CN108412947A - A kind of low frequency wide area structure vibration-repressing device that control frequency domain is tunable - Google Patents

A kind of low frequency wide area structure vibration-repressing device that control frequency domain is tunable Download PDF

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Publication number
CN108412947A
CN108412947A CN201810562822.7A CN201810562822A CN108412947A CN 108412947 A CN108412947 A CN 108412947A CN 201810562822 A CN201810562822 A CN 201810562822A CN 108412947 A CN108412947 A CN 108412947A
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counter weight
vibration
weight base
axis
conductor tube
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CN108412947B (en
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李斌
郭通
牛文超
张生坤
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Northwestern Polytechnical University
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Northwestern Polytechnical University
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/02Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
    • F16F15/03Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using magnetic or electromagnetic means
    • F16F15/035Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using magnetic or electromagnetic means by use of eddy or induced-current damping
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/02Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
    • F16F15/04Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using elastic means

Abstract

A kind of low frequency wide area structure vibration-repressing device that control frequency domain is tunable, including matrix beam and multiple resonating body.Matrix beam is the metallic plate of bar shaped, and the threaded hole of multiple axis is evenly equipped on the metallic plate, and multiple resonating body are mounted on by the axis in the resonating body in the threaded hole respectively.The centre-to-centre spacing of each adjacent resonating body is 8~20cm.The present invention by by matrix beam vibration energy transfer to resonating body with realize matrix beam vibration decay;By way of the additional magnet in resonating body or counterweight casing, change damping or the mass parameter of resonating body, to adjust and widen low bandgap, improves structural low-frequency vibration characteristic.The present invention significantly improves the damping characteristic of structure, so that the rigidity of structure is introduced non-linear, the low bandgap of the further widened structure of energy.Meanwhile the present invention reduce structural wear, extend total system 10 times of service life or more, and have the characteristics that it is easy to use, occupy little space, have the wider scope of application in engineering.

