关键词: 单圆弧波纹管, 膜片, Galerkin法, Floquet指数, 稳定性

Abstract: The single arc bellows diaphragm is regarded as the combined structure of the circular plate with initial deflection by the pseudo-plate method. In the research, the nonlinear dynamic equations of single circular arc diaphragm under static and dynamic loads are obtained by using the nonlinear bending theory for thin plate and thin shell. Given boundary conditions and continuous conditions to the equations, the deflection and tension of the diaphragm under the synergistic effect of static-dynamic loading can be predicted. The forced vibration equation of the nonlinear system of the single arc bellows diaphragm can be also obtained on the basis of the Galerkin method. The bifurcation problem of the system without external excitation is studied and stability of the single arc bellows diaphragm at the equilibrium point is discussed in terms of the Floquet index. Meanwhile, the change of the equilibrium position of the system under effect dynamic load only and under coupling effect of static-dynamic load is taken into account in this research. The results indicate that the Hopf bifurcation of the single circular arc diaphragm system becomes more delayed under dynamic-static loading than under dynamic loading only.

Key words: single arc bellows, diaphragm, the Galerkin methods, the Floquet index, stability