Internal resonance in nonlinear vibration of functionally graded （FG） circular cylin- drical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considere...Internal resonance in nonlinear vibration of functionally graded （FG） circular cylin- drical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considered to be temperature-dependent. Based on the Karman-Donnell＇s nonlinear shell theory, the kinetic and potential energy of FG cylindrical thin shells are formu- lated. The primary target is to investigate the two-mode internal resonance, which is triggered by geometric and material parameters of shells. Following a secular perturbation procedure, the underlying dynamic characteristics of the two-mode interactions in both exact and near resonance cases are fully discussed. It is revealed that the system will undergo a bifurcation in near resonance case, which induces the dynamic response at high energy level being distinct from the motion at low energy level. The effects of temperature and volume fractions of composition on the exact resonance condition and bifurcation characteristics of FG cylindrical shells are also investigated.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11072204 and 11372257)
文摘Internal resonance in nonlinear vibration of functionally graded （FG） circular cylin- drical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considered to be temperature-dependent. Based on the Karman-Donnell＇s nonlinear shell theory, the kinetic and potential energy of FG cylindrical thin shells are formu- lated. The primary target is to investigate the two-mode internal resonance, which is triggered by geometric and material parameters of shells. Following a secular perturbation procedure, the underlying dynamic characteristics of the two-mode interactions in both exact and near resonance cases are fully discussed. It is revealed that the system will undergo a bifurcation in near resonance case, which induces the dynamic response at high energy level being distinct from the motion at low energy level. The effects of temperature and volume fractions of composition on the exact resonance condition and bifurcation characteristics of FG cylindrical shells are also investigated.