Description

A kind of low frequency wide area structure vibration-repressing device that control frequency domain is tunable
Technical field
The present invention relates to vibration control fields, are specifically related to a kind of low frequency wide area structure vibration suppression that control frequency domain is tunable Device.
Background technology
Beam structure is widely present in the engineering fields such as building, machinery as a kind of foundation structure, and vibration control is always Since be all researcher concern emphasis.In general, vibration control is divided into passive control and active control, passive control is aobvious Work feature is to be not required to outside energy injection, and traditional approach mainly has additional power bump leveller, visco-elastic damping layer etc., but is limited by The limitations such as installation space, and it is difficult to realize wide band strong effectiveness in vibration suppression.Active control then needs outside energy to inject, and there are stabilizations Poor, the of high cost disadvantage of property, therefore the highly desirable passive control mode for designing new model of researcher.
Phonon crystal refers to a kind of novel cycle composite material for having periodicity and locally resonant feature.Elastic wave is in week When phase property elastic composite Propagation, the transmission that elastic wave band gaps hinder elastic wave is will produce, to realize the vibration damping of structure. The research of phonon crystal successfully realizes " elastic fluid medium wave propagation manipulation ", is for a kind of new side of passive type vibration control Method has wide application prospects in terms of structural vibration control.
Bragg band gap and local LOCALLY RESONANT ELASTIC WAVE can be divided into according to band gap mechanism of production, Bragg band gap is mainly by structural cycle Property caused by, it is larger by structure parameters influence, occurrence frequency mainly by Bragg conditions control, lattice dimensions at least with elasticity The half wavelength of wave is suitable, this feature makes it be difficult to generate low bandgap on small size periodic structure.Locally resonant band gap Energy localization effect when then based on resonating body local vibration is, it can be achieved that structure Asia size wavelength band gap.Therefore, locally resonant type Phonon crystal can be used as low frequency, small space the effective means for subtracting vibration suppression.
Locally resonant type phonon crystal design studies at present have no and resonating body are discussed in detail mostly based on preset parameter structure Parameter Modulation, especially damping parameter modulate the affecting laws to structural elasticity wavestrip gap, this will seriously limit locally resonant type The effect frequency range of phonon crystal.Harbin Institute of Technology discloses one in the patent of invention that notification number is 104141720 A of CN Flase floor of the kind based on locally resonant type phonon crystal theory, the flase floor parameters fix, are only capable of inhibiting specific frequency domain model Interior structural vibration is enclosed, therefore the scope of application has very big limitation.PLA University of Science and Technology for National Defense is in notification number A kind of locally resonant type phonon crystal girder construction with super damping characteristic is disclosed in the patent of invention of 107701635 A of CN, The damping characteristic of the invention is provided by a rubber strip, but occupied space is big and cannot achieve band gap frequency modulation, therefore in aircraft, automobile The vibration damping of the high-precision equipment such as engine is also greatly limited in.Taiwan Univ. Hsin-Haou Huang 2011 exist Dispatch proposes a kind of with particular resonance on Journal of the Mechanics and Physics of Solids periodicals The mechanical model of the phonon crystal of device, but the model is only capable of adjusting band gap by tuned resonator rigidity.Harvard University Filippo Cassadei send the documents for 2014 on Journal of Apaplied Physics proposes that one kind being based on stream coupling admittedly The phonon crystal model of cooperation, the model change resonating body rigidity to adjust band gap frequency essentially by structure large deformation Domain.
Invention content
To overcome use scope existing in the prior art limited, it is unsuitable for aircraft, automobile engine high-precision is equipped The deficiency of vibration damping, the present invention propose a kind of low frequency wide area structure vibration-repressing device that control frequency domain is tunable.
The present invention includes matrix beam and multiple resonating body.The matrix beam is the metallic plate of bar shaped, on the metallic plate It is evenly equipped with the threaded hole of multiple axis, the multiple resonating body is mounted on by the axis in the resonating body in the threaded hole respectively. The centre-to-centre spacing of each adjacent resonating body is 8~20cm.
The resonating body includes axis, magnet, conductor tube, linear bearing, helical spring, counter weight base and counterweight casing. The linear bearing is sleeved on the middle part of axis, and makes to be slidably matched therebetween.Counter weight base is set with and is fixed on the straight line The external peripheral surface of bearing.The lower end of conductor tube is sleeved on the external peripheral surface of the counter weight base, and makes under the conductor tube The upper surface of end face and counter weight base chassis.The upper end of counterweight casing is set with and is fixed on the external peripheral surface of the conductor tube; The lower face of the counterweight casing coordinates with the upper surface on counter weight base chassis.Magnet is fixed on the upper surface center of the axis.Spiral shell It revolves spring pocket and is mounted in the lower end of the axis, and the top of the helical spring is made to be embedded in the spring groove of the chassis lower surface.
The counter weight base internal diameter is slightly larger than the outer diameter of linear bearing, makes to be slidably matched therebetween.In the counter weight base The external peripheral surface of lower end has the chassis of radially protruding, is useful for being embedded in the spring groove of helical spring in the lower surface on the chassis. There is the radial threaded hole for penetrating through the shell on the shell of the counter weight base upper end, by screw thread by counter weight base and linear bearing It holds out against.
