frequency, by the quantitative relationship between ZnO nano-wire vibration frequency and PM2.5 particle quality, thus detect the quality of PM2.5 particle.
A kind of mass sensitivity device of the surrounding air PM2.5 particle based on ZnO nanowire array, a groove is had at the back side of silicon substrate, thickness between bottom portion of groove and silicon substrate front is between 20 microns ~ 50 microns, the rectangular ventilation holes of two-stage step is carved with in silicon substrate front, above, the side of one-level step two longer sides and surface are electrodes, ZnO nano-wire is lateral growth at the electrode of one-level step above on two sides of air vent, ZnO nano-wire is suspended on above air vent, and the two ends of ZnO nano-wire are connected on two electrodes.
The length of the rectangular ventilation holes of described two-stage step is 10 microns, above the width of one-level step be 4 μm, below the width of one-level step be 3 μm.
On described electrode, lateral growth has ZnO nanowire array to adopt lateral growth method fixing between two electrodes, the mean diameter of ZnO nano-wire is about 150nm, the length of ZnO nano-wire is consistent, it is 4 μm, therefore the resonant frequency bandwidth of ZnO nanowire array is narrower, improves the accuracy of finely ground particles quality detection.
The metal component layer of described electrode is followed successively by TiAlNiAu from top to bottom, and the gross thickness of electrode is 200nm, and each metal component layer is 50nm.
The surface wettability of described ZnO nano-wire realizes the reversible transformation between hydrophilic-hydrophobic by UV-irradiation, ultraviolet irradiation is applied to it and increases the adsorbability of ZnO nano-wire to particle, and after the detection of PM2.5 granular mass terminates, remove ultraviolet lighting, and back and forth pass into clean air, the microparticle be adsorbed on nano wire is removed, realizes the automatically cleaning of device.
The preparation method of the mass sensitivity device of described a kind of surrounding air PM2.5 particle based on ZnO nanowire array, concrete preparation process is as follows:
First S1 prepares the groove of substrate back, adopt laser boring, the method for solution corrosion or ICP the silicon substrate back side is carved one long and wide be the groove of 10 microns;
The silicon substrate that back in S1 is carved groove by S2 cleans up and dries up rear back side wax and protect;
S3 is by after the silicon substrate front baking in S2, and front spin coating positive photoetching rubber, dries, exposes, develops, made by lithography at positive photoetching rubber position above silicon substrate front, its rear channel after post bake the groove of long 10 μm, wide 4 μm through later;
The silicon substrate that photoresist in S3 carves groove is put into KOH solution by S4, is not eroded away the rectangular recess of dark 1.5 μm of rule by the position that photoresist is protected, then wash away photoresist with acetone in silicon substrate front;
S5 is by the silicon substrate in S4 again through a photoetching and solution corrosion, and in S4, the central authorities of the rectangular recess that silicon substrate front carves carve long 10 μm a, through hole of wide 3 μm, prepared by the air vent now with two-stage step;
S6 will be carved with the silicon substrate of rear channel and two-stage step air vent again through a photoetching in S5, make at the side electrode position of air vent the groove that electrode prepares position by lithography;
The silicon substrate being carved with electrode position groove in S6 is put into magnetron sputtering apparatus by S7, at sidewall and surface portion sputtered with Ti, Al, Ni, Au layer successively of air vent side first order step, each metal layer thickness is 200nm, wash away photoresist with acetone again, now prepared by the electrode of air vent side;
Silicon substrate after the electrode of air vent side in S7 has been prepared by S8, again through a photoetching, makes the groove of ZnO Seed Layer position on electrode sidewall side by lithography near the position of air vent;
Silicon substrate after photoetching in S8 is put into magnetron sputtering by S9, and at the ZnO film that electrode sidewall surface sputtering 200nm is thick, prepared by the ZnO Seed Layer now on electrode;
S10 is by the zinc nitrate hexahydrate (Zn (NO of equimolar ratio example
3)
26H
2o) and hexamethylenetetramine (HMTA) be dissolved in deionized water, stir, be mixed with the solution of 25mmol/L as precursor solution;
S11 gets 15mL precursor solution and puts into hydrothermal reaction kettle, then electrode top in S9 is capped silicon substrate put into hydrothermal reaction kettle, at 80 DEG C, react growing ZnO nano-wire, continue 8h;
Growth has the substrate of ZnO nano-wire to take out by S12, repeatedly rinses, dry in nitrogen with deionized water;
The length rinsed well in S12 is had the substrate of ZnO nano-wire again through a photoetching by S13, in the other side of air vent, does not namely grow and has ZnO nano-wire side, make the groove that electrode position goes out by lithography;
Substrate after photoetching in S13 is put into magnetic control sputtering device by S14, at sidewall and surface portion sputtered with Ti, Al, Ni, Au layer successively of air vent other side first order step, each metal layer thickness is 200nm, photoresist is washed away again with acetone, now prepared by the electrode of the other side of air vent, now ZnO nanowire array is fixing between two electrodes, has just made the main part of PM2.5 particulate matter quantity sensor part.
