Using spherical coordinates, the coupling nonlinear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O varia- tional principle, and the viscous damping is int...Using spherical coordinates, the coupling nonlinear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O varia- tional principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.展开更多
Based on Biot＇s dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arb...Based on Biot＇s dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived. Influence of the reflected wave generated by the boundary was revealed. Numerical results indicate that the vibration frequency has some effect on the vertical displacement of satu rated soil. The vertical displacement at the surface of saturated soil lags in phase with the load. Furthermore, the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied, but when the load becomes stable, the effect is inapparent.展开更多
基金supported by the National Natural Science Foundation of China(11102006,11172145)the Research Fund for the Doctoral Program of Higher Education(20101102120013)
文摘Using spherical coordinates, the coupling nonlinear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O varia- tional principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.
基金Project supported by the National Natural Science Foundation of China(No.50478081)
文摘Based on Biot＇s dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived. Influence of the reflected wave generated by the boundary was revealed. Numerical results indicate that the vibration frequency has some effect on the vertical displacement of satu rated soil. The vertical displacement at the surface of saturated soil lags in phase with the load. Furthermore, the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied, but when the load becomes stable, the effect is inapparent.
