A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a s...A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.展开更多
By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Comp...By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain （FDTD） based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity.展开更多
In this paper,a novel symplectic conservative perturbation series expansion method is proposed to investigate the dynamic response of linear Hamiltonian systems accounting for perturbations,which mainly originate from...In this paper,a novel symplectic conservative perturbation series expansion method is proposed to investigate the dynamic response of linear Hamiltonian systems accounting for perturbations,which mainly originate from parameters dispersions and measurement errors.Taking the perturbations into account,the perturbed system is regarded as a modification of the nominal system.By combining the perturbation series expansion method with the deterministic linear Hamiltonian system,the solution to the perturbed system is expressed in the form of asymptotic series by introducing a small parameter and a series of Hamiltonian canonical equations to predict the dynamic response are derived.Eventually,the response of the perturbed system can be obtained successfully by solving these Hamiltonian canonical equations using the symplectic difference schemes.The symplectic conservation of the proposed method is demonstrated mathematically indicating that the proposed method can preserve the characteristic property of the system.The performance of the proposed method is evaluated by three examples compared with the Runge-Kutta algorithm.Numerical examples illustrate the superiority of the proposed method in accuracy and stability,especially symplectic conservation for solving linear Hamiltonian systems with perturbations and the applicability in structural dynamic response estimation.展开更多
For the multi-frequency acoustic analysis, a series expansion method has been introduced to reduce the computation time of the frequency-independent parts, but the Runge phenomenon will arise when this method is emplo...For the multi-frequency acoustic analysis, a series expansion method has been introduced to reduce the computation time of the frequency-independent parts, but the Runge phenomenon will arise when this method is employed in high frequency band. Therefore, this method is improved by analyzing the application condition and proposing the selection principle of the series truncation number. The argument interval can be adjusted with the wavenumber factor. Therefore, the problem of unstable numeration and poor precision can be solved, and the application scope of this method is expanded. The numerical example of acoustic radiation shows that the improved method is correct for acoustic analysis in wider frequency band with less series truncation number and computation amount.展开更多
在估计实际品质因子Q值时,因受频段选择、子波叠加、噪声干扰、非本征衰减等因素影响,容易导致Q值估计误差偏大。为此,提出基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法(Am-plitude ratio average in frequency ...在估计实际品质因子Q值时,因受频段选择、子波叠加、噪声干扰、非本征衰减等因素影响,容易导致Q值估计误差偏大。为此,提出基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法(Am-plitude ratio average in frequency domain,FARA法)。该算法首先利用参考频段内振幅比的连乘消除非本征衰减的影响;然后基于振幅因子在参考频点处的1~4阶泰勒级数展开表达式,推导适用于含非本征衰减地震记录的单频点Q值计算公式;其次,采用高、低频双参考频段结合方式削弱参考频段的影响;最后,采用主值频段内所有频点的平均化处理提高算法的稳定性。模型试验表明,采用高、低参考频段结合的模式可以显著提高所提方法的Q值估计精度,相对于对数谱面积双差值(LSADD)法,新方法受时差、时窗及噪声等因素的影响更小。实例应用表明,不同阶次的FARA法Q估计值的一致性较好,且整体大于LSADD法的Q估计值,与模型试验结果吻合,表明由新方法获得的Q值更可靠。展开更多
This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, ...This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employ- ing the Fourier-Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential func- tion and the modal coordinates of wave height. Based on the B ernoulli-Euler beam theory and the D＇Alembert＇s prin- ciple, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordi- nate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the cou- pling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange＇s equations in terms of quasi-coordinates. Lastly, the cou-piing dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.展开更多
文摘A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
文摘By using a Fourier series expansion method combined with Chew＇s perfectly matched layers （PMLs）, we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain （FDTD） based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity.
基金the National Nature Science Foundation of China(No.11772026)the Defense Industrial Technology Development Program(Nos.JCKY2016204B101,JCKY2018601B001)+1 种基金the Beijing Municipal Science and Technology Commission via project(No.Z191100004619006)the Beijing Advanced Discipline Center for Unmanned Aircraft System for the financial supports.
