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A Transmission-Type Electrically Tunable Polarizer Based on Graphene Ribbons at Terahertz Wave Band 被引量:1
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作者 唐祎程 朱志宏 +4 位作者 张检发 郭楚才 刘肯 袁晓东 秦石乔 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第2期91-94,共4页
We theoretically and numerically demonstrate that a transmission-type electrically tunable polarizer can be realized by using graphene ribbons supported on a dielectric film with a graphene sheet behind. The polarizat... We theoretically and numerically demonstrate that a transmission-type electrically tunable polarizer can be realized by using graphene ribbons supported on a dielectric film with a graphene sheet behind. The polarization mechanism originates from the antenna plasmon resonance of graphene stripes. The results of full-wave numerical simulations reveal that transmittance of 0.70 for one polarization and 0.0073 for another polarization can be obtained at normal incidence. The transmission-type electrically tunable polarizer provides and facilitates a variety of applications, including filtering, detecting, and imaging. 展开更多
关键词 THz A Transmission-Type Electrically Tunable Polarizer Based on Graphene Ribbons at Terahertz wave band
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Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits 被引量:6
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作者 张浩 温激鸿 +2 位作者 陈圣兵 王刚 温熙森 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第3期269-274,共6页
Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive (RL) shunting circuits can produce a narrow resonant band-gap (R... Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive (RL) shunting circuits can produce a narrow resonant band-gap (RG), and active negative capacitive (NC) shunting circuits can broaden the Bragg band-gaps (BGs). In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances. 展开更多
关键词 phononic metamaterial band-gap hybrid shunting circuits flexural wave
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A method to study interactions between narrow-banded random waves and multi-chamber perforated structures 被引量:9
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作者 Zhenhua Huang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第4期285-292,共8页
A time-domain method, based on linear velocity potential theory, is presented to study the interaction between narrow-banded random waves and perforated structures. A simple relation is derived to estimate the jet len... A time-domain method, based on linear velocity potential theory, is presented to study the interaction between narrow-banded random waves and perforated structures. A simple relation is derived to estimate the jet length of flows through the perforated wall. The reflection coefficient of narrow banded random waves from perforated structures is calculated by assuming a Rayleigh distribution of the heights of incident random waves. For reflection of narrow-banded waves from a single-chamber perforated breakwater, a comparison of the predicted and measured reflection coefficients shows that the method presented in this paper can provide a prediction better than that of regular waves. Numerical results are also reported on the reflection of narrow-banded waves from multi-chamber perforated breakwaters. 展开更多
关键词 Surface waves Narrow-banded randomwaves Perforated structures wave reflection
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Physical design and cooling test of C-band standing wave accelerating tube 被引量:2
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作者 柏伟 许州 +1 位作者 金晓 黎明 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第2期319-323,共5页
The physical design and cooling test of a C-band 2MeV standing wave (SW) accelerating tube are described in this paper. The designed accelerating structure consists of 3-cell buncher and 4-cell accelerating section ... The physical design and cooling test of a C-band 2MeV standing wave (SW) accelerating tube are described in this paper. The designed accelerating structure consists of 3-cell buncher and 4-cell accelerating section with a total length of about 163mm, excited with 1MW magnetron. Dynamic simulation presents that about 150mA beam pulse current and 30% capture efficiency can be achieved. By means of nonlinear Gauss fit on electron transverse distribution, the diameter of beam spot FWHM (full width at half maximum of density distribution) is about 0.55mm. Cooling test results of the accelerating tube show that frequencies of cavities are tuned to 5527MHz and the field distribution of bunching section is about 3:9:10. 展开更多
关键词 C-band standing wave accelerating tube space charge effect
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A staggered double vane circuit for a W-band traveling-wave tube amplifier 被引量:1
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作者 赖剑强 魏彦玉 +4 位作者 刘洋 黄民智 唐涛 王文祥 宫玉彬 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第6期548-553,共6页
