Using the air-sea data set of January, 1983 (the mature phase of the 1982/83 El Nino event), the net radiation on the sea surface, the fluxes of the latent and the sensible heat from ocean to the atmosphere and the ne...Using the air-sea data set of January, 1983 (the mature phase of the 1982/83 El Nino event), the net radiation on the sea surface, the fluxes of the latent and the sensible heat from ocean to the atmosphere and the net heat gain of the sea surface are calculated over the Indian and the Pacific Oceans for the domain of 35°N-35°S and 45°E-75°W. The results indicate that the upward transfer of the latent and the sensible heat fluxes over the winter hemisphere is larger than that over the summer hemisphere. The sensible heat over the tropical mid Pacific in the Southern Hemisphere is transported from the atmosphere to the ocean, though its magnitude is rather small. The latent heat flux gained by the air over the eastern Pacific is less than the mean value of the normal year. The net radiation, on which the cloud amount has considerable impact, is essentially zonally distributed. Moreover, the sea surface temperature (SST) has a very good correlation with the net radiation, the region of warm SST coinciding with that of the low net radiation. The net radiation obtained by the mid Pacific Ocean is reduced by the SST anomaly during the El Nino event, whereas the atmosphere over there get more latent heat flux, and this results in the diminution of the net heat gain of the ocean. The overview of the heat budget is that the ocean over the winter hemisphere is the energy source of the atmosphere, and that over the summer hemisphere its energy sink.展开更多
This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describi...This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.展开更多
Beam steering in implant defined coherently coupled vertical cavity surface emitting laser (VCSEL) arrays is simulated using the FDTD solution software. Angular deflection dependent on relative phase differences amo...Beam steering in implant defined coherently coupled vertical cavity surface emitting laser (VCSEL) arrays is simulated using the FDTD solution software. Angular deflection dependent on relative phase differences among elements, inter-element spacing, element size and emitted wavelength is analyzed detailedly and systematically. We design and fabricate 1×2 implant defined VCSEL arrays for optimum beam steering performance. Electroni- cally controlled beam steering with a maximum deflection angle of 1.6° is successfully achieved in the 1 × 2 VCSEL arrays. The percentage of the power in the central lobe is above 39% when steering. The results show that the steering is controllable. Compared with other beam steering methods, the fabrication process is simple and of low cost.展开更多
This paper reports the phase separation behavior of ABS films cast on the surfaces of homopelymers or random copolymers.It is found that phase separation of ABS films was induced by the surfaces of the substrate polym...This paper reports the phase separation behavior of ABS films cast on the surfaces of homopelymers or random copolymers.It is found that phase separation of ABS films was induced by the surfaces of the substrate polymers.The relationship between the miscibility of the sub- strate polymers and the phase separation behavior of ABS films was also examined.展开更多
The lack of experimental data and / or limited experimental information concerning both surface and transport properties of liquid alloys often require the prediction of these quantities. An attempt has been made to l...The lack of experimental data and / or limited experimental information concerning both surface and transport properties of liquid alloys often require the prediction of these quantities. An attempt has been made to link the thermophysical properties of a ternary Cu-Sn-Ti system and its binary Cu-Sn, Cu-Ti and SnoTi subsystems with the bulk through the study of the concentration dependence of various thermodynamic, structural, surface and dynamic properties in the frame of the statistical mechanical theory in conjunction with the quasi-lattice theory (QLT). This formalism provides valuable qualitative insight into mixing processes that occur in molten alloys.展开更多
On the basis of existing techniques, a compact micro-displacement sensor of phase grating interference (PGI) is described, which adopts cylindrical hologram diffraction grating as the calibration standard. The optic...On the basis of existing techniques, a compact micro-displacement sensor of phase grating interference (PGI) is described, which adopts cylindrical hologram diffraction grating as the calibration standard. The optical principle of the sensor is explained, and the relation between the grating motion displacement and the phase shift of interference stripes is deduced. The improvement of the integral structure and the method of photoelectric signal processing are described in detail. With the software system based on the virtual instrument development platform Labwindows/CVI and other hardwares such as the precision displacement worktable, the surfaces of typical parts are measured and the characterization results are given. The sensor has wide measuring range and high resolution, its sensitivity and resolution being independent of the wavelength of the incident light. The vertical measuring range is 0-6 mm, and the vertical resolution is 0.005μm. The experimental results show that the sensor can be used to measure and characterize the surface topography parameters of the plane and curved surface.展开更多