The internal diameter of the counterweight sleeve upper end is identical as the outer diameter of conductor tube;It is evenly equipped on the shell of counterweight sleeve upper end more A radial direction penetrates through the threaded hole of the shell.The outer diameter of the counterweight lower end is identical as the outer diameter on the chassis on counter weight base.
The internal diameter of the conductor tube is identical as the minimum outer diameter of counter weight base.The length of the conductor tube must be more than the length of axis Degree.
The outer diameter of the magnet is slightly less than the internal diameter of the conductor tube, make the magnet external peripheral surface and conductor tube it is interior There is the gap of 1~2mm between circumferential surface.
The present invention includes matrix beam and resonating body, by by matrix beam vibration energy transfer to resonating body, to realize base Body beam vibration is decayed.
Compared with prior art, the technique effect that the present invention obtains is:
1, the tunable low frequency wide area structure vibration-repressing device of control frequency domain provided by the invention, passes through the period on matrix beam The mode for arranging resonating body decays in matrix beam vibration energy transfer to resonating body to enhance matrix beam vibration.
2, the tunable low frequency wide area structure vibration-repressing device of control frequency domain provided by the invention, by being added in resonating body The mode of magnet and counterweight casing changes damping and the mass parameter of resonating body, to adjust and widen low bandgap, improves knot Structure low-frequency vibration characteristic.
3, the tunable low frequency wide area structure vibration-repressing device of control frequency domain provided by the invention, is utilized eddy-current damping original Reason, compared with traditional rubber damping, hence it is evident that the damping characteristic for improving structure makes the rigidity of structure introduce non-linear, can be further The low bandgap of widened structure.
4, the tunable low frequency wide area structure vibration-repressing device of control frequency domain provided by the invention, it is former based on eddy-current damping Reason, magnet generate a kind of contactless field force inhibition structural vibration with conductor tube relative motion, reduce structural wear, extend entire 10 times of service life of structural system or more.
5, the tunable low frequency wide area structure vibration-repressing device of control frequency domain provided by the invention, it is attached by way of external hanging type Counterweight casing, casing is added to be conveniently increased and decreased so that the adjustment of band gap frequency domain is more prone to.
6, the tunable low frequency wide area structure vibration-repressing device of control frequency domain provided by the invention, it is convenient for disassembly and assembly, with tradition suppression Structure of shaking is compared, and occupied space reduces 50% or more, can accurately adjust structure band gap frequency domain, is had in engineering and is widely applicable in Range.
Description of the drawings
Fig. 1 is the structural schematic diagram of the embodiment of the present invention.
Fig. 2 is the vertical view of the embodiment of the present invention.
Fig. 3 is the structural schematic diagram of resonating body.
Matrix vibration of beam transport curve when Fig. 4 is different movable quality.
Matrix vibration of beam transport curve when Fig. 5 is different magnet numbers.
In figure:
1. matrix beam;2. axis;3. magnet;4. conductor tube;5. linear bearing;6. helical spring;7. counter weight base;8. counterweight Casing;9. screw;10. matrix vibration of beam transport curve when counterweight casing quality 155g;11. when counterweight casing quality 65g Matrix vibration of beam transport curve;12. matrix vibration of beam transport curve when adding 2 magnet;13. when without additional magnet Matrix vibration of beam transport curve;14. resonating body.
Specific implementation mode
The present embodiment is a kind of low frequency wide area structure vibration-repressing device that Parameter adjustable is humorous, including matrix beam and multiple resonance Body.The matrix beam 1 is the metallic plate of bar shaped, and the threaded hole of multiple axis 2, the multiple resonance are evenly equipped on the metallic plate Body 14 is mounted on by the lower end of the resonating body axis in the threaded hole respectively.The centre-to-centre spacing of each adjacent resonating body is 8~20cm.In the present embodiment, the centre distance of adjacent resonating body 14 is 10cm.
The resonating body includes axis 2, magnet 3, conductor tube 4, linear bearing 5, helical spring 6, counter weight base 7 and counterweight Casing 8.The linear bearing 5 is sleeved on the middle part of axis 2, and makes to be slidably matched therebetween.Counter weight base 7 is set with and is fixed on The external peripheral surface of the linear bearing.The lower end of conductor tube 4 is sleeved on the external peripheral surface of the counter weight base, and this is made to lead The upper surface of the lower face and counter weight base chassis of body pipe 4.The upper end of counterweight casing 8 is set with and is fixed on the outer of the conductor tube Circumferential surface;The lower face of the counterweight casing coordinates with the upper surface on counter weight base chassis.Magnet 3 is fixed on institute by screw 9 State the upper surface center of axis 2.Helical spring 6 is sleeved on the lower end of the axis, and the top of the helical spring is made to be embedded in the bottom In the spring groove of disk lower surface.
The top end face center of the axis 2 has tapped blind hole, for installing magnet 3;The axis lower end is external screw thread face.
The counter weight base 7 is hollow revolving body, and internal diameter is slightly larger than the outer diameter of linear bearing 5, makes to slide therebetween Cooperation.External peripheral surface in the counter weight base lower end has the chassis of radially protruding, and the outer diameter and counterweight casing 8 on the chassis are most Big outer diameter is identical, is useful for being embedded in the spring groove of helical spring 6 in the lower surface on the chassis.The shell of 7 upper end of the counter weight base There is the radial threaded hole for penetrating through the shell on body, is held out against counter weight base and linear bearing 5 by screw thread.