The advantage that the present invention compared with prior art has:
Present invention utilizes surface effect and the small-size effect of nano-material, do not need the method asking quality integration by passing into a large amount of gas, can realize the highly sensitive detection to little mass particle and response fast, meanwhile, the present invention possesses self-cleaning function, increase its serviceable life, and it is little to have volume, lightly portable feature, environmental suitability is strong, be applicable to burying the detection node being distributed in sensor network in a large number, carry out the Monitoring and forecasting system in real-time of air quality.
Accompanying drawing explanation
Fig. 1 planimetric map of the present invention
Fig. 2 sectional view of the present invention
The preparation flow of Fig. 3 device of the present invention
Fig. 4 basic functional principle schematic diagram of the present invention;
The SEM image of Fig. 5 ZnO nanowire array;
In figure: 1-silicon substrate, 2-environmental gas, 3-ventilation slot, 4-electrode, 5-ZnO nano-wire, 6-PM2.5 particle
Embodiment
In order to make object of the present invention, technical scheme and advantage clearly understand, following examples by reference to the accompanying drawings, are further elaborated to the present invention.
The present invention is the mass sensitivity device of a kind of ambient air particulate matter based on ZnO nanowire array (PM2.5), specifically a kind of change by detecting ZnO nano-wire vibration frequency and detect the method for PM2.5 granular mass.
The concrete structure of the mass sensitivity device of a kind of surrounding air PM2.5 particle based on ZnO nanowire array disclosed by the invention is as follows:
There is a larger groove at the back side of Si substrate 1, thickness between bottom portion of groove and Si substrate 1 front is 20 microns, the rectangular ventilation holes 3 of two-stage step is carved with in Si substrate 1 front, for the circulation of environmental gas 2, the width of one-level step is 4 μm above, the width of one-level step is 3 μm below, above, the side of one-level step two longer sides and surface are electrodes, ZnO nano-wire 5 is lateral growths at the electrode of one-level step above on two sides of air vent, ZnO nano-wire 5 is suspended on above ventilation slot, and the two ends of ZnO nano-wire 5 are connected on two electrodes.
Described electrode component is followed successively by TiAlNiAu from top to bottom, and its thickness is that each component of 200nm is 50nm.
The preparation of described PM2.5 particulate matter quantity sensor part, first in order to make substrate better contact with electrode, and be applicable to high frequency electrical signal, select Si as the substrate of device of the present invention, make the air vent of two-stage step by lithography, after the side of one-level step above air vent and surface are made electrode, then lateral growth ZnO nano-wire.Its concrete preparation method is as follows:
(1) first prepare the groove of substrate back, laser boring can be adopted, Si substrate back carves a long and wide groove of about 10 microns by the method for solution corrosion or ICP.As shown in accompanying drawing 3 (a).
(2) Si substrate back in (1) being carved groove cleans up and dries up rear back side wax and protect.
(3) by after the Si substrate front baking in (2), front spin coating positive photoetching rubber, as shown in accompanying drawing 3 (b), dry, expose, develop, made by lithography at positive photoetching rubber position above Si substrate face, its rear channel after post bake the groove of long 10 μm, wide 4 μm through later, as shown in accompanying drawing 3 (c).
(4) Si substrate photoresist in (3) being carved groove puts into KOH solution; do not eroded away the rectangular recess of dark 1.5 μm of rule by the position that photoresist is protected in Si substrate face; photoresist is washed away again, as shown in accompanying drawing 3 (d) with acetone.