The effect of phosphorus passivation on 4H-SiC(0001) silicon (Si) dangling bonds is investigated using ab initio atomistic thermodynamic calculations. Phosphorus passivation commences with chemisorption of phospho...The effect of phosphorus passivation on 4H-SiC(0001) silicon (Si) dangling bonds is investigated using ab initio atomistic thermodynamic calculations. Phosphorus passivation commences with chemisorption of phosphorus atoms at high-symmetry coordinated sites. To determine the most stable structure during the passivation process of phosphorus, a surface phase diagram of phosphorus adsorption on SiC (0001) surface is constructed over a coverage range of 1/9-1 monolayer (ML). The calculated results indicate that the 1/3 ML configuration is most energetically favorable in a reasonable environment. At this coverage, the total electron density of states demonstrates that phosphorus may effectively reduce the interface state density near the conduction band by removing 4H-SiC (0001) Si dangling bonds. It provides an atomic level insight into how phosphorus is able to reduce the near interface traps.展开更多
We find that the superconductivity in the thin films of the formerly believed non-superconducting parent compound FeTe is accompanied by an emergence of second order with a correlation length of 742 nm and 258 nm at 1...We find that the superconductivity in the thin films of the formerly believed non-superconducting parent compound FeTe is accompanied by an emergence of second order with a correlation length of 742 nm and 258 nm at 10 K and 300 K, respectively. The structural phase transition found in iron pnictide superconductors, in non-superconducting FeTe bulk samples, and in FeSe superconducting thin films is not observed in the superconducting FeTe thin films. The interplay between superconductivity and long range order may suggest the crucial role of competition between electronic localization and itinerancy which leads to strong quantum fluctuations in the FeTe system.展开更多
The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined a...The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.展开更多
On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables an...On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional (2D) symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures' configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.展开更多
The CuxSi(1-x) thin films have been grown by pulsed laser deposition(PLD) with in situ annealing on Si(001) and Si(111),respectively.The transformation of phase was detected by X-ray diffraction(XRD).The res...The CuxSi(1-x) thin films have been grown by pulsed laser deposition(PLD) with in situ annealing on Si(001) and Si(111),respectively.The transformation of phase was detected by X-ray diffraction(XRD).The results showed that the as-deposited films were composed of Cu on both Si(001) and Si(111).The annealed thin films consisted of Cu +η "-Cu3Si on Si(001) while Cu +η'-Cu3Si on Si(111),respectively,at annealed temperature(Ta)= 300-600℃.With the further increasing of Ta,at Ta= 700℃,there was only one main phase,η"-Cu3Si on Si(001) while η'-Cu3Si on Si(111),respectively.The annealed thin films transformed from continuous dense structure to scattered-grain morphology with increasing Ta detected by field emission scanning electron microscope(FESEM).It was also showed that the grain size would enlarge with increasing annealing time(ta).展开更多
A dynamic solution is presented for the propagation of waves in an electric-magneto-elastic plate composed of piezoelectric, piezomagnetic materials and elastic matrix. The electric-magneto-elastic plate is polarized ...A dynamic solution is presented for the propagation of waves in an electric-magneto-elastic plate composed of piezoelectric, piezomagnetic materials and elastic matrix. The electric-magneto-elastic plate is polarized along the thickness direction. The generalized displacements are expressed as the sum of the gradient of a scalar (dilatation wave) and the curl of a vector (shear wave). With the help of dynamic equilibrium equations and geometric equations, we can obtain dynamic equations of the dilatation wave and the shear wave. The conclusion that the types of the dilatation waves and the shear waves remain unchanged after being reflected by the boundary can be obtained through the analysis of these kinetic equations. The dispersion properties and phase velocity surface of the dilatation and shear wave can be obtained by solutions of dynamic equilibrium equations. Influences of the piezoelectric and piezomagnetic parameters on wave characteristics are discussed.展开更多
