CN109936107B - Power transmission line frequency-staggering coupling vibration attenuation control method - Google Patents
Power transmission line frequency-staggering coupling vibration attenuation control method Download PDFInfo
- Publication number
- CN109936107B CN109936107B CN201910249672.9A CN201910249672A CN109936107B CN 109936107 B CN109936107 B CN 109936107B CN 201910249672 A CN201910249672 A CN 201910249672A CN 109936107 B CN109936107 B CN 109936107B
- Authority
- CN
- China
- Prior art keywords
- transmission line
- tension
- pay
- phase
- frequency
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 230000005540 biological transmission Effects 0.000 title claims abstract description 115
- 230000008878 coupling Effects 0.000 title claims abstract description 22
- 238000010168 coupling process Methods 0.000 title claims abstract description 22
- 238000005859 coupling reaction Methods 0.000 title claims abstract description 22
- 238000000034 method Methods 0.000 title claims abstract description 21
- 230000016507 interphase Effects 0.000 claims abstract description 9
- 125000006850 spacer group Chemical group 0.000 claims description 21
- 239000004020 conductor Substances 0.000 claims description 8
- 238000013016 damping Methods 0.000 abstract description 6
- 230000003796 beauty Effects 0.000 abstract description 4
- 230000007423 decrease Effects 0.000 description 7
- 238000010586 diagram Methods 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
- 238000010276 construction Methods 0.000 description 3
- 238000012938 design process Methods 0.000 description 2
- 239000006185 dispersion Substances 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
Images
Landscapes
- Suspension Of Electric Lines Or Cables (AREA)
Abstract
本发明公开了一种输电线路错频耦合减振控制方法。本发明主要是将传统采用的三相输电线路放线张力相同、弧垂相同、走向平行的输电线原始构型，改为采用三相放线张力差异化的输电线减振构型，张力的差异化引起三相弹簧振子的频率差异化，通过相间振子的频率错配和耦合实现整个系统的减振控制；输电线减振构型相对于原始构型的弧垂变化幅度控制在适度范围内，以保障线路安全运营且线型整体协调美观。本发明通过调整三相输电线路的放线张力，较好地解决了大跨柔性结构振动控制问题。
The invention discloses a control method for frequency-staggered coupling vibration reduction of a transmission line. The present invention mainly changes the original configuration of the traditional three-phase transmission line with the same pay-off tension, the same sag and parallel orientation, to a transmission line vibration-damping configuration with different three-phase pay-off tensions. The difference causes the frequency difference of the three-phase spring oscillators, and the vibration reduction control of the whole system is realized through the frequency mismatch and coupling of the interphase oscillators; the amplitude of the sag change of the transmission line vibration reduction configuration relative to the original configuration is controlled within a moderate range , in order to ensure the safe operation of the line and the overall coordination and beauty of the line. The invention better solves the problem of vibration control of large-span flexible structures by adjusting the pay-off tension of the three-phase transmission line.
Description
技术领域technical field
本发明属于大跨柔性结构减振技术领域，具体涉及一种基于放线张力差异化的输电线路错频耦合减振控制方法。The invention belongs to the technical field of vibration reduction of large-span flexible structures, and in particular relates to a control method for frequency-staggered coupling vibration reduction of transmission lines based on differential pay-off tension.