Based on the combination of a staggered double vane slow wave structure (SWS) and round electron beam, a 200-W W-band traveling-wave tube (TWT) amplifier is studied in this paper. The main advantages of round beam... Based on the combination of a staggered double vane slow wave structure (SWS) and round electron beam, a 200-W W-band traveling-wave tube (TWT) amplifier is studied in this paper. The main advantages of round beam operation over the sheet beam is that the round beam can be formed more easily and the focus requirement can be dramatically reduced. It operates in the fundamental mode at the first spatial harmonic. The geometric parameters are optimized and a transition structure for the slow wave circuit is designed which can well match the signal that enters into and goes out from the tube. Then a TWT model is established and the particle-in-cell (PIC) simulation results show that the tube can provide over 200-W output power in a frequency range of 88 GHz-103 GHz with a maximum power of 289 W at 95 GHz, on the assumption that the input power is 0.1 W and the beam power is 5.155 kW. The corresponding conversion efficiency and gain at 95 GHz are expected to be 5.6% and 34.6 dB, respectively. Such amplifiers can potentially be used in high power microwave-power-modules (MPM) and for other portable applications. 展开更多
关键词 traveling-wave tube staggered double vane slow wave structure W-band
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Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map 被引量:7
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作者 Ni Zhen Feng-Lian Li +1 位作者 Yue-Sheng Wang Chuan-Zeng Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第4期1143-1153,共11页
In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses... In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann (DtN) map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition. 展开更多
关键词 Phononic crystal band structure Cylindrical wave expansion Dirichlet-to-Neumann (DtN) map Bloch theorem
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Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms
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作者 钟兰花 吴福根 钟会林 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第2期19-23,共5页
The complete band gaps (CBGs) of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, ... The complete band gaps (CBGs) of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed. 展开更多
关键词 water surface wave band gap plane wave expansion method
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Using coupling slabs to tailor surface-acoustic-wave band structures in phononic crystals consisting of pillars attached to elastic substrates 被引量:3
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作者 Heng Zhang SiYuan Yu +5 位作者 FuKang Liu Zhen Wang MingHui Lu XiaoBo Hu YanFeng Chen XianGang Xu 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2017年第4期45-50,共6页
The propagation of surface acoustic waves(SAWs) in two-dimensional phononic crystals(PnCs) with and without coupling-enhancement slabs was theoretically investigated using a three-dimensional finite element method.Dif... The propagation of surface acoustic waves(SAWs) in two-dimensional phononic crystals(PnCs) with and without coupling-enhancement slabs was theoretically investigated using a three-dimensional finite element method.Different piezoelectric substrates,for example,lithium niobate(LiNbO_3),gallium nitride(GaN),and aluminium nitride(A1N),were taken into account.Compared to the PnCs without coupling-enhancement slabs,the coupling between each pillar and its nearest neighbor was largely enhanced in the presence of slabs.The bandwidth of the first directional band gap increased markedly compared with its initial value for the PnCs without a slab(within square symmetry).In addition,with increasing thicknesses of the slabs bonded between neighboring pillars,the first directional band-gap and second directional band gap of the PnCs tend to merge.Therefore,the structure with coupling-enhancement slabs can be used as an excellent electrical band elimination filter for most electro-SAW devices,offering a new strategy to realize chip-scale applications in electroacoustic signal processing,optoacoustic modulation,and even SAW microfluidic devices. 展开更多
关键词 surface acoustic waves(SAWs) phononic crystals(PnCs) tailored band structure
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Dispersion characteristics of a slow wave structure with a modified photonic band gap 被引量:1
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作者 高喜 杨梓强 +1 位作者 曹卫平 姜彦南 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第3期129-134,共6页
This paper studies the dispersion characteristics of a modified photonic band-gap slow-wave structure with an open boundary by simulation and experiment. A mode launcher with a wheel radiator and a coupling probe is p... This paper studies the dispersion characteristics of a modified photonic band-gap slow-wave structure with an open boundary by simulation and experiment. A mode launcher with a wheel radiator and a coupling probe is presented to excite a pure TM01-like mode. The cold test and simulation results show that the TM01-like mode is effectively excited and no parasitic modes appear. The dispersion characteristics obtained from the cold test are in good agreement with the calculated results. 展开更多
