This paper represents an attempt at the application of catastrophe theory to the dynamic stability of engineering structures. The authors not only obtain a catastrophic model of vibrational buckling of elastic arches,...This paper represents an attempt at the application of catastrophe theory to the dynamic stability of engineering structures. The authors not only obtain a catastrophic model of vibrational buckling of elastic arches, but also give the critical condition of losing stability.展开更多
Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for...Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture vas established, and a critical condition associated with the model is given.展开更多
The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's...The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.展开更多
文摘This paper represents an attempt at the application of catastrophe theory to the dynamic stability of engineering structures. The authors not only obtain a catastrophic model of vibrational buckling of elastic arches, but also give the critical condition of losing stability.
文摘Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture vas established, and a critical condition associated with the model is given.
基金The project is supported by the National Natural Science Foundation of China
文摘The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.