文摘In this paper,a novel symplectic conservative perturbation series expansion method is proposed to investigate the dynamic response of linear Hamiltonian systems accounting for perturbations,which mainly originate from parameters dispersions and measurement errors.Taking the perturbations into account,the perturbed system is regarded as a modification of the nominal system.By combining the perturbation series expansion method with the deterministic linear Hamiltonian system,the solution to the perturbed system is expressed in the form of asymptotic series by introducing a small parameter and a series of Hamiltonian canonical equations to predict the dynamic response are derived.Eventually,the response of the perturbed system can be obtained successfully by solving these Hamiltonian canonical equations using the symplectic difference schemes.The symplectic conservation of the proposed method is demonstrated mathematically indicating that the proposed method can preserve the characteristic property of the system.The performance of the proposed method is evaluated by three examples compared with the Runge-Kutta algorithm.Numerical examples illustrate the superiority of the proposed method in accuracy and stability,especially symplectic conservation for solving linear Hamiltonian systems with perturbations and the applicability in structural dynamic response estimation.
基金supported by the National Natural Science Foundation of China(51379083,51479079,51579109)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20120142110051)
文摘For the multi-frequency acoustic analysis, a series expansion method has been introduced to reduce the computation time of the frequency-independent parts, but the Runge phenomenon will arise when this method is employed in high frequency band. Therefore, this method is improved by analyzing the application condition and proposing the selection principle of the series truncation number. The argument interval can be adjusted with the wavenumber factor. Therefore, the problem of unstable numeration and poor precision can be solved, and the application scope of this method is expanded. The numerical example of acoustic radiation shows that the improved method is correct for acoustic analysis in wider frequency band with less series truncation number and computation amount.
文摘第五代通信技术(5th-Generation,5G)为室内定位领域带来了新的可能性,超宽带(ultra wide band,UWB)定位技术与5G定位技术都具有带宽大、频率高的特性,但是定位性能却略有差异.针对单一传感器定位的准确性、稳定性差的问题,本文提出了5G+UWB的融合定位算法,构建了基于到达时间差(time difference of arrival,TDOA)的5G室内定位、基于三边定位算法的UWB室内定位以及基于融合定位算法的5G+UWB室内定位模型.首先验证了通过加权最小二乘(weighted least squares,WLS)算法得到的各单系统的初步定位结果,之后验证了结合Taylor级数展开法得到的改进后定位结果.在此基础上,进一步对通过融合算法将两个单系统定位结果进行融合后的组合定位结果进行实验验证.实验结果表明:UWB单系统定位结果呈现准确性较低、稳定性较高的特点,5G单系统定位结果呈现准确性较高、稳定性较低的特点,二者组合后可得到准确性和稳定性都相对较好的定位结果,组合系统定位精度最高可达0.22 m,最低可达0.73 m,可实现亚米级定位.
文摘在估计实际品质因子Q值时,因受频段选择、子波叠加、噪声干扰、非本征衰减等因素影响,容易导致Q值估计误差偏大。为此,提出基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法(Am-plitude ratio average in frequency domain,FARA法)。该算法首先利用参考频段内振幅比的连乘消除非本征衰减的影响;然后基于振幅因子在参考频点处的1~4阶泰勒级数展开表达式,推导适用于含非本征衰减地震记录的单频点Q值计算公式;其次,采用高、低频双参考频段结合方式削弱参考频段的影响;最后,采用主值频段内所有频点的平均化处理提高算法的稳定性。模型试验表明,采用高、低参考频段结合的模式可以显著提高所提方法的Q值估计精度,相对于对数谱面积双差值(LSADD)法,新方法受时差、时窗及噪声等因素的影响更小。实例应用表明,不同阶次的FARA法Q估计值的一致性较好,且整体大于LSADD法的Q估计值,与模型试验结果吻合,表明由新方法获得的Q值更可靠。
基金project was supported by the National Natural Science Foundation of China (Grants 11472041, 11302244, 11532002)Guangxi Natural Science Foundation (2015GXNSFBA 139013)
文摘This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employ- ing the Fourier-Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential func- tion and the modal coordinates of wave height. Based on the B ernoulli-Euler beam theory and the D＇Alembert＇s prin- ciple, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordi- nate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the cou- pling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange＇s equations in terms of quasi-coordinates. Lastly, the cou-piing dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.