背景技术Background technique
架空输电线路属于大跨柔性结构，当受强风、地震及脱冰等极端环境激励作用时，线路会产生大幅的低频振动，容易引起相间闪络跳闸，甚至造成断线倒塔等严重事故。传统的阻尼减振装置只能安装在输电塔附近，对整个线路来说，并不能起到有效的减振控制作用；谐振减振装置的适用频带又窄，对于在宽频环境激励作用下的输电线路而言，其减振效果具有很大的局限性。本发明申请人前期的发明专利“多振子耦合输电线路减振系统”(ZL201710260918.3)提出：频率错配、耦合强度、时间延迟是实现振幅死亡的三个关键因素，通过调整这三个参数，可以使整个输电线系统达到一个最优的状态，从而实现输电线振幅死亡，达到减振控制的目的。在此基础上，如何提供一种简单有效的可以实现频率错配的方法，是我们进一步研究的目的。Overhead transmission lines are large-span flexible structures. When stimulated by extreme environments such as strong winds, earthquakes, and de-icing, the lines will generate large low-frequency vibrations, which may easily cause phase-to-phase flashovers and trips, and even cause serious accidents such as line breakage and tower collapse. The traditional damping and vibration reduction device can only be installed near the transmission tower, and cannot play an effective vibration reduction control role for the entire line; the applicable frequency band of the resonance vibration reduction device is narrow, and it is not suitable for power transmission under the excitation of a broadband environment. As far as the line is concerned, its vibration reduction effect has great limitations. The applicant's earlier invention patent "Multi-oscillator coupled transmission line vibration reduction system" (ZL201710260918.3) proposed that frequency mismatch, coupling strength, and time delay are the three key factors to achieve amplitude death. By adjusting these three parameters , which can make the entire transmission line system reach an optimal state, so as to realize the amplitude death of the transmission line and achieve the purpose of vibration reduction control. On this basis, how to provide a simple and effective method that can realize frequency mismatch is the purpose of our further research.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供一种能较好地解决大跨柔性结构振动控制问题的输电线路错频耦合减振控制方法，即调整三相输电线路的放线张力，张力的差异化引起三相弹簧振子的频率差异化，通过相间振子的频率错配和耦合实现整个系统的减振控制。The purpose of the present invention is to provide a transmission line cross-frequency coupling vibration reduction control method that can better solve the vibration control problem of large-span flexible structures, that is, to adjust the pay-off tension of the three-phase transmission line, and the difference in tension causes the three-phase spring The frequency of the oscillators is differentiated, and the vibration reduction control of the entire system is realized through the frequency mismatch and coupling of the interphase oscillators.
本发明的目的是通过如下的技术方案来实现的：The purpose of this invention is to realize through the following technical scheme:
该输电线路错频耦合减振控制方法，是一种基于设置有间隔棒输电线路的放线张力差异化减振控制方法；所述设置有间隔棒输电线路是，在每相输电线路上设置有若干间隔棒，间隔棒将每相输电线路的四分裂导线间隔分开，在三相输电线路相互之间也设置有相间间隔棒；其特点是：将传统采用的三相输电线路放线张力相同、弧垂相同、走向平行的输电线原始构型，改为采用三相放线张力差异化的输电线减振构型，张力的差异化引起三相弹簧振子的频率差异化，通过相间振子的频率错配和耦合实现整个系统的减振控制；输电线减振构型相对于原始构型的弧垂变化幅度控制在适度范围内，以保障线路安全运营且线型整体协调美观。The transmission line frequency-staggered coupling vibration damping control method is a differential vibration damping control method based on the transmission line provided with spacer bars; the transmission line provided with spacer bars is: A number of spacer bars, the spacer bars separate the four-split conductors of each phase transmission line, and interphase spacer bars are also arranged between the three-phase transmission lines; its characteristics are: the traditional three-phase transmission lines have the same pay-off tension, The original configuration of the transmission line with the same sag and parallel orientation is changed to a transmission line vibration reduction configuration with different three-phase pay-off tensions. Mismatch and coupling realize the vibration reduction control of the entire system; the sag variation of the transmission line vibration reduction configuration relative to the original configuration is controlled within a moderate range to ensure the safe operation of the line and the overall coordination and beauty of the line shape.
所述输电线减振构型相对于原始构型的弧垂变化幅度控制在适度范围内的具体方法是：将空间位置最高的一相输电线路的放线张力上调3％～5％，其余两相输电线路的放线张力统一下调3％～5％；或者，将空间位置最高的一相输电线路的放线张力保持不变，其余两相输电线路的放线张力统一下调6％～10％。The specific method for controlling the sag variation amplitude of the transmission line vibration reduction configuration relative to the original configuration within a moderate range is: increasing the pay-off tension of the one-phase transmission line with the highest spatial position by 3% to 5%, and the remaining two The pay-off tension of the phase transmission line shall be uniformly reduced by 3% to 5%; or, the pay-off tension of the one-phase transmission line with the highest spatial position shall remain unchanged, and the pay-off tension of the remaining two-phase transmission lines shall be uniformly reduced by 6% to 10%. .