Investigation has been made on the causes of hot cracking in the surfacing layer of Ni_3Al basealloy by analysing the solidification process of fusion pool and the distribution of thermal stresses. The re-sults show t...Investigation has been made on the causes of hot cracking in the surfacing layer of Ni_3Al basealloy by analysing the solidification process of fusion pool and the distribution of thermal stresses. The re-sults show that the cracking is directly related to both the occurrence of eutectic phase β' (NiAI) within theinterdendritic region and high thernial stresses in the surfacing layer ,and which are caused by selecting highwelding rate. When the process of electric arc weld is changed from straight line rnovement to that along’Z’pattern,the cracking in the surfacing layer of Ni_3Al base alloy is prevented owing to being reduced of boththe cooling rate of liquid in the fusion liool and the speed of the moving heat source. Lowering the outputpower of the electric arc welding could lead to the reducing of rnelting volume of the base material ,and lowerthe arnount of iron atoms dissolving in the fusion pool ,so that the trend of the eutectic reaction within the in-terdendritic region is reduced,and which is helpful to suppress the cracking in the surfacing layer of Ni_3Albase alloy.展开更多
In this paper we study asyrnptotic behaviour of solutions of second ordernonlinear delay differential equations on cylindrical surface. We give d necessaryand sufficient condition for the oscillations, and we give som...In this paper we study asyrnptotic behaviour of solutions of second ordernonlinear delay differential equations on cylindrical surface. We give d necessaryand sufficient condition for the oscillations, and we give some sufficient conditionsfor the forced oscillations.展开更多
Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wav...Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectie eigenvalue problem. The band gaps and spatial filtering phenomena are examined to find the stop bands and directional stop bands. Special attention is directed to the effects of the relative density and the length ratio on the band gaps and phase constant surfaces. This work provides new opportunities for designing hierarchical honeycomb structures in sound insulation applications.展开更多
文摘Using the air-sea data set of January, 1983 (the mature phase of the 1982/83 El Nino event), the net radiation on the sea surface, the fluxes of the latent and the sensible heat from ocean to the atmosphere and the net heat gain of the sea surface are calculated over the Indian and the Pacific Oceans for the domain of 35°N-35°S and 45°E-75°W. The results indicate that the upward transfer of the latent and the sensible heat fluxes over the winter hemisphere is larger than that over the summer hemisphere. The sensible heat over the tropical mid Pacific in the Southern Hemisphere is transported from the atmosphere to the ocean, though its magnitude is rather small. The latent heat flux gained by the air over the eastern Pacific is less than the mean value of the normal year. The net radiation, on which the cloud amount has considerable impact, is essentially zonally distributed. Moreover, the sea surface temperature (SST) has a very good correlation with the net radiation, the region of warm SST coinciding with that of the low net radiation. The net radiation obtained by the mid Pacific Ocean is reduced by the SST anomaly during the El Nino event, whereas the atmosphere over there get more latent heat flux, and this results in the diminution of the net heat gain of the ocean. The overview of the heat budget is that the ocean over the winter hemisphere is the energy source of the atmosphere, and that over the summer hemisphere its energy sink.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61271356 and 51575541the National Research Foundation of Korea under Grant Nos 2013-M2A2A9043241 and 2013-R1A2A2A01016042the Hunan Provincial Innovation Foundation For Postgraduate under Grant No CX2016B046
文摘This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.
基金Supported by the‘Supporting First Action’Joint Foundation for Outstanding Postdoctoral Program under Grant Nos Y7YBSH0001 and Y7BSH14001the National Natural Science Foundation of China under Grant No 61434006the National Key Basic Research Program of China under Grant No 2017YFB0102302
文摘Beam steering in implant defined coherently coupled vertical cavity surface emitting laser (VCSEL) arrays is simulated using the FDTD solution software. Angular deflection dependent on relative phase differences among elements, inter-element spacing, element size and emitted wavelength is analyzed detailedly and systematically. We design and fabricate 1×2 implant defined VCSEL arrays for optimum beam steering performance. Electroni- cally controlled beam steering with a maximum deflection angle of 1.6° is successfully achieved in the 1 × 2 VCSEL arrays. The percentage of the power in the central lobe is above 39% when steering. The results show that the steering is controllable. Compared with other beam steering methods, the fabrication process is simple and of low cost.