关键词 modified photonic band-gap slow-wave structure TM01-like mode cold test
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A Broadband T/R Front-End of Millimeter Wave Holographic Imaging
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作者 Yun Sun Minghui Yang +3 位作者 Hengrong Cui Minhua Chen Yukun Zhu Xiaowei Sun 《Journal of Computer and Communications》 2015年第3期35-39,共5页
A broadband T/R frond-end of active holographic imaging system is presented. Compact autodyne mode circuit structure front-end is adopted to achieve higher signal to noise ratio and higher reliability, which is benefi... A broadband T/R frond-end of active holographic imaging system is presented. Compact autodyne mode circuit structure front-end is adopted to achieve higher signal to noise ratio and higher reliability, which is beneficial to the after-end imagining. The factors that influence the dynamic range and the transverse resolution ratio of holographic imaging system have been analyzed. Wide-band oscillator, wide-band low noise amplifier and the tapered slot antennas are implemented to meet the requirements of the holographic imagining system. According to the measured results, the output power is uniform in the broadband working frequency. The sub-harmonic suppression is better than 25 dBc from the frequency of 28 GHz to 33 GHz. The isolation between antennas channel is greater than 20 dB. The experimental result shows that the performance of the front-end is good enough to meet the needs of active millimeter-wave holographic imaging system. 展开更多
关键词 MILLIMETER wave BROAD-band T/R FRONT-END Module HOLOGRAPHIC Imaging
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Design of a re-entrant double-staggered ladder circuit for V-band coupled-cavity traveling-wave tubes
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作者 刘洋 徐进 +6 位作者 赖剑强 许雄 沈飞 魏彦玉 黄民智 唐涛 宫玉彬 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第7期291-297,共7页
The re-entrant double-staggered ladder slow-wave structure is employed in a high-power V-band coupled-cavity traveling-wave tube. This structure has a wide bandwidth, a moderate interaction impedance, and excellent th... The re-entrant double-staggered ladder slow-wave structure is employed in a high-power V-band coupled-cavity traveling-wave tube. This structure has a wide bandwidth, a moderate interaction impedance, and excellent thermal dissipation properties, as well as easy fabrication. A well-matched waveguide coupler is proposed for the structure. Combining the design of attenuators, a full-scale three-dimensional circuit model for the V-band coupled-cavity traveling- wave tube is constructed. The electromagnetic characteristics and the beam wave interaction of this structure are investigated. The beam current is set to be 100 mA, and the cathode voltage is tuned from 16.8 kV to 15.8 kV. The calculation results show that this tube can produce a saturated average output power over 100 W with an instantaneous bandwidth greater than 1.25 GHz in the frequency ranging from 58 GHz to 62 GHz. The corresponding gain and electronic efficiency can reach over 32 dB and 6.5%, respectively. 展开更多
关键词 coupled-cavity traveling-wave tube V band re-entrant double-staggered ladder slow-wave structure
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A curvelet-based method to determine wave directions from nautical X-band radar images
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作者 ZHA Guozhen HE Qingyou +1 位作者 GUAN Changlong CHEN Jitao 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2018年第1期11-19,共9页
A new method to determine wave directions from nautical X-band images is proposed. The signatures of ocean waves show obvious scale and directional characteristics in nautical X-band radar images. Curvelet transform... A new method to determine wave directions from nautical X-band images is proposed. The signatures of ocean waves show obvious scale and directional characteristics in nautical X-band radar images. Curvelet transform(CT) possesses very high scale and directional sensitivities. Therefore, it has good capability to analyze ocean wave fields. The radar images are decomposed at different scales, in different directions, and at different positions by CT, and curvelet coefficients are obtained. Given to the scale and directional characteristics of surface waves,the information of ocean waves is centralized in the curvelet coefficients of certain directions and at certain scales.Therefore, the wave orientations can be determined. The 180 ambiguity is removed by calculating crosscorrelation coefficients(CCCs) between continuous collected images. The proposed method is verified by the dataset collected on the Northwest coast of the Zhangzi Island in the Yellow Sea of China from March to April 2009. 展开更多
关键词 X-band radar wave direction surface wave curvelet transform