进一步，空间位置最高的一相输电线路的放线张力与其余两相输电线路的放线张力的差异化控制到10％。这样，整个系统的错频耦合减振效果非常明显，甚至达到接近振幅死亡的最优控制状态。Further, the difference between the pay-off tension of the one-phase transmission line with the highest spatial position and the pay-off tension of the remaining two-phase transmission lines is controlled to 10%. In this way, the frequency-staggered coupling vibration reduction effect of the whole system is very obvious, and even reaches the optimal control state close to the amplitude death.
具体的，输电线路的放线张力与输电线路的弧垂之间的关系如式(1)所示：Specifically, the relationship between the pay-off tension of the transmission line and the sag of the transmission line is shown in formula (1):
式(1)中，T为输电线路的放线张力，m为单相输电线路单位长度的等效质量，L为输电线路的档距，h为输电线路的弧垂；In formula (1), T is the pay-off tension of the transmission line, m is the equivalent mass per unit length of the single-phase transmission line, L is the span of the transmission line, and h is the sag of the transmission line;
由公式(1)可计算单相输电线路弧垂调整后，其放线张力的变化值。According to formula (1), the change value of the pay-off tension of the single-phase transmission line after the sag adjustment can be calculated.
具体的，输电线路面外、面内的振动频率与其放线张力的关系如式(2)、式(3)所示：Specifically, the relationship between the vibration frequency outside and inside the surface of the transmission line and its pay-off tension is shown in equations (2) and (3):
式(2)、式(3)中，T为输电线路的放线张力，m为单相输电线路单位长度的等效质量，L为输电线路的档距，Fn为输电线路n阶面外振动频率，fn为输电线路n阶面内反对称振动频率；In equations (2) and (3), T is the pay-off tension of the transmission line, m is the equivalent mass per unit length of the single-phase transmission line, L is the span of the transmission line, and Fn is the n-order out-of-plane of the transmission line. Vibration frequency, f n is the in-plane antisymmetric vibration frequency of the n-order transmission line;
由式(2)、式(3)可计算输电线路的放线张力的变化值所引起的输电线路振动频率的变化值。From the formula (2) and formula (3), the change value of the vibration frequency of the transmission line caused by the change value of the pay-off tension of the transmission line can be calculated.
本发明减振方法打破常规的设计思路，即通常的架空输电线路设计过程中，三相线路的放线张力取相同的值，施工后三相线路的构型相同、走向平行的方式，利用三相放线张力的小量差异化而实现整个系统的错频耦合减振。试验研究表明，采用本发明的减振方法，当三相线路放线张力的差异化达到10％时，整个系统的错频耦合减振效果非常明显，甚至达到接近振幅死亡的最优控制状态。The vibration reduction method of the invention breaks the conventional design idea, that is, in the design process of the usual overhead transmission line, the pay-off tension of the three-phase line takes the same value, and the three-phase line after construction has the same configuration and parallel orientation. A small amount of difference in the tension of the phase pay-off line realizes the off-frequency coupling vibration reduction of the whole system. The experimental study shows that with the vibration reduction method of the present invention, when the difference of the pay-off tension of the three-phase line reaches 10%, the cross-frequency coupling vibration reduction effect of the whole system is very obvious, and even reaches the optimal control state close to the amplitude death.
附图说明Description of drawings
图1为设置有间隔棒的三相四分裂输电线路的结构示意图。FIG. 1 is a schematic structural diagram of a three-phase four-split power transmission line provided with spacer bars.
图2为图1中带有间隔棒的四分裂导线部分的放大图。FIG. 2 is an enlarged view of the four-split wire portion of FIG. 1 with spacer bars.
图3为图1所示三相四分裂输电线路的三相输电线多振子耦合动力学系统示意图。FIG. 3 is a schematic diagram of a three-phase transmission line multi-vibrator coupling dynamics system of the three-phase four-split transmission line shown in FIG. 1 .