(5) by the Si substrate in (4) again through a photoetching and solution corrosion, the central authorities of the rectangular recess that Si substrate face carves carve long 10 μm a, through hole of wide 3 μm in (4), prepared by the air vent now with two-stage step, as shown in accompanying drawing 3 (e), accompanying drawing 3 (f).
(6) the Si substrate of rear channel and two-stage step air vent will be carved with in (5) again through a photoetching, make the groove that electrode prepares position by lithography, as shown in accompanying drawing 3 (g) at the side electrode position of air vent.
(7) the Si substrate being carved with electrode position groove in (6) is put into magnetron sputtering apparatus, at sidewall and surface portion sputtered with Ti, Al, Ni, Au layer successively of air vent side first order step, each metal layer thickness is 200nm, photoresist is washed away again with acetone, now prepared by the electrode of air vent side, as shown in accompanying drawing 3 (h).
(8) the Si substrate after having been prepared by the electrode of air vent side in (7), again through a photoetching, makes the groove of ZnO Seed Layer position on electrode sidewall side by lithography near the position of air vent, as shown in accompanying drawing 3 (i).
(9) the Si substrate after photoetching in (8) is put into magnetron sputtering, at the ZnO film that electrode sidewall surface sputtering 200nm is thick, prepared by the ZnO Seed Layer now on electrode, as shown in accompanying drawing 3 (j).
(10) by the zinc nitrate hexahydrate (Zn (NO of equimolar ratio example
3)
26H
2o) and hexamethylenetetramine (HMTA) be dissolved in deionized water, stir, be mixed with the solution of 25mmol/L as precursor solution.
(11) get 15mL precursor solution and put into hydrothermal reaction kettle, then electrode top in (9) is capped Si substrate put into hydrothermal reaction kettle, at 80 DEG C, react growing ZnO nano-wire, continue 8h.
(12) there is the substrate of ZnO nano-wire to take out growth, repeatedly rinse with deionized water, dry in nitrogen, as shown in accompanying drawing 3 (k).
(13) length rinsed well in (12) there is the substrate of ZnO nano-wire again through a photoetching, the groove that electrode position goes out is made by lithography, as shown in accompanying drawing 3 (l) the other side of air vent (namely do not grow and have ZnO nano-wire side).
(14) substrate after photoetching in (13) is put into magnetic control sputtering device, at sidewall and surface portion sputtered with Ti, Al, Ni, Au layer successively of air vent other side first order step, each metal layer thickness is 200nm, photoresist is washed away again with acetone, now prepared by the electrode of the other side of air vent, now ZnO nanowire array is fixing between two electrodes, just make the main part of PM2.5 particulate matter quantity sensor part, as shown in accompanying drawing 3 (m).
See accompanying drawing 4, basic functional principle schematic diagram of the present invention.
The basic functional principle of device of the present invention is:
When environmental gas 2 flows through ZnO nanowire array 5, particle 6 is attached on ZnO nano-wire 5, causes the change of the local frequency of ZnO nano-wire 5, by measuring ZnO nano-wire local frequency changing value, theoretical according to Euler-Bernoulli, draw the quality of particle 6 in environmental gas 2.
Described Euler-Bernoulli theory is that the method by measuring nano-wire array resonant frequency obtains PM2.5 particle quality.Theoretical according to Euler-Bernoulli, the length that two ends are fixed is L, quality is M
0nano wire (system A) natural frequency expression formula be: (1)
Wherein, M
0be the quality of nano wire, L is nanowire length, and E is nano wire elastic modulus, and I is moment of inertia (engineering science definition), is constant.
Length is that the quality of the L nano wire of ignoring places a quality is that after the particle (system B) of M, the expression formula of natural frequency is: (2)
Wherein, M is the quality of particle, and L is nanowire length, and E is nano wire elastic modulus, and I is moment of inertia (engineering science definition), is constant.
Length is L, quality is M
0nano wire on place the system (system C) that quality is the object of M, be equivalent to the coupling of system A and system B two individual system, according to Dunkerley equation, the natural frequency f of system C is: (3)
Wherein, M
0be the quality of nano wire, M is the quality of particle, and L is nanowire length, and E is nano wire elastic modulus, and I is moment of inertia (engineering science definition), and is respectively two different constants.
