Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation fo...Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation for the elastically supported fluid-conveying pipe is transformed into ordinary differential equations using the Galerkin truncation method.The Chebyshev interval approach,integrated with the assumed mode method is then used to investigate the effects of uncertainties of support stiffness,fluid speed,and pipe length on the natural frequencies and mode shapes of the pipe.Additionally,both symmetrical and asymmetrical support stiffnesses are discussed.The accuracy and effectiveness of the Chebyshev interval approach are verified through comparison with the Monte Carlo method.The results reveal that,for the same deviation coefficient,uncertainties in symmetrical support stiffness have a greater impact on the first four natural frequencies than those of the asymmetrical one.There may be significant differences in the sensitivity of natural frequencies and mode shapes of the same order to uncertain parameters.Notably,mode shapes susceptible to uncertain parameters exhibit wider fluctuation intervals near the elastic supports,requiring more attention.展开更多
双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Ku...双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Kutta进行求解。将该法得到的数值结果与精确解进行比较,验证了方法的有效性,数据结果的误差与其他方法相比有较高的精确度。Hyperbolic partial differential equation is one of the important partial differential equations. The Chebyshev spectral method is proposed to solve the telegraph equation. Chebyshev-gauss-lobatto is used to assign points, the derivative matrix is constructed by Chebyshev polynomial, and the telegraph equation is approximated as an ordinary differential equation. The error estimation of the discrete Chebyshev spectral method for the telegraph equation was proved. Runge-Kutta was used to solve the problem. The numerical results obtained by the method are compared with the exact solution, and the effectiveness of the method is verified. The error of the data results is more accurate than that of other methods.展开更多
This paper presents a design method to implement an antenna array characterized by ultra-wide beam coverage,low profile,and low Sidelobe Level(SLL)for the application of Unmanned Aerial Vehicle(UAV)air-to-ground commu...This paper presents a design method to implement an antenna array characterized by ultra-wide beam coverage,low profile,and low Sidelobe Level(SLL)for the application of Unmanned Aerial Vehicle(UAV)air-to-ground communication.The array consists of ten broadside-radiating,ultrawide-beamwidth elements that are cascaded by a central-symmetry series-fed network with tapered currents following Dolph-Chebyshev distribution to provide low SLL.First,an innovative design of end-fire Huygens source antenna that is compatible with metal ground is presented.A low-profile,half-mode Microstrip Patch Antenna(MPA)is utilized to serve as the magnetic dipole and a monopole is utilized to serves as the electric dipole,constructing the compact,end-fire,grounded Huygens source antenna.Then,two opposite-oriented end-fire Huygens source antennas are seamlessly integrated into a single antenna element in the form of monopole-loaded MPA to accomplish the ultrawide,broadside-radiating beam.Particular consideration has been applied into the design of series-fed network as well as antenna element to compensate the adverse coupling effects between elements on the radiation performance.Experiment indicates an ultrawide Half-Power Beamwidth(HPBW)of 161°and a low SLL of-25 dB with a high gain of 12 d Bi under a single-layer configuration.The concurrent ultrawide beamwidth and low SLL make it particularly attractive for applications of UAV air-to-ground communication.展开更多
利用重心插值配点法求解二维定常对流扩散方程。首先介绍了两种重心插值配点法,并给出微分矩阵。其次,离散二维定常对流扩散方程以及初边值条件,利用置换法和附加法处理边界条件。采用第二类Chebyshev节点和等距节点进行数值计算,比较...利用重心插值配点法求解二维定常对流扩散方程。首先介绍了两种重心插值配点法,并给出微分矩阵。其次,离散二维定常对流扩散方程以及初边值条件,利用置换法和附加法处理边界条件。采用第二类Chebyshev节点和等距节点进行数值计算,比较了两种边界条件施加方法下两种重心插值法的数值算法。数值算例表明了重心插值配点法的高精度性。The two-dimensional steady convection-diffusion equation is solved by barycentric interpolation method. Firstly, the two barycentric interpolation collocation methods are introduced, and the differential matrices are given. Secondly, the two-dimensional steady convection-diffusion equation and initial boundary conditions are dispersed, and the boundary conditions are treated by substitution and addition. Numerical calculations are carried out by using the second type of Chebyshev node and the equidistant node. Numerical examples demonstrate that this barycentric interpolation collocation method has high accuracy.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12272211,12072181,and 12121002).
