正弦波纹扁球壳的非线性强迫振动

Nonlinear Forced Vibration of Sinusoidal Corrugated Shallow Spherical Shell

波纹壳是传感器弹性元件的一类重要形式,也是精密仪器仪表弹性元件中的一类重要形式。由于波纹壳形状复杂、参数众多、厚度薄,对其进行非线性分析非常重要同时也是十分困难的。本文考虑一种在传感器弹性元件中有重要应用价值的正弦波纹浅球壳体,将这种壳体视为结构上的圆柱正交异性扁球壳,根据Andryewa的思想,分别得到了正弦波纹壳径向、环向在拉伸、弯曲下的等价的四个各向异性参数;建立了正弦波纹扁球壳的非线性强迫振动微分方程;得到了正弦波纹扁球壳非线性强迫振动的共振周期解及幅频特性曲线。

The corrugated shells are important elastic elements, which can be widely applied in precise instruments and other engineering. It is quite difficult to analyse nonlinear problems of corrugated shells because of their complicated shape and too many parameters. A sinusoidal corrugated shallow spherical shell was discussed which is used as elastic elements. The problem of nonlinear forced vibration of the shell was studied. According to Andryewa＇s theory, four equivalent orthotropic parameters of the corrugated shal- low shell were obtained. The differential equations of nonlinear vibration of the shell were obtained. The cycle solution of nonlinear vibration was developed.