By (1) and (2) substitute into (3) formula, the particle quality can deriving placement is: (4) wherein, M
0be the quality of nano wire, M is the quality of particle, and L is nanowire length, and E is nano wire elastic modulus, and I is moment of inertia (engineering science definition), and is respectively two different constants.
Specific works flow process of the present invention is as follows:
(1) when passing into device of the present invention without environmental gas, high frequency electrical signal being added to device, measuring the local frequency of nano-wire array;
(2) ultraviolet irradiation is added to device of the present invention;
(3) in device of the present invention, environmental gas is passed into;
(4) high frequency electrical signal is added, the local frequency of nano-wire array after measurement adsorption particle thing;
(5) theoretical according to Euler-Bernoulli, draw the quality of particle PM2.5 in environmental gas.
(6) ultraviolet lighting is removed to these sensitive detection parts;
(7) back and forth clean air is blasted to device of the present invention, remove the particle of absorption.
See accompanying drawing 4, grow the SEM image of ZnO nanowire array.On a planar substrate, its average length is about 4 μm, and mean diameter is 150nm in ZnO nano-wire growth.
Described ZnO nanowire array, because nano-wire array adopts lateral growth method fixing between two electrodes, therefore its length is consistent, the resonant frequency narrow bandwidth of array, improves the accuracy of finely ground particles quality detection.Due to the small-size effect of nano wire, the detection sensitivity of device to Tiny Mass particle is high, without the need to asking quality average to the particle in a large amount of gas, accelerates detection efficiency.
Because ZnO is a kind of photochromics, under UV-irradiation, its surface wettability can realize the reversible transformation between hydrophilic-hydrophobic, therefore, in the course of work of device, add ultraviolet lighting, increase the adsorbability of nano wire 5 pairs of particles 6, after quality detection terminates, remove ultraviolet lighting, and ventilate, realize the automatically cleaning of device.
The detection that the present invention will be converted into the detection of quality electricity frequency, make device volume little, environmental suitability is high, and meanwhile, utilize the surface effect of ZnO nano-wire, device layout of the present invention has self-cleaning function, is suitable for the application scenario of environmental monitoring.
The present invention possesses self-cleaning function, increase its serviceable life, and it is little to have volume, lightly portable feature, and environmental suitability is strong, is applicable to burying the detection node being distributed in sensor network in a large number, carries out the Monitoring and forecasting system in real-time of air quality.
Claims (6)
1. the mass sensitivity device based on the surrounding air PM2.5 particle of ZnO nanowire array, it is characterized in that: there is a groove at the back side of silicon substrate, thickness between bottom portion of groove and silicon substrate front is between 20 microns ~ 50 microns, the rectangular ventilation holes of two-stage step is carved with in silicon substrate front, above, the side of one-level step two longer sides and surface are electrodes, ZnO nano-wire is lateral growth at the electrode of one-level step above on two sides of air vent, ZnO nano-wire is suspended on above air vent, and the two ends of ZnO nano-wire are connected on two electrodes.
2. the mass sensitivity device of a kind of surrounding air PM2.5 particle based on ZnO nanowire array according to claim 1, it is characterized in that, the length of the rectangular ventilation holes of described two-stage step is 10 microns, the width of one-level step is 4 μm above, below the width of one-level step be 3 μm.
3. the mass sensitivity device of a kind of surrounding air PM2.5 particle based on ZnO nanowire array according to claim 1, it is characterized in that, on described electrode, lateral growth has ZnO nanowire array to adopt lateral growth method fixing between two electrodes, the mean diameter of ZnO nano-wire is 150nm, the length of ZnO nano-wire is consistent, be about 4 μm, therefore the resonant frequency bandwidth of ZnO nanowire array is narrower, improves the accuracy of finely ground particles quality detection.
4. the mass sensitivity device of a kind of surrounding air PM2.5 particle based on ZnO nanowire array according to claim 1, it is characterized in that, the metal component layer of described electrode is followed successively by Ti, Al, Ni, Au from top to bottom, the gross thickness of electrode is 200nm, and each metal component layer is 50nm.
5. the mass sensitivity device of a kind of surrounding air PM2.5 particle based on ZnO nanowire array according to claim 1, it is characterized in that, the surface wettability of described ZnO nano-wire can by UV-irradiation realize Qin Shui ?the reversible transformation of hydrophobic, ultraviolet irradiation is applied to it and increases the adsorbability of ZnO nano-wire to particle, and after the detection of PM2.5 granular mass terminates, remove ultraviolet lighting, and back and forth pass into clean air, the microparticle be adsorbed on nano wire is removed, realizes the automatically cleaning of device.