文摘Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation for the elastically supported fluid-conveying pipe is transformed into ordinary differential equations using the Galerkin truncation method.The Chebyshev interval approach,integrated with the assumed mode method is then used to investigate the effects of uncertainties of support stiffness,fluid speed,and pipe length on the natural frequencies and mode shapes of the pipe.Additionally,both symmetrical and asymmetrical support stiffnesses are discussed.The accuracy and effectiveness of the Chebyshev interval approach are verified through comparison with the Monte Carlo method.The results reveal that,for the same deviation coefficient,uncertainties in symmetrical support stiffness have a greater impact on the first four natural frequencies than those of the asymmetrical one.There may be significant differences in the sensitivity of natural frequencies and mode shapes of the same order to uncertain parameters.Notably,mode shapes susceptible to uncertain parameters exhibit wider fluctuation intervals near the elastic supports,requiring more attention.
文摘双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Kutta进行求解。将该法得到的数值结果与精确解进行比较,验证了方法的有效性,数据结果的误差与其他方法相比有较高的精确度。Hyperbolic partial differential equation is one of the important partial differential equations. The Chebyshev spectral method is proposed to solve the telegraph equation. Chebyshev-gauss-lobatto is used to assign points, the derivative matrix is constructed by Chebyshev polynomial, and the telegraph equation is approximated as an ordinary differential equation. The error estimation of the discrete Chebyshev spectral method for the telegraph equation was proved. Runge-Kutta was used to solve the problem. The numerical results obtained by the method are compared with the exact solution, and the effectiveness of the method is verified. The error of the data results is more accurate than that of other methods.
基金supported by the National Natural Science Foundation of China(No.62371080 and 62031006)the National Science Foundation of Chongqing,China(No.CSTB2022NSCQ-MSX0597)the Venture&Innovation Support Program for Chongqing Overseas Returnees,China(No.cx2022063)。
文摘This paper presents a design method to implement an antenna array characterized by ultra-wide beam coverage,low profile,and low Sidelobe Level(SLL)for the application of Unmanned Aerial Vehicle(UAV)air-to-ground communication.The array consists of ten broadside-radiating,ultrawide-beamwidth elements that are cascaded by a central-symmetry series-fed network with tapered currents following Dolph-Chebyshev distribution to provide low SLL.First,an innovative design of end-fire Huygens source antenna that is compatible with metal ground is presented.A low-profile,half-mode Microstrip Patch Antenna(MPA)is utilized to serve as the magnetic dipole and a monopole is utilized to serves as the electric dipole,constructing the compact,end-fire,grounded Huygens source antenna.Then,two opposite-oriented end-fire Huygens source antennas are seamlessly integrated into a single antenna element in the form of monopole-loaded MPA to accomplish the ultrawide,broadside-radiating beam.Particular consideration has been applied into the design of series-fed network as well as antenna element to compensate the adverse coupling effects between elements on the radiation performance.Experiment indicates an ultrawide Half-Power Beamwidth(HPBW)of 161°and a low SLL of-25 dB with a high gain of 12 d Bi under a single-layer configuration.The concurrent ultrawide beamwidth and low SLL make it particularly attractive for applications of UAV air-to-ground communication.
文摘利用重心插值配点法求解二维定常对流扩散方程。首先介绍了两种重心插值配点法,并给出微分矩阵。其次,离散二维定常对流扩散方程以及初边值条件,利用置换法和附加法处理边界条件。采用第二类Chebyshev节点和等距节点进行数值计算,比较了两种边界条件施加方法下两种重心插值法的数值算法。数值算例表明了重心插值配点法的高精度性。The two-dimensional steady convection-diffusion equation is solved by barycentric interpolation method. Firstly, the two barycentric interpolation collocation methods are introduced, and the differential matrices are given. Secondly, the two-dimensional steady convection-diffusion equation and initial boundary conditions are dispersed, and the boundary conditions are treated by substitution and addition. Numerical calculations are carried out by using the second type of Chebyshev node and the equidistant node. Numerical examples demonstrate that this barycentric interpolation collocation method has high accuracy.