The counterweight casing 8 is also hollow revolving body.The outer diameter phase of the internal diameter of the counterweight sleeve upper end and conductor tube 4 Together;The threaded hole that multiple radial directions penetrate through the shell is evenly equipped on the shell of counterweight sleeve upper end, when the counterweight casing is sleeved on institute After stating in conductor tube, the counterweight casing is held out against with conductor tube by screw.The outer diameter of the counterweight lower end and counterweight bottom The outer diameter on the chassis on seat 7 is identical.
The conductor tube 4 is pipe.The internal diameter of the conductor tube is identical as the minimum outer diameter of counter weight base 7.The conductor tube Length must be more than axis 2 length.
The outer diameter of the magnet 3 is slightly less than the internal diameter of the conductor tube, makes the external peripheral surface and conductor tube of the magnet There is the gap of 1~2mm between inner circumferential surface.There is threaded hole at the center of the magnet.
When assembly:
The magnet 3 and the upper surface of the axis 2 fasten, and are respectively positioned in the conductor tube 4, and magnet 3 is pancake shape, magnet 3 outer diameters are smaller 2~4mm than 4 internal diameter of the conductor tube.
4 lower face of the conductor tube is connected with 7 upper surface of the counter weight base, and fastens;Counterweight casing 8 is hung on conductor 4 periphery of pipe simultaneously fastens, and 8 lower face of counterweight casing is fitted closely with section on counter weight base 7, and counter weight base 7 is same with counterweight casing 8 Axis and outer diameter is equal.
7 lower face of the counter weight base is welded with 6 upper surface of the helical spring, and linear bearing 5 is made to be packed into counterweight bottom In the blind hole at 7 centers of seat, the two fastens.
The axis 2 is packed into the linear bearing 5, and the lower face of the axis 2 connect and fastens with matrix beam 1.
It is welded with matrix beam 1 lower face of the helical spring 6.
Conductor tube 4, magnet 3, helical spring 6, counter weight base 7, counterweight casing 8, linear bearing 5 are coaxial with the axis 2.
At work, the resonating body rigidity for introducing eddy-current damping is the present embodiment:
ke=k (1+i η) (η=ω c/k)
K is undamped resonating body rigidity, and c is damped coefficient, and η is fissipation factor, and ω is angular speed, and (1+i η) is equivalent multiple Stiffness coefficient.
It brings resonating body rigidity and the assembling of 1 stiffness matrix of matrix beam into kinetics equation, obtains shaking for periodic structure unit cell Dynamic simple harmonic quantity equation:
(Kc(q)-ω2Mc)lc=Fc(Kc=K+ke)
KcFor unit cell global stiffness, McFor unit cell gross mass, lcFor displacement vector, FcFor force vector, a wave vector q is often given One group of ω can be solved to get to corresponding energy band curve, respective frequencies vibration will have in bandgap range substantially to decay.
The unit cell is the coupling body of the short beam composition at single resonating body and place.The short beam is that matrix beam is equal After being divided into five sections, one short beam of each section of formation.
Found out by the above process, adjust resonance weight and damping parameter energy Effective Regulation low bandgap range and widened low Band gap range.
In the present embodiment, the weight of counter weight base 7, conductor tube 4 and 5 three of linear bearing in the resonating body 14 is total The weight of 65g, axis 2 and screw for fixing amounts to 40g;The weight of matrix beam 1 is 16.2g.
Transport T=10*lgw/W is defined, end excitation mode is taken to verify effectiveness in vibration suppression;The w is beam end position Response is moved, W is excitation end movement response.
In the present embodiment, by changing the weight or unit cell itself damped coefficient of unit cell, change being total to for unit cell to realize Vibration frequency, and then change band gap frequency domain.
When changing band gap frequency domain by changing the weight of unit cell to realize, plug-in two counterweight casings 8 in conductor tube, Change the movable quality of resonating body, is tested by aforementioned condition.The piece weight of the counterweight casing is 45g.Fig. 4 is to test knot Fruit.In figure, when by plug-in 2 counterweight casings 8, base when the vibration transmissibility curve 10 of matrix beam 1 is with without plug-in counterweight casing 8 The comparison of the vibration transmissibility curve 11 of body beam 1, it can be seen that with the increase of 8 weight of counterweight casing, band gap lower limit declines, and Band gap width broadens, and band gap center frequency is resonating body intrinsic frequency, and structural vibration has greater attenuation in band gap frequency domain.In figure Ordinate 0db is band gap frequency domain with lower part.
When changing band gap frequency domain by changing itself damped coefficient of unit cell to realize, increase by 2 magnetic on the top of axis 2 Iron 3;Since unit cell itself damped coefficient is 0.5Ns/m, often increase by one block of magnet 3, itself damped coefficient of the unit cell will also increase Add 0.5Ns/m.The unit cell damped coefficient of 2 magnet 3 is 1.5Ns/m;The unit cell damped coefficient of no additional magnet 3 is 0.5N·s/m.Fig. 5 is test result.Compare when magnet 3 in figure is 2 the vibration transmissibility curve 12 of matrix beam 1 with without attached The vibration transmissibility curve of matrix beam 1 when adding magnet 3 finds to increase with 3 quantity of magnet, and resonating body damping increases, the band gap upper limit It moves up, lower limit moves down, and bandgap range expands.
It is therefore seen that the frequency domain tunable low frequency wide area structure vibration-repressing device provided in this embodiment that controls is reasonable for structure, It can be by adjusting the quantity of counterweight casing 8 or the quantity of magnet 3, to realize that resonance weight or damping parameter tune, in turn It accurately controls band gap frequency domain and widens bandgap range.