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Multi-wavelength continuous-wave Nd:YVO4 self-Raman laser under in-band pumping
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作者 Li Fan Xiao-Dong Zhao +4 位作者 Yun-Chuan Zhang Xiao-Dong Gu Hao-Peng Wan Hui-Bo Fan Jun Zhu 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第8期184-189,共6页
Multi-wavelength continuous-wave self-Raman laser with an a-cut composite YVO4/Nd:YVO4/YVO4 crystal pumped by an 879-nm wavelength-locked laser diode is demonstrated for the first time.Multi-wavelength Raman lasers at... Multi-wavelength continuous-wave self-Raman laser with an a-cut composite YVO4/Nd:YVO4/YVO4 crystal pumped by an 879-nm wavelength-locked laser diode is demonstrated for the first time.Multi-wavelength Raman lasers at 1168.4,1176,1178.7,and 1201.6 nm are achieved by the first Stokes shift of the multi-wavelength fundamental lasers at 1064,1066.7,1073.6,1084,and 1085.6 nm with two Raman shifts of 890 and 816 cm^-1.A maximum Raman output power of 2.56 W is achieved through the use of a 20-mm-long composite crystal,with a corresponding optical conversion efficiency of 9.8%.The polarization directions of different fundamental and Raman lasers are investigated and found to be orthogonalπandσpolarizations.These orthogonally polarized multi-wavelength lasers with small wavelength separation pave the way to the development of a potential laser source for application in spectral analysis,laser radar and THz generation. 展开更多
关键词 MULTI-waveLENGTH CONTINUOUS-wave self-Raman laser in-band PUMPING
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Elimination of the impact of vessels on ocean wave height inversion with X-band wave monitoring radar
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作者 王立 吴雄斌 +2 位作者 马克涛 田云 费跃军 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2016年第5期1114-1121,共8页
Directional wave spectra and integrated wave parameters can be derived from X-band radar sea surface images.A vessel on the sea surface has a significant influence on wave parameter inversions that can be seen as inte... Directional wave spectra and integrated wave parameters can be derived from X-band radar sea surface images.A vessel on the sea surface has a significant influence on wave parameter inversions that can be seen as intensive backscatter speckles in X-band wave monitoring radar sea surface images.A novel algorithm to eliminate the interference of vessels in ocean wave height inversions from X-band wave monitoring radar is proposed.This algorithm is based on the characteristics of the interference.The principal components(PCs) of a sea surface image sequence are extracted using empirical orthogonal function(EOF)analysis.The standard deviation of the PCs is then used to identify vessel interference within the image sequence.To mitigate the interference,a suppression method based on a frequency domain geometric model is applied.The algorithm framework has been applied to OSMAR-X,a wave monitoring system developed by Wuhan University,based on nautical X-band radar.Several sea surface images captured on vessels by OSMAR-X are processed using the method proposed in this paper.Inversion schemes are validated by comparisons with data from in situ wave buoys.The root-mean-square error between the significant wave heights(SWH) retrieved from original interference radar images and those measured by the buoy is reduced by 0.25 m.The determinations of surface gravity wave parameters,in particular SWH,confirm the applicability of the proposed method. 展开更多
关键词 X-band wave monitoring radar vessel interference empirical orthogonal function(EOF) significant wave heights(SWH) frequency domain geometric model
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Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces
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作者 Min Zheng Pei-jun Wei 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2009年第5期608-614,共7页
Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces were studied. By using the transfer matrix method (TMM) and the Bloch wave theory in the periodic structure, the dispersion equation was ... Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces were studied. By using the transfer matrix method (TMM) and the Bloch wave theory in the periodic structure, the dispersion equation was derived for the periodically lami- nated binary system with imperfect interfaces (the traction vector jumps or the displacement vector jumps). The dispersion equation was solved numerically and wave band gaps were obtained in the Brillouin zone. Band gaps in the case of imperfect interfaces were compared with that in the case of perfect interfaces. The influence of imperfect interfaces on wave band gaps and some interesting phenomena were discussed. 展开更多
关键词 phononic crystal transfer matrix band gap imperfect interface Bloch wave
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Measurement of the carrier recovery time in SOA based on four-wave mixing on narrow-band ASE spectrum