图4为图1所示三相四分裂输电线路应用本发明方法的原理示意图。FIG. 4 is a schematic diagram of the principle of applying the method of the present invention to the three-phase four-split transmission line shown in FIG. 1 .
具体实施方式Detailed ways
下面结合附图和实施例对本发明作进一步详细的描述。The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.
参见图1，为设置有间隔棒6的三相四分裂输电线路的结构示意图，图1中，2、3、4分别表示第一、第二、第三相四分裂导线输电线路，7、8、9分别表示第一、第二、第三相四分裂导线输电线路之间设置的相间间隔棒，L为输电线路的档距，L1、L2、L3分别表示相间间隔棒7、8、9在沿线方向布置的间距。Referring to FIG. 1, it is a schematic structural diagram of a three-phase four-split transmission line provided with
为不失一般性，本发明实施例以图1所示三相四分裂输电线路为例来说明，带有间隔棒6的四分裂导线部分5的放大图如图2所示，图2中，1表示某一相的四分裂导线。将间隔棒6看作一个质量块，当间隔棒6发生位移时，输电线产生非线性弹性恢复力，因此，单个间隔棒与所连接的输电线可以简化为一个非线性弹簧振子。每相输电线路上有多个间隔棒振子，三相输电线通过相间间隔棒7、8、9构成一个大的多振子耦合动力学系统，如图3所示。Without loss of generality, the embodiment of the present invention is illustrated by taking the three-phase four-split transmission line shown in FIG. 1 as an example, and the enlarged view of the four-
参见图4，应用本发明输电线路错频耦合减振控制方法的具体过程及原理说明如下：Referring to FIG. 4 , the specific process and principle of applying the transmission line staggered frequency coupling vibration reduction control method of the present invention are described as follows:
从图4中可见，2、3、4三相输电线路的原始构型是：采用三相放线张力相同的常规设计，三相输电线弧垂相同，走向平行。It can be seen from Figure 4 that the original configuration of the 2, 3, and 4 three-phase transmission lines is: a conventional design with the same three-phase pay-off tension, the same sag of the three-phase transmission lines, and parallel directions.
10、11、12三相输电线路为分别对应于2、3、4三相输电线路采用本发明方法之后的输电线减振构型：采用三相放线张力差异化的优化设计，张力的差异化会引起三相弹簧振子的频率差异化，通过相间振子的频率错配和耦合实现整个系统的减振控制。The 10, 11, and 12 three-phase transmission lines are respectively corresponding to the 2, 3, and 4 three-phase transmission lines after adopting the method of the present invention. The frequency difference of the three-phase spring oscillators will be caused by the frequency difference, and the vibration reduction control of the whole system can be realized through the frequency mismatch and coupling of the interphase oscillators.
图4中，13、14、15为三相输电线减振构型相对于原始构型的弧垂变化幅度，从图4中可见，第一相四分裂导线输电线路2的放线张力上调变大，其弧垂变小；第二相四分裂导线输电线路3的放线张力下调变小，其弧垂变大；第三相四分裂导线输电线路4的放线张力下调变小，其弧垂变大；适度控制弧垂变化幅度，保障线路安全运营且线型整体协调美观。In Figure 4, 13, 14, and 15 are the sag changes of the three-phase transmission line's vibration reduction configuration relative to the original configuration. It can be seen from Figure 4 that the pay-off tension of the first-phase four-split-
在通常的架空输电线路设计过程中，三相线路的放线张力一般会取相同的值，因而施工后三相线路的构型相同，走向平行。本发明减振方法打破常规的设计思路，利用三相放线张力的小量差异化实现系统的错频耦合减振。试验研究表明，当三相线路放线张力的差异化达到10％时，整个系统的错频耦合减振效果非常明显，甚至达到接近振幅死亡的最优控制状态。In the usual overhead transmission line design process, the pay-off tension of the three-phase line generally takes the same value, so the configuration of the three-phase line after construction is the same, and the directions are parallel. The vibration damping method of the invention breaks the conventional design thinking, and realizes the frequency-staggered coupling vibration damping of the system by utilizing a small difference of the three-phase pay-off tension. The experimental study shows that when the difference of the pay-off tension of the three-phase line reaches 10%, the effect of the off-frequency coupling vibration reduction of the whole system is very obvious, and even reaches the optimal control state close to the amplitude death.