Claims (6)

1. a kind of tunable low frequency wide area structure vibration-repressing device of control frequency domain, which is characterized in that including matrix beam and multiple total Vibration body;The matrix beam is the metallic plate of bar shaped, and the threaded hole of multiple axis, the multiple resonance are evenly equipped on the metallic plate Body is mounted on by the axis in the resonating body in the threaded hole respectively;The centre-to-centre spacing of each adjacent resonating body be 8~ 20cm。
2. the tunable low frequency wide area structure vibration-repressing device of control frequency domain as described in claim 1, which is characterized in that described is total to Vibration body includes axis, magnet, conductor tube, linear bearing, helical spring, counter weight base and counterweight casing;The linear bearing suit At the middle part of axis, and make to be slidably matched therebetween;Counter weight base is set with and is fixed on the external peripheral surface of the linear bearing; The lower end of conductor tube is sleeved on the external peripheral surface of the counter weight base, and makes lower face and the counter weight base chassis of the conductor tube Upper surface;The upper end of counterweight casing is set with and is fixed on the external peripheral surface of the conductor tube;The lower face of the counterweight casing Coordinate with the upper surface on counter weight base chassis;Magnet is fixed on the upper surface center of the axis;Helical spring is sleeved on the axis Lower end, and the top of the helical spring is made to be embedded in the spring groove of the chassis lower surface.
3. the tunable low frequency wide area structure vibration-repressing device of control frequency domain as described in claim 1, which is characterized in that the counterweight Base inner diameter is slightly larger than the outer diameter of linear bearing, makes to be slidably matched therebetween;External peripheral surface in the counter weight base lower end The chassis for having radially protruding is useful for being embedded in the spring groove of helical spring in the lower surface on the chassis;The counter weight base upper end Shell on have the radial threaded hole for penetrating through the shell, counter weight base and linear bearing are held out against by screw thread.
4. the tunable low frequency wide area structure vibration-repressing device of control frequency domain as described in claim 1, which is characterized in that the counterweight The internal diameter of sleeve upper end is identical as the outer diameter of conductor tube;It is evenly equipped with multiple radial directions on the shell of counterweight sleeve upper end and penetrates through the shell Threaded hole;The outer diameter of the counterweight lower end is identical as the outer diameter on the chassis on counter weight base.
5. the tunable low frequency wide area structure vibration-repressing device of control frequency domain as described in claim 1, which is characterized in that the conductor The internal diameter of pipe is identical as the minimum outer diameter of counter weight base;The length of the conductor tube must be more than the length of axis.
6. the tunable low frequency wide area structure vibration-repressing device of control frequency domain as described in claim 1, which is characterized in that the magnet Outer diameter be slightly less than the internal diameter of the conductor tube, make have 1 between the external peripheral surface of the magnet and the inner circumferential surface of conductor tube The gap of~2mm.
CN201810562822.7A 2018-06-04 2018-06-04 Low-frequency wide-domain structure vibration suppression device with tunable control frequency domain Active CN108412947B (en)

