A two-dimensional phononic crystal （PC） structure possessing a relatively low frequency range of complete bandgap is presented. The structure is composed of periodic spindle-shaped plumbum inclusions in a rubber mat...A two-dimensional phononic crystal （PC） structure possessing a relatively low frequency range of complete bandgap is presented. The structure is composed of periodic spindle-shaped plumbum inclusions in a rubber matrix which forms a square lattice. The dispersion relation, transmission spectrum and displacement field are studied using the finite element method in conjunction with the Bloch theorem. Numerical results show that the present PC structure can achieve a large complete bandgap in a relatively low frequency range compared with two inclusions of different materials, which is useful in low-frequency noise and vibration control and can be designed as a low frequency acoustic filter and waveguides. Moreover, the transmission spectrum and effective mass are evaluated to validate the obtained band structure. It is interesting to see that within the band gap the effective mass becomes negative, resulting in an imaginary wave speed and wave exponential attenuation. Finally, sensitivity analysis of the effect of geometrical parameters of the presented PC structure on the lowest bandgap is performed to investigate the variations of the bandgap width and frequency.展开更多
A three-dimensional （3D） coordination polymer {[Co（bdc）（dpb）]·H2O}n （1） was prepared by solvothermal reaction of 1,3-dipyridyl benzene （dpb） with deprotonated 1,3-benzene- dicarboxylate （H2bdc）, and w...A three-dimensional （3D） coordination polymer {[Co（bdc）（dpb）]·H2O}n （1） was prepared by solvothermal reaction of 1,3-dipyridyl benzene （dpb） with deprotonated 1,3-benzene- dicarboxylate （H2bdc）, and was characterized by elemental analysis, IR spectroscopy, and X-ray single-crystal diffraction. It crystallizes in the monoclinic system, space group C2/c with α = 15.478（6）, b = 12.865（5）, c = 24.091（10） ？, β = 95.599（5）°, V = 4774（3） ？3, C24H18CoN2O5, Mr = 473.34, Dc = 1.267 g/cm3, F（000） = 1864.0, μ = 0.748 mm-1 and Z = 8. Each Co（II） ion links three bdc2- anions to form an infinitely 1D ladder-shaped chain containing binuclear [（COO）Co]2 cluster, and dpb links adjacent 1D chains to form a 3D pcu framework. In addition, the UV-vis of 1 was also studied.展开更多
A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. An H-shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula...A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. An H-shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula of counting the number of closed 6-walks is given on a graph, and some necessary conditions of a graph Γ cospectral to an H-shape are given.展开更多
Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwat...Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.展开更多
文摘A two-dimensional phononic crystal （PC） structure possessing a relatively low frequency range of complete bandgap is presented. The structure is composed of periodic spindle-shaped plumbum inclusions in a rubber matrix which forms a square lattice. The dispersion relation, transmission spectrum and displacement field are studied using the finite element method in conjunction with the Bloch theorem. Numerical results show that the present PC structure can achieve a large complete bandgap in a relatively low frequency range compared with two inclusions of different materials, which is useful in low-frequency noise and vibration control and can be designed as a low frequency acoustic filter and waveguides. Moreover, the transmission spectrum and effective mass are evaluated to validate the obtained band structure. It is interesting to see that within the band gap the effective mass becomes negative, resulting in an imaginary wave speed and wave exponential attenuation. Finally, sensitivity analysis of the effect of geometrical parameters of the presented PC structure on the lowest bandgap is performed to investigate the variations of the bandgap width and frequency.
基金supported by the National Natural Science Foundation of China(21301005,21271008,51173002)Natural Science Foundation of Anhui Province(1308085QB34)the young teacher’s research foundation of Anhui University of Science and Technology(11227,2012QNZ08)
文摘A three-dimensional （3D） coordination polymer {[Co（bdc）（dpb）]·H2O}n （1） was prepared by solvothermal reaction of 1,3-dipyridyl benzene （dpb） with deprotonated 1,3-benzene- dicarboxylate （H2bdc）, and was characterized by elemental analysis, IR spectroscopy, and X-ray single-crystal diffraction. It crystallizes in the monoclinic system, space group C2/c with α = 15.478（6）, b = 12.865（5）, c = 24.091（10） ？, β = 95.599（5）°, V = 4774（3） ？3, C24H18CoN2O5, Mr = 473.34, Dc = 1.267 g/cm3, F（000） = 1864.0, μ = 0.748 mm-1 and Z = 8. Each Co（II） ion links three bdc2- anions to form an infinitely 1D ladder-shaped chain containing binuclear [（COO）Co]2 cluster, and dpb links adjacent 1D chains to form a 3D pcu framework. In addition, the UV-vis of 1 was also studied.
文摘A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. An H-shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula of counting the number of closed 6-walks is given on a graph, and some necessary conditions of a graph Γ cospectral to an H-shape are given.
基金supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant no.51021004)the Research Fund of State Key Laboratory in Ocean Engineering of Shanghai Jiaotong University(Grant no.1104)the Scientific Research Foundation of Civil Aviation University of China(Grant no.09QD08X)
文摘Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.