文摘This paper reports the phase separation behavior of ABS films cast on the surfaces of homopelymers or random copolymers.It is found that phase separation of ABS films was induced by the surfaces of the substrate polymers.The relationship between the miscibility of the sub- strate polymers and the phase separation behavior of ABS films was also examined.
基金This work was financially supported by THERMOLAB - ESA MAP PROJECT, Contract No. AO-99-022. A part of this work was performed in the framework of the E.C. action COST 531 project: "Lead-free solder materials".
文摘The lack of experimental data and / or limited experimental information concerning both surface and transport properties of liquid alloys often require the prediction of these quantities. An attempt has been made to link the thermophysical properties of a ternary Cu-Sn-Ti system and its binary Cu-Sn, Cu-Ti and SnoTi subsystems with the bulk through the study of the concentration dependence of various thermodynamic, structural, surface and dynamic properties in the frame of the statistical mechanical theory in conjunction with the quasi-lattice theory (QLT). This formalism provides valuable qualitative insight into mixing processes that occur in molten alloys.
基金This project is supported by National Natural Sciences Foundation of China (No.50175037).
文摘On the basis of existing techniques, a compact micro-displacement sensor of phase grating interference (PGI) is described, which adopts cylindrical hologram diffraction grating as the calibration standard. The optical principle of the sensor is explained, and the relation between the grating motion displacement and the phase shift of interference stripes is deduced. The improvement of the integral structure and the method of photoelectric signal processing are described in detail. With the software system based on the virtual instrument development platform Labwindows/CVI and other hardwares such as the precision displacement worktable, the surfaces of typical parts are measured and the characterization results are given. The sensor has wide measuring range and high resolution, its sensitivity and resolution being independent of the wavelength of the incident light. The vertical measuring range is 0-6 mm, and the vertical resolution is 0.005μm. The experimental results show that the sensor can be used to measure and characterize the surface topography parameters of the plane and curved surface.
基金Project supported by the National High Technology Research and Development Program of China(Grant No.2014AA052401)the National Natural Science Foundation of China(Grant No.61474013)the National Grid Science&Technology Project,China(Grant No.5455DW150006)
文摘The effect of phosphorus passivation on 4H-SiC(0001) silicon (Si) dangling bonds is investigated using ab initio atomistic thermodynamic calculations. Phosphorus passivation commences with chemisorption of phosphorus atoms at high-symmetry coordinated sites. To determine the most stable structure during the passivation process of phosphorus, a surface phase diagram of phosphorus adsorption on SiC (0001) surface is constructed over a coverage range of 1/9-1 monolayer (ML). The calculated results indicate that the 1/3 ML configuration is most energetically favorable in a reasonable environment. At this coverage, the total electron density of states demonstrates that phosphorus may effectively reduce the interface state density near the conduction band by removing 4H-SiC (0001) Si dangling bonds. It provides an atomic level insight into how phosphorus is able to reduce the near interface traps.
基金Project supported by the National Basic Research Program of China(Grant Nos.2006CB921107 and 2010CB630704)the National Natural Science Foundation of China(Grant No.10774165)
文摘We find that the superconductivity in the thin films of the formerly believed non-superconducting parent compound FeTe is accompanied by an emergence of second order with a correlation length of 742 nm and 258 nm at 10 K and 300 K, respectively. The structural phase transition found in iron pnictide superconductors, in non-superconducting FeTe bulk samples, and in FeSe superconducting thin films is not observed in the superconducting FeTe thin films. The interplay between superconductivity and long range order may suggest the crucial role of competition between electronic localization and itinerancy which leads to strong quantum fluctuations in the FeTe system.
基金Project supported by the National Natural Science Foundation of China (Grant No 50875255)
文摘The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.
基金supported by the National Natural Science Foundation of China (10972182, 10772147, 10632030)the National Basic Research Program of China (2006CB 601202)+3 种基金the Doctorate Foundation of Northwestern Polytechnical University (CX200908)the Graduate Starting Seed Fund of Northwestern Polytechnical University (Z200930)the NPU Foundation for Fundamental Researchthe Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (GZ0802)
文摘On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional (2D) symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures' configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.
