Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal stra...Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the mothod introduced here.展开更多
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x...This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.展开更多
In recent years, several attempts have been made in designing planar array antennas with high directivity. This paper is aimed at investigating the impact of element spacing on the directivity of planar array of monop...In recent years, several attempts have been made in designing planar array antennas with high directivity. This paper is aimed at investigating the impact of element spacing on the directivity of planar array of monopole antenna. The directivity of antenna with reduced grating lobes can be obtained by carefully varying the inter-element spacing of array antenna. Based on this conception, this paper presents the investigation carried out on the relationship between inter-element spacing and the directivity of planar array of monopole antenna. It went further to highlight the effect on the total fields radiated by the antenna. The inter-element spacing is one of the most important antenna parameters that determine the directivity of the antenna. For a planar array of monopole, the directivity can be improved by varying the inter-element spacing. Four elements uniform planar array antenna and Hadamard matrix method was used to determine element positioning in the array matrix. The simulated results obtained using Matlab, showed that good directivity was obtained by using element spacing between 0.1λ - 0.5λ. Increasing the spacing beyond 0.6λ - 1.0λ also improved the directivity, but generated many grating lobes. As inter-element spacing increased, the grating lobes increased in size, number and levels. The study, therefore, inferred that the best directivity (radiation pattern) can only be obtained when the element spacing is within 0.1 - 0.5λ.展开更多
文摘Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the mothod introduced here.
基金The research of Fan Lili was supported by two grants from the National Natural Science Foundation of China (10871151 10925103)+1 种基金the research of Liu Hongxia was supported by National Natural Science Foundation of China (10871082)the research of Yin Hui was supported by National Natural Sciences Foundation of China (10901064)
文摘This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.
文摘In recent years, several attempts have been made in designing planar array antennas with high directivity. This paper is aimed at investigating the impact of element spacing on the directivity of planar array of monopole antenna. The directivity of antenna with reduced grating lobes can be obtained by carefully varying the inter-element spacing of array antenna. Based on this conception, this paper presents the investigation carried out on the relationship between inter-element spacing and the directivity of planar array of monopole antenna. It went further to highlight the effect on the total fields radiated by the antenna. The inter-element spacing is one of the most important antenna parameters that determine the directivity of the antenna. For a planar array of monopole, the directivity can be improved by varying the inter-element spacing. Four elements uniform planar array antenna and Hadamard matrix method was used to determine element positioning in the array matrix. The simulated results obtained using Matlab, showed that good directivity was obtained by using element spacing between 0.1λ - 0.5λ. Increasing the spacing beyond 0.6λ - 1.0λ also improved the directivity, but generated many grating lobes. As inter-element spacing increased, the grating lobes increased in size, number and levels. The study, therefore, inferred that the best directivity (radiation pattern) can only be obtained when the element spacing is within 0.1 - 0.5λ.