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作者 程乘 张新亮 +2 位作者 张羽 刘磊 黄德修 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第10期305-308,共4页
Carrier recovery time is a key parameter that determines the performance of a semiconductor optical amplifier (SOA). A measurement method of carrier recovery time in SOA based on a nearly degenerate four-wave mixing... Carrier recovery time is a key parameter that determines the performance of a semiconductor optical amplifier (SOA). A measurement method of carrier recovery time in SOA based on a nearly degenerate four-wave mixing of narrowband amplified spontaneous emission (ASE) spectra is presented. The results show the carrier times are 50.2, 44.6, and 23.6 ps when the injected currents are 120, 180, and 240 mA, respectively, which are in agreement with the nominal values of the sample. 展开更多
关键词 amplified spontaneous emission narrow band nearly degenerate four-wave mixing semiconductor optical amplifier
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mm-Wave Communication Systems at W-Band
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作者 樊勇 吴正德 唐小宏 《Journal of Electronic Science and Technology of China》 2005年第4期289-292,共4页
Two communication systems at W-band are introduced, including the system design, the modulation scheme, etc. TV delivery system delivers picture of quality meeting grade 4.5 over 8 km (no rain). Digital communicatio... Two communication systems at W-band are introduced, including the system design, the modulation scheme, etc. TV delivery system delivers picture of quality meeting grade 4.5 over 8 km (no rain). Digital communication system is capable of operating at data rates up to 8.448 Mb/s beyond 10 km under a BER of 10^-6 (clear). 展开更多
关键词 MILLIMETER-wave TV delivery digital communication W-band
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A novel algorithm for ocean wave direction inversion from X-band radar images based on optical flow method
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作者 WANG Li CHENG Yunfei +1 位作者 HONG Lijuan LIU Xinyu 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2018年第3期88-93,共6页
As one of the important sea state parameters for navigation safety and coastal resource management, the ocean wave direction represents the propagation direction of the wave. A novel algorithm based on an optical flow... As one of the important sea state parameters for navigation safety and coastal resource management, the ocean wave direction represents the propagation direction of the wave. A novel algorithm based on an optical flow method is developed for the ocean wave direction inversion of the ocean wave fields imaged by the X-band radar continuously. The proposed algorithm utilizes the echo images received by the X-band wave monitoring radar to estimate the optical flow motion, and then the actual wave propagation direction can be obtained by taking a weighted average of the motion vector for each pixel. Compared with the traditional ocean wave direction inversion method based on frequency-domain, the novel algorithm is fully using a time-domain signal processing method without determination of a current velocity and a modulation transfer function(MTF). In the meantime,the novel algorithm is simple, efficient and there is no need to do something more complicated here. Compared with traditional ocean wave direction inversion method, the ocean wave direction of derived by using this proposed method matches well with that measured by an in situ buoy nearby and the simulation data. These promising results demonstrate the efficiency and accuracy of the algorithm proposed in the paper. 展开更多
关键词 X-band radar optical flow weighted average ocean wave direction radar image
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THEORY AND EXPERIMENTAL INVESTIGAION OF FLEXURAL WAVE PROPAGATION IN THIN RECTANGULAR PLATE WITH PERIODIC STRUCTURE 被引量:4
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作者 Wen Jihong Yu Dianlong Wang Gang Zhao Hongang Liu Yaozong 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2005年第3期385-388,共4页
With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane... With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion (PWE) method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates. 展开更多
关键词 Phononic crystals Flexural wave band gaps Thin rectangular plate
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Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method 被引量:4
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作者 祝雪丰 刘盛春 +2 位作者 徐涛 王铁海 程建春 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第4期316-321,共6页
The super-cell plane wave expansion method is employed to calculate band structures for the design of a siliconbased one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low im... The super-cell plane wave expansion method is employed to calculate band structures for the design of a siliconbased one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal. 展开更多
关键词 Lamb wave phononic crystal super-cell plane wave expansion band structures
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