The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-f...The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions. With all combinations of simplysupported （S） and clamped （C） boundary conditions applied to the natural mode, the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates, with the aid of which the normal modes and frequencies are solved exactly. It was believed that the exact eigensolutions for cases SSCC, SCCC and CCCC were unable to be obtained, however, they are successfully found in this paper. Comparisons between the present results and the FEM results validate the present exact solutions, which can thus be taken as the benchmark for verifying different approximate approaches.展开更多
The development of a dual-frequency multi-constellation satellite-based augmentation system(DFMC SBAS)is in progress worldwide.The broadcasted dual-frequency range error(DFRE)integrity parameter reflects the effects o...The development of a dual-frequency multi-constellation satellite-based augmentation system(DFMC SBAS)is in progress worldwide.The broadcasted dual-frequency range error(DFRE)integrity parameter reflects the effects of satellite ephemeris and clock corrections.A user uses the DFRE to calculate the protection level and then determines whether the DFMC SBAS service satisfies the requirements of the current flight phase.However,the calculation of the DFRE has not been reported.Herein,a DFRE estimation method is proposed based on the projection method.Using the ephemeris-clock covariance matrix of each satellite,the maximal projection direction was solved,and the projection of the covariance matrix on this direction was used as the DFRE to form an envelope for the maximal corrected error.Results show that the DFRE can form an envelope of the maximal corrected error with a set probability,and the integrity performance in the user segment satisfies the Category I precision approach requirement.展开更多
基金supported by the National Natural Science Foundation of China (10772014)
文摘The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions. With all combinations of simplysupported （S） and clamped （C） boundary conditions applied to the natural mode, the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates, with the aid of which the normal modes and frequencies are solved exactly. It was believed that the exact eigensolutions for cases SSCC, SCCC and CCCC were unable to be obtained, however, they are successfully found in this paper. Comparisons between the present results and the FEM results validate the present exact solutions, which can thus be taken as the benchmark for verifying different approximate approaches.
基金the State Key Laboratory of Geo-Information Engineering,No.SKLGIE2018-Z-2-2.
文摘The development of a dual-frequency multi-constellation satellite-based augmentation system(DFMC SBAS)is in progress worldwide.The broadcasted dual-frequency range error(DFRE)integrity parameter reflects the effects of satellite ephemeris and clock corrections.A user uses the DFRE to calculate the protection level and then determines whether the DFMC SBAS service satisfies the requirements of the current flight phase.However,the calculation of the DFRE has not been reported.Herein,a DFRE estimation method is proposed based on the projection method.Using the ephemeris-clock covariance matrix of each satellite,the maximal projection direction was solved,and the projection of the covariance matrix on this direction was used as the DFRE to form an envelope for the maximal corrected error.Results show that the DFRE can form an envelope of the maximal corrected error with a set probability,and the integrity performance in the user segment satisfies the Category I precision approach requirement.
