In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and pr...In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and prove convergence of formal so- lutions under conditions. -We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function.展开更多
The dynamic buckling of an elastic-plastic column subjected to axial impact by a rigid body has been discussed in this paper. The whole traveling process of elastic-plastic waves under impact action is analyzed with t...The dynamic buckling of an elastic-plastic column subjected to axial impact by a rigid body has been discussed in this paper. The whole traveling process of elastic-plastic waves under impact action is analyzed with the characteristics method. The regularity of stress changes in both column ends and the first separating time of a rigid body and column are obtained. By using the energy principle and taking into account the propagation and reflection of stress waves the lateral disturbance equation is derived and the power series solution is given. In addition, the critical buckling condition can be obtained from the stability analysis of the solution. By numerical computation and analysis, the relationship among critical velocity and impact mass, hardening modulus, and buckling time is given.展开更多
Under investigation in this paper is a hyperbolic mean curvature flow for convex evolving curves.Firstly,in view of Lie group analysis,infinitesimal generators,symmetry groups and an optimal system of symmetries of th...Under investigation in this paper is a hyperbolic mean curvature flow for convex evolving curves.Firstly,in view of Lie group analysis,infinitesimal generators,symmetry groups and an optimal system of symmetries of the considered hyperbolic mean curvature flow are presented.At the same time,some group invariant solutions are computed through reduced equations.In particular,we construct explicit solutions by applying the power series method.Furthermore,the convergence of the solutions of power series is certificated.Finally,conservation laws of the hyperbolic mean curvature flow are established via Ibragimov's approach.展开更多
The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge condit...The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions. It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously. The complex modulus approach is employed in conjunction with the elastic-viscoelastic correspondence principle to obtain the solution. The governing equations are solved by means of a power series solution. Finally, a sensitivity analysis including evaluation of effects of various edge conditions, thickness variations, coefficients of the elastic foundation, and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.展开更多
文摘In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and prove convergence of formal so- lutions under conditions. -We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function.
基金Project supported by the National Natural Science Foundation of China (No. 10472076).
文摘The dynamic buckling of an elastic-plastic column subjected to axial impact by a rigid body has been discussed in this paper. The whole traveling process of elastic-plastic waves under impact action is analyzed with the characteristics method. The regularity of stress changes in both column ends and the first separating time of a rigid body and column are obtained. By using the energy principle and taking into account the propagation and reflection of stress waves the lateral disturbance equation is derived and the power series solution is given. In addition, the critical buckling condition can be obtained from the stability analysis of the solution. By numerical computation and analysis, the relationship among critical velocity and impact mass, hardening modulus, and buckling time is given.
基金Supported by the Natural Science Foundation of Shanxi(202103021224068).
文摘Under investigation in this paper is a hyperbolic mean curvature flow for convex evolving curves.Firstly,in view of Lie group analysis,infinitesimal generators,symmetry groups and an optimal system of symmetries of the considered hyperbolic mean curvature flow are presented.At the same time,some group invariant solutions are computed through reduced equations.In particular,we construct explicit solutions by applying the power series method.Furthermore,the convergence of the solutions of power series is certificated.Finally,conservation laws of the hyperbolic mean curvature flow are established via Ibragimov's approach.
文摘The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions. It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously. The complex modulus approach is employed in conjunction with the elastic-viscoelastic correspondence principle to obtain the solution. The governing equations are solved by means of a power series solution. Finally, a sensitivity analysis including evaluation of effects of various edge conditions, thickness variations, coefficients of the elastic foundation, and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.
