在动静载荷作用下单圆弧波纹管膜片非线性稳定性分析

借助拟板法把单圆弧波纹管膜片处理成具有初挠度圆环板的组合结构.利用薄板薄壳的非线性弯曲理论,得到单圆弧膜片在静态和动态载荷协同作用下的非线性动力学方程组.给定该方程组的边界条件与连续条件,可以预测静态载荷及其动态载荷协同作用下膜片的挠度和张力,从而根据Galerkin方法得到单圆弧波纹管膜片非线性系统的受迫振动方程.根据Floquet指数研究了无外激励下系统的分岔问题,讨论了单圆弧波纹管膜片在平衡点领域的稳定性问题,同时考虑了系统在纯动态载荷作用和动静态载荷协同作用下其平衡位置的变化情况.研究结果表明单圆弧膜片系统在动静态载荷协同作用下比在纯动态作用下系统发生Hopf分岔更为滞后.

Nonlinear stability analysis of the single arc bellows diaphragm under static-dynamic load

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.