输电线面外、面内振动频率与放线张力的关系如下：The relationship between the out-of-plane and in-plane vibration frequency of the transmission line and the pay-off tension is as follows:
式(2)、式(3)中，T为输电线路的放线张力，m为单相输电线路单位长度的等效质量，L为输电线路的档距，Fn为输电线路n阶面外振动频率，fn为输电线路n阶面内反对称振动频率。In equations (2) and (3), T is the pay-off tension of the transmission line, m is the equivalent mass per unit length of the single-phase transmission line, L is the span of the transmission line, and Fn is the n-order out-of-plane of the transmission line. Vibration frequency, f n is the in-plane antisymmetric vibration frequency of the n-order transmission line.
根据式(2)或(3)可知，对于通常的大跨越多分裂输电线系统，当某相输电线的放线张力增大或减小10％时，其各阶振动频率就会升高或降低5％左右，该相输电线上弹簧振子的频率也会随之升高或降低。相与相之间弹簧振子频率的不同，意味着在整个系统振动过程中，各相振子很难出现同步振动，这种不同步会引起相间振子的相互牵扯与制约以及振动能量的分散传递与耗散，从而起到减振控制的目的。According to formula (2) or (3), for the usual large-span multi-split transmission line system, when the pay-off tension of a certain phase transmission line increases or decreases by 10%, the vibration frequency of each order will increase or decrease. If it is reduced by about 5%, the frequency of the spring oscillator on the power line of this phase will also increase or decrease accordingly. The difference in the frequency of the spring oscillators between the phases means that it is difficult for the oscillators of each phase to vibrate synchronously during the entire system vibration process. dispersion, so as to achieve the purpose of vibration reduction control.
弧垂与放线张力之间的关系如下：The relationship between sag and pay-off tension is as follows:
式(1)中，T为输电线路的放线张力，m为单相输电线路单位长度的等效质量，L为输电线路的档距，h为输电线路的弧垂。In formula (1), T is the pay-off tension of the transmission line, m is the equivalent mass per unit length of the single-phase transmission line, L is the span of the transmission line, and h is the sag of the transmission line.
根据式(1)可知，对于通常的大跨越多分裂输电线系统，当某相输电线的放线张力增大或减小10％时，其跨中弧垂就会减小或增大10％左右。10％的弧垂变化对输电线的线型不会有明显的影响，能保障三相线路的整体协调和美观。综合考虑线路安全运营以及施工方便等原因，具体操作时可以选择将空间位置最高的相的放线张力上调3％～5％，其余相的放线张力统一下调3％～5％，或选择将空间位置最高的相的放线张力保持不变，其余相统一下调6％～10％。According to formula (1), for the usual large-span multi-split transmission line system, when the pay-off tension of a certain phase transmission line increases or decreases by 10%, the mid-span sag will decrease or increase by 10%. about. A 10% sag change will not have a significant impact on the line type of the transmission line, and can ensure the overall coordination and beauty of the three-phase line. Considering the safety operation of the line and the convenience of construction, the specific operation can choose to increase the pay-off tension of the phase with the highest spatial position by 3% to 5%, and reduce the pay-off tension of the other phases by 3% to 5% uniformly. The payoff tension of the phase with the highest spatial position remains unchanged, and the remaining phases are uniformly reduced by 6% to 10%.