6. the preparation method of the mass sensitivity device of a kind of surrounding air PM2.5 particle based on ZnO nanowire array according to the arbitrary claim of claim 1 to 5, it is characterized in that, concrete preparation process is as follows:
First S1 prepares the groove of substrate back, adopt laser boring, the method for solution corrosion or ICP the silicon substrate back side is carved one long and wide be the groove of 10 microns;
The silicon substrate that back in S1 is carved groove by S2 cleans up and dries up rear back side wax and protect;
S3 is by after the silicon substrate front baking in S2, and front spin coating positive photoetching rubber, dries, exposes, develops, made by lithography at positive photoetching rubber position above silicon substrate front, its rear channel after post bake the groove of long 10 μm, wide 4 μm through later;
The silicon substrate that photoresist in S3 carves groove is put into KOH solution by S4, is not eroded away the rectangular recess of dark 1.5 μm of rule by the position that photoresist is protected, then wash away photoresist with acetone in silicon substrate front;
S5 is by the silicon substrate in S4 again through a photoetching and solution corrosion, and in S4, the central authorities of the rectangular recess that silicon substrate front carves carve long 10 μm a, through hole of wide 3 μm, prepared by the air vent now with two-stage step;
S6 will be carved with the silicon substrate of rear channel and two-stage step air vent again through a photoetching in S5, make at the side electrode position of air vent the groove that electrode prepares position by lithography;
The silicon substrate being carved with electrode position groove in S6 is put into magnetron sputtering apparatus by S7, at sidewall and surface portion sputtered with Ti, Al, Ni, Au layer successively of air vent side first order step, each metal layer thickness is 200nm, wash away photoresist with acetone again, now prepared by the electrode of air vent side;
Silicon substrate after the electrode of air vent side in S7 has been prepared by S8, again through a photoetching, makes the groove of ZnO Seed Layer position on electrode sidewall side by lithography near the position of air vent;
Silicon substrate after photoetching in S8 is put into magnetron sputtering by S9, and at the ZnO film that electrode sidewall surface sputtering 200nm is thick, prepared by the ZnO Seed Layer now on electrode;
S10 is by the zinc nitrate hexahydrate (Zn (NO of equimolar ratio example
3)
26H
2o) and hexamethylenetetramine (HMTA) be dissolved in deionized water, stir, be mixed with the solution of 25mmol/L as precursor solution;
S11 gets 15mL precursor solution and puts into hydrothermal reaction kettle, then electrode top in S9 is capped silicon substrate put into hydrothermal reaction kettle, at 80 DEG C, react growing ZnO nano-wire, continue 8h;
Growth has the substrate of ZnO nano-wire to take out by S12, repeatedly rinses, dry in nitrogen with deionized water;
The length rinsed well in S12 is had the substrate of ZnO nano-wire again through a photoetching by S13, in the other side of air vent, does not namely grow and has ZnO nano-wire side, make the groove that electrode position goes out by lithography;
Substrate after photoetching in S13 is put into magnetic control sputtering device by S14, at sidewall and surface portion sputtered with Ti, Al, Ni, Au layer successively of air vent other side first order step, each metal layer thickness is 200nm, photoresist is washed away again with acetone, now prepared by the electrode of the other side of air vent, now ZnO nanowire array is fixing between two electrodes, has just made the main part of PM2.5 particulate matter quantity sensor part.
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| CN110231263A (en) * | 2019-05-23 | 2019-09-13 | 武汉大学 | A kind of PM2.5 mass sensor and preparation method thereof with self-cleaning function |
| CN110376256A (en) * | 2019-07-25 | 2019-10-25 | 天津大学 | Sensor based on nano-wire array and the detection method using the sensor |
| CN113821927A (en) * | 2021-09-24 | 2021-12-21 | 华北电力科学研究院有限责任公司 | Method and device for evaluating unstable vibration influence of rotating machinery overhanging section |
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| CN113821927A (en) * | 2021-09-24 | 2021-12-21 | 华北电力科学研究院有限责任公司 | Method and device for evaluating unstable vibration influence of rotating machinery overhanging section |
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