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Cited By (6)

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Publication number Priority date Publication date Assignee Title
CN110195756A (en) * 2019-06-28 2019-09-03 上海超颖声学科技有限公司 A kind of vibration suppression structure
CN110439949A (en) * 2019-09-03 2019-11-12 东南大学 A kind of periodic structure with nonlinear energy trap
CN110594331A (en) * 2019-09-19 2019-12-20 哈尔滨工程大学 Hierarchical periodic structure metamaterial beam suitable for multi-frequency-band vibration reduction
CN110594332A (en) * 2019-09-24 2019-12-20 哈尔滨工程大学 Wide-frequency-band vibration-damping noise-reducing metamaterial multi-span beam structure
CN114370474A (en) * 2021-12-31 2022-04-19 中国舰船研究设计中心 Frequency conversion phononic crystal vibration suppression device for structure
CN114992271A (en) * 2022-07-18 2022-09-02 上海秦耀航空试验技术有限公司 Airplane vibration reduction component, aviation wall plate and band gap design method

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CN106763476A (en) * 2016-11-15 2017-05-31 上海交通大学 A kind of sandwich sandwich plate vibration absorbing structure based on miniature locally resonant subarray
CN107701635A (en) * 2017-06-19 2018-02-16 中国人民解放军国防科学技术大学 Broad band low frequency locally resonant structure with super damping characteristic

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JP2001153175A (en) * 1999-11-29 2001-06-08 Bridgestone Corp Active vibration absorber
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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110195756A (en) * 2019-06-28 2019-09-03 上海超颖声学科技有限公司 A kind of vibration suppression structure
CN110439949A (en) * 2019-09-03 2019-11-12 东南大学 A kind of periodic structure with nonlinear energy trap
CN110594331A (en) * 2019-09-19 2019-12-20 哈尔滨工程大学 Hierarchical periodic structure metamaterial beam suitable for multi-frequency-band vibration reduction
CN110594332A (en) * 2019-09-24 2019-12-20 哈尔滨工程大学 Wide-frequency-band vibration-damping noise-reducing metamaterial multi-span beam structure
CN114370474A (en) * 2021-12-31 2022-04-19 中国舰船研究设计中心 Frequency conversion phononic crystal vibration suppression device for structure
CN114370474B (en) * 2021-12-31 2023-12-05 中国舰船研究设计中心 Variable-frequency phonon crystal vibration suppression device for structure
CN114992271A (en) * 2022-07-18 2022-09-02 上海秦耀航空试验技术有限公司 Airplane vibration reduction component, aviation wall plate and band gap design method
CN114992271B (en) * 2022-07-18 2022-11-18 上海秦耀航空试验技术有限公司 Airplane vibration reduction component, aviation wall plate and band gap design method

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