A numerical procedure to calculate the pre-buckling and post- buckling response of general structures is presented. This procedure is based on the pseudo-arclength algorithm suggested by E. Riks et al., which has some...A numerical procedure to calculate the pre-buckling and post- buckling response of general structures is presented. This procedure is based on the pseudo-arclength algorithm suggested by E. Riks et al., which has some numerical difficulties during implementation of large applied analysis programs. To overcome these difficulties, a scheme based on rank-1 modification of the matrix is proposed. Some examples show this procedure behaves well in passing through the limit point and is rather efficient.展开更多
Composite cylindrical shells,as key components,are widely employed in large rotating machines.However,due to the frequency bifurcations and dense frequency spectra caused by rotation,the nonlinear vibration usually ha...Composite cylindrical shells,as key components,are widely employed in large rotating machines.However,due to the frequency bifurcations and dense frequency spectra caused by rotation,the nonlinear vibration usually has the behavior of complex multiple internal resonances.In addition,the varying temperature fields make the responses of the system further difficult to obtain.Therefore,the multiple internal resonances of composite cylindrical shells with porosities induced by rotation with varying temperature fields are studied in this paper.Three different types of the temperature fields,the Coriolis forces,and the centrifugal force are considered here.The Hamilton principle and the modified Donnell nonlinear shell theory are used to obtain the equilibrium equations of the system,which are transformed into the ordinary differential equations(ODEs)by the multi-mode Galerkin technique.Thereafter,the pseudo-arclength continuation method,which can identify the regions of instability,is introduced to obtain the numerical results.The detailed parametric analysis of the rotating composite shells is performed.Multiple internal resonances caused by the interaction between backward and forward wave modes and the energy transfer phenomenon are detected.Besides,the nonlinear amplitude-frequency response curves are different under different temperature fields.展开更多
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the...Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.展开更多
The spline interpolation is used to approximate the closed orbits, and the problem of following the dosed orbit in large-scale is turned to tracking the solution curve of a nonlinear equation system in higher-dimensio...The spline interpolation is used to approximate the closed orbits, and the problem of following the dosed orbit in large-scale is turned to tracking the solution curve of a nonlinear equation system in higher-dimensional space. The deformation of the closed orbit of Lorenz equation is calculated.展开更多
文摘A numerical procedure to calculate the pre-buckling and post- buckling response of general structures is presented. This procedure is based on the pseudo-arclength algorithm suggested by E. Riks et al., which has some numerical difficulties during implementation of large applied analysis programs. To overcome these difficulties, a scheme based on rank-1 modification of the matrix is proposed. Some examples show this procedure behaves well in passing through the limit point and is rather efficient.
基金supported by the National Natural Science Foundation of China(No.11972204)。
文摘Composite cylindrical shells,as key components,are widely employed in large rotating machines.However,due to the frequency bifurcations and dense frequency spectra caused by rotation,the nonlinear vibration usually has the behavior of complex multiple internal resonances.In addition,the varying temperature fields make the responses of the system further difficult to obtain.Therefore,the multiple internal resonances of composite cylindrical shells with porosities induced by rotation with varying temperature fields are studied in this paper.Three different types of the temperature fields,the Coriolis forces,and the centrifugal force are considered here.The Hamilton principle and the modified Donnell nonlinear shell theory are used to obtain the equilibrium equations of the system,which are transformed into the ordinary differential equations(ODEs)by the multi-mode Galerkin technique.Thereafter,the pseudo-arclength continuation method,which can identify the regions of instability,is introduced to obtain the numerical results.The detailed parametric analysis of the rotating composite shells is performed.Multiple internal resonances caused by the interaction between backward and forward wave modes and the energy transfer phenomenon are detected.Besides,the nonlinear amplitude-frequency response curves are different under different temperature fields.
基金supported by the National Natural Science Foundation of China (Grant No. 10671130)the Science Foundation of Shanghai Municipal Education Commission (Grant No. 05DZ07)+2 种基金Shanghai Leading Academic Discipline Project (Grant No. T0401)Leading Foundation of Shanghai Science and Technology Commission (Grant No. 06JC14092)the Foundation of the Scientific Computing Key Laboratory of Shang-hai Universities
文摘Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
基金Project supported by the National Natural Science Foundation of China.
文摘The spline interpolation is used to approximate the closed orbits, and the problem of following the dosed orbit in large-scale is turned to tracking the solution curve of a nonlinear equation system in higher-dimensional space. The deformation of the closed orbit of Lorenz equation is calculated.
