波纹管的特征值分析

EIGENVALUE ANALYSIS ON BELLOWS

基于Novozhilov薄壳理论 ,用有限元法建立了旋转波纹管非轴对称自由振动的广义特征值方程并进行了求解。选取两结点非协调曲边旋转壳单元作为波纹管的离散单元 ,并将所有相关变量沿其环向进行了Fourier展开。该方法不仅给出了子午线曲率连续变化的U型波纹管任意环向谐波所对应的特征值 ,而且对子午线曲率有突变的C型波纹管旋转壳也能很好地适应。算例结果表明 ,波纹管不存在一个最低固有频率对应的固定环向波数 ,但其轴对称振型和低阶非轴对称振型在动态分析中占绝对优势 ,高阶振型的作用并不明显。

On the basis of the thin shells theory of Novozhilov theory, the generalized eigenvalue equations for revolving bellows corresponding to non axisymmetric nature vibration are established and solved with finite element method. By discretizing the bellows with incompatible curved elements of revolving shells, and expanding all dependent variables into Fourier series in circumferential direction, the eigenvalue being corresponding to arbitrary harmonic wave of U shaped bellows with continuously changable curvity of meridian is given. The given eigenvalue is also favourable to that of C shaped bellows with abrupt curvity. The correctness of present result is exemplified, and some practical conclusions are obtained. Although there exists no fixed circumferential harmonic number corresponding to the lowest natural frequency of bellow, the symmetric and lower order non axisymmetric modes are in the absolute predominance, while the higher order modes play an unimportant role in its dynamic analysis.