The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical non...The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.展开更多
By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the sep...By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of the single-layer shallow cylindrical reticulated shell is approved by using the digital simulation method and Poincare mapping.展开更多
Various aspects of the influence of the quasi-real photons and the Coulomb resonances on the formation of the crosssection of inelastic scattering of high energy electrons on atomic nuclei are investigated. Emiss is t...Various aspects of the influence of the quasi-real photons and the Coulomb resonances on the formation of the crosssection of inelastic scattering of high energy electrons on atomic nuclei are investigated. Emiss is the energy that disappears in the processes of knocking-on of protons in the reactions . A new hypothesis that interprets the origin of the energy losses is proposed. Specific experiments that can confirm or refute this hypothesis are proposed as well. The “regularized” cross-sections of electro-disintegration of nuclei by high-energy electrons are calculated in the framework of the nuclear shell model. It is shown that for the experimental verification of the existence of Coulomb resonances, it is necessary to investigate the processes at relatively small angles of scattering. The peculiarities of numerical methods that are crucial in the investigation of inelastic scattering of high-energy electrons on nuclei in the framework of the nuclear shell model are analyzed in this work as well. The cross-sections of the scattering of high-energy electrons on the angle are calculated. It is shown that the orthogonality of the wave functions of a knocked-on proton in the initial and final states plays an important role in the interpretation of this process.展开更多
基金Project supported by the Natural Science Foundation of Gansu Province of China (No.ZS021-A25-007-Z)
文摘The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.
基金Project supported by the Natural Science Foundation of Gansu Province of China(No.3Zs042-B25-006)
文摘By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of the single-layer shallow cylindrical reticulated shell is approved by using the digital simulation method and Poincare mapping.
文摘Various aspects of the influence of the quasi-real photons and the Coulomb resonances on the formation of the crosssection of inelastic scattering of high energy electrons on atomic nuclei are investigated. Emiss is the energy that disappears in the processes of knocking-on of protons in the reactions . A new hypothesis that interprets the origin of the energy losses is proposed. Specific experiments that can confirm or refute this hypothesis are proposed as well. The “regularized” cross-sections of electro-disintegration of nuclei by high-energy electrons are calculated in the framework of the nuclear shell model. It is shown that for the experimental verification of the existence of Coulomb resonances, it is necessary to investigate the processes at relatively small angles of scattering. The peculiarities of numerical methods that are crucial in the investigation of inelastic scattering of high-energy electrons on nuclei in the framework of the nuclear shell model are analyzed in this work as well. The cross-sections of the scattering of high-energy electrons on the angle are calculated. It is shown that the orthogonality of the wave functions of a knocked-on proton in the initial and final states plays an important role in the interpretation of this process.