基金Funded by National Natural Science Foundation of China(Nos.51102101,51272196,51372188,51521001)the 111 Project(No.B13035)+2 种基金the International Science&Technology Cooperation Program of China(No.2014DFA53090)the Natural Science Foundation of Hubei Province,China(No.2014CFB870)the Fundamental Research Funds for the Central Universities,China(No.WUT:2015III023)
文摘The CuxSi(1-x) thin films have been grown by pulsed laser deposition(PLD) with in situ annealing on Si(001) and Si(111),respectively.The transformation of phase was detected by X-ray diffraction(XRD).The results showed that the as-deposited films were composed of Cu on both Si(001) and Si(111).The annealed thin films consisted of Cu +η "-Cu3Si on Si(001) while Cu +η'-Cu3Si on Si(111),respectively,at annealed temperature(Ta)= 300-600℃.With the further increasing of Ta,at Ta= 700℃,there was only one main phase,η"-Cu3Si on Si(001) while η'-Cu3Si on Si(111),respectively.The annealed thin films transformed from continuous dense structure to scattered-grain morphology with increasing Ta detected by field emission scanning electron microscope(FESEM).It was also showed that the grain size would enlarge with increasing annealing time(ta).
文摘A dynamic solution is presented for the propagation of waves in an electric-magneto-elastic plate composed of piezoelectric, piezomagnetic materials and elastic matrix. The electric-magneto-elastic plate is polarized along the thickness direction. The generalized displacements are expressed as the sum of the gradient of a scalar (dilatation wave) and the curl of a vector (shear wave). With the help of dynamic equilibrium equations and geometric equations, we can obtain dynamic equations of the dilatation wave and the shear wave. The conclusion that the types of the dilatation waves and the shear waves remain unchanged after being reflected by the boundary can be obtained through the analysis of these kinetic equations. The dispersion properties and phase velocity surface of the dilatation and shear wave can be obtained by solutions of dynamic equilibrium equations. Influences of the piezoelectric and piezomagnetic parameters on wave characteristics are discussed.
基金supported by the foundation of '863' high technology in China
文摘Investigation has been made on the causes of hot cracking in the surfacing layer of Ni_3Al basealloy by analysing the solidification process of fusion pool and the distribution of thermal stresses. The re-sults show that the cracking is directly related to both the occurrence of eutectic phase β' (NiAI) within theinterdendritic region and high thernial stresses in the surfacing layer ,and which are caused by selecting highwelding rate. When the process of electric arc weld is changed from straight line rnovement to that along’Z’pattern,the cracking in the surfacing layer of Ni_3Al base alloy is prevented owing to being reduced of boththe cooling rate of liquid in the fusion liool and the speed of the moving heat source. Lowering the outputpower of the electric arc welding could lead to the reducing of rnelting volume of the base material ,and lowerthe arnount of iron atoms dissolving in the fusion pool ,so that the trend of the eutectic reaction within the in-terdendritic region is reduced,and which is helpful to suppress the cracking in the surfacing layer of Ni_3Albase alloy.
文摘In this paper we study asyrnptotic behaviour of solutions of second ordernonlinear delay differential equations on cylindrical surface. We give d necessaryand sufficient condition for the oscillations, and we give some sufficient conditionsfor the forced oscillations.
基金Project supported by the National Basic Research Program of China(No.2011CB610300)the National Natural Science Foundation of China(Nos.11172239 and 11372252)+3 种基金the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)the Fundamental Research Funds for the Central Universities(Nos.310201401JCQ01001 and 3102015ZY036)China Postdoctoral Science Foundation(No.2013M540724)Shaanxi postdoctoral research projects
文摘Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectie eigenvalue problem. The band gaps and spatial filtering phenomena are examined to find the stop bands and directional stop bands. Special attention is directed to the effects of the relative density and the length ratio on the band gaps and phase constant surfaces. This work provides new opportunities for designing hierarchical honeycomb structures in sound insulation applications.