Claims (4)
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910249672.9A CN109936107B (en) | 2019-03-29 | 2019-03-29 | Power transmission line frequency-staggering coupling vibration attenuation control method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910249672.9A CN109936107B (en) | 2019-03-29 | 2019-03-29 | Power transmission line frequency-staggering coupling vibration attenuation control method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109936107A CN109936107A (en) | 2019-06-25 |
| CN109936107B true CN109936107B (en) | 2020-08-04 |
Family
ID=66988740
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910249672.9A Active CN109936107B (en) | 2019-03-29 | 2019-03-29 | Power transmission line frequency-staggering coupling vibration attenuation control method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109936107B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE2534020A1 (en) * | 1975-07-28 | 1977-02-24 | Mannesmann Roehren Werke Ag | Spacer and oscillation damper for overhead HT transmission lines - has foam-filled tube to anchor ends of spacer arms |
| CN101924338A (en) * | 2010-08-09 | 2010-12-22 | 中国电力科学研究院 | A method for suppressing galloping phase-to-phase flashover of single-conductor transmission lines |
| CN106638311A (en) * | 2016-11-15 | 2017-05-10 | 湖南科技大学 | Multi-cable compounded damping cable |
| CN106898984A (en) * | 2017-04-20 | 2017-06-27 | 湖南科技大学 | Many coupling transmission line of electricity vibration insulating systems |
| CN206685856U (en) * | 2017-04-20 | 2017-11-28 | 湖南科技大学 | More coupling transmission line of electricity vibration insulating systems |
-
2019
- 2019-03-29 CN CN201910249672.9A patent/CN109936107B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE2534020A1 (en) * | 1975-07-28 | 1977-02-24 | Mannesmann Roehren Werke Ag | Spacer and oscillation damper for overhead HT transmission lines - has foam-filled tube to anchor ends of spacer arms |
| CN101924338A (en) * | 2010-08-09 | 2010-12-22 | 中国电力科学研究院 | A method for suppressing galloping phase-to-phase flashover of single-conductor transmission lines |
| CN106638311A (en) * | 2016-11-15 | 2017-05-10 | 湖南科技大学 | Multi-cable compounded damping cable |
| CN106898984A (en) * | 2017-04-20 | 2017-06-27 | 湖南科技大学 | Many coupling transmission line of electricity vibration insulating systems |
| CN206685856U (en) * | 2017-04-20 | 2017-11-28 | 湖南科技大学 | More coupling transmission line of electricity vibration insulating systems |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109936107A (en) | 2019-06-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Zhang et al. | Dirac degeneracy and elastic topological valley modes induced by local resonant states | |
| Lu et al. | Flexural vibration bandgaps of the multiple local resonance elastic metamaterial plates with irregular resonators | |
| Wang et al. | Multi-flexural band gaps in an Euler–Bernoulli beam with lateral local resonators | |
| Bel et al. | Analytical study of magnetoacoustic gravity waves | |
| Chiou et al. | Focusing and waveguiding of Lamb waves in micro-fabricated piezoelectric phononic plates | |
| Niordson | On the optimal design of a vibrating beam | |
| CN108615521B (en) | An Acoustic Topological Insulator | |
| EP2302712A1 (en) | Method for resonance frequency tuning of micromachined structures | |
| WO2015025716A1 (en) | Piezo-resonator and process for production thereof | |
| CN108374858B (en) | Elementary substance phonon crystal vibration isolator with adjustable band gap based on stress rigidization effect | |
| CN104389935B (en) | The phonon crystal vibration damping equipment of the adjustable periodic array of a kind of cell element characteristic | |
| Fang et al. | Bidirectional elastic diode with frequency-preserved nonreciprocity | |
| CN105864350A (en) | Damping device and method for beam-array-shaped periodical piezoelectric composite structure | |
| JP2017523645A (en) | Microacoustic device with improved temperature compensation | |
| CN109936107B (en) | Power transmission line frequency-staggering coupling vibration attenuation control method | |
| Jiang et al. | Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap | |
| CN110735874A (en) | An ultra-low frequency broadband periodic vibration isolation structure with built-in negative stiffness element | |
| Karki et al. | Stopping and reversing sound via dynamic dispersion tuning in a phononic metamaterial | |
| CN206685856U (en) | More coupling transmission line of electricity vibration insulating systems | |
| CN104753013A (en) | Line anti-vibration hammer capable of adjusting resonant frequencies | |
| CN106898984B (en) | More coupling transmission line of electricity vibration insulating systems | |
| US3906249A (en) | Mounting device for oscillatory crystal which converts torsional vibrations to flexural vibrations | |
| Wang et al. | A periodic piezoelectric smart structure with the integrated passive/active vibration-reduction performances | |
| CN104653692B (en) | A kind of space three-freedom actively actuator | |
| Zhu et al. | Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |