The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytica...The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.展开更多
The meteor radar can detect the zenith angle,azimuth,radial velocity,and altitude of meteor trails so that one can invert the wind profiles in the mesosphere and low thermosphere(MLT)region,based on the Interferometri...The meteor radar can detect the zenith angle,azimuth,radial velocity,and altitude of meteor trails so that one can invert the wind profiles in the mesosphere and low thermosphere(MLT)region,based on the Interferometric and Doppler techniques.In this paper,the horizontal wind field,gravity wave(GW)disturbance variance,and GW fluxes are analyzed through the meteor radar observation from 2012−2022,at Mohe(53.5°N,122.4°E)and Zuoling(30.5°N,114.6°E)stations of the(Chinese)Meridian Project.The Lomb−Scargle periodogram method has been utilized to analyze the periodic variations for time series with observational data gaps.The results show that the zonal winds at both stations are eastward dominated,while the meridional winds are southward dominated.The variance of GW disturbances in the zonal and meridional directions increases gradually with height,and there is a strong pattern of annual variation.The zonal momentum flux of GW changes little with height,showing weak annual variation.The meridional GW flux varies gradually from northward to southward with height,and the annual periodicity is stronger.For both stations,the maximum values of zonal and meridional wind occur close to the peak heights of GW flux,with opposite directions.This observational evidence is consistent with the filtering theory.The horizontal wind velocity,GW flux,and disturbance variance of the GW at Mohe are overall smaller than those at Zuoling,indicating weaker activities in the MLT at Mohe.The power spectral density(PSD)calculated by the Lomb−Scargle periodogram shows that there are 12-month period and 6-month period in horizontal wind field,GW disturbance variance and GW flux at both stations,and especially there is also a 4-month cycle in the disturbance variance.The PSD of the 12-month and 6-month cycles exhibits maximum values below 88 km and above 94 km.展开更多
基金supported by the National Natural Science Foundation of China(12172023).
文摘The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.
基金supported by the Fundamental Research Funds for the Central Universities,CHD(NO.300102263205 and NO.300102264916)the West Light Cross-Disciplinary Innovation team of Chinese Academy of Sciences(NO.E1294301).supported by the Fundamental Research Funds for the Central Universities,CHD(NO.300102263205 and NO.300102264916)the West Light Cross-Disciplinary Innovation team of Chinese Academy of Sciences(NO.E1294301).
文摘The meteor radar can detect the zenith angle,azimuth,radial velocity,and altitude of meteor trails so that one can invert the wind profiles in the mesosphere and low thermosphere(MLT)region,based on the Interferometric and Doppler techniques.In this paper,the horizontal wind field,gravity wave(GW)disturbance variance,and GW fluxes are analyzed through the meteor radar observation from 2012−2022,at Mohe(53.5°N,122.4°E)and Zuoling(30.5°N,114.6°E)stations of the(Chinese)Meridian Project.The Lomb−Scargle periodogram method has been utilized to analyze the periodic variations for time series with observational data gaps.The results show that the zonal winds at both stations are eastward dominated,while the meridional winds are southward dominated.The variance of GW disturbances in the zonal and meridional directions increases gradually with height,and there is a strong pattern of annual variation.The zonal momentum flux of GW changes little with height,showing weak annual variation.The meridional GW flux varies gradually from northward to southward with height,and the annual periodicity is stronger.For both stations,the maximum values of zonal and meridional wind occur close to the peak heights of GW flux,with opposite directions.This observational evidence is consistent with the filtering theory.The horizontal wind velocity,GW flux,and disturbance variance of the GW at Mohe are overall smaller than those at Zuoling,indicating weaker activities in the MLT at Mohe.The power spectral density(PSD)calculated by the Lomb−Scargle periodogram shows that there are 12-month period and 6-month period in horizontal wind field,GW disturbance variance and GW flux at both stations,and especially there is also a 4-month cycle in the disturbance variance.The PSD of the 12-month and 6-month cycles exhibits maximum values below 88 km and above 94 km.
