波纹管的特征值分析
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摘要
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.
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.
引文
[1] 王永岗.储油罐用波纹管的非线性分析及地震反应研究[D].北京:石油大学机电工程学院,2000.
[2] 谢志诚,付承诵,郑思梁.有曲率突变的轴对称壳(波纹壳)的有限元解[J].应用数学和力学,1981,2(1):113-130.
[3] 张进国,张对红,吕英民.旋转波纹管的固有频率的计算[J].管道技术与设备,1998,(3):3-6.
[4] LITing xin,HUJian,CENHan zhao,etal.Researchinthefieldofaxialnaturalfrequencyandspringratebe haviorofbellows[A].In:Proc5thIntConfonPresVesTech[C].SanFrancisco,Calif,1984.519-529.
[5] 朱益民,任文敏,张维.单层波纹管的轴对称振动[J].工程力学,1991,8(1):9-14.
[6] StandardsoftheExpansionJointManufacturersAssocia tion(EJMA)[S].INC(5thedn.),WhitePlains,NewYork,1980.
[7] 王永岗,吕英民,张进国.波纹管力学性能研究水平述评[J].石油机械,1999,27(12):47-50.
[8] NOVOZHILOVVV .FoundationsoftheNonlinearTheoryofElasticity[M ].Rochester,NewYork:GraylockPress,Inc,1953.
[9] GUYANRJ.Reductionofstiffnessandmassmatrices[J].AIAAJ ,1965,3(2):380-391.
[2] 谢志诚,付承诵,郑思梁.有曲率突变的轴对称壳(波纹壳)的有限元解[J].应用数学和力学,1981,2(1):113-130.
[3] 张进国,张对红,吕英民.旋转波纹管的固有频率的计算[J].管道技术与设备,1998,(3):3-6.
[4] LITing xin,HUJian,CENHan zhao,etal.Researchinthefieldofaxialnaturalfrequencyandspringratebe haviorofbellows[A].In:Proc5thIntConfonPresVesTech[C].SanFrancisco,Calif,1984.519-529.
[5] 朱益民,任文敏,张维.单层波纹管的轴对称振动[J].工程力学,1991,8(1):9-14.
[6] StandardsoftheExpansionJointManufacturersAssocia tion(EJMA)[S].INC(5thedn.),WhitePlains,NewYork,1980.
[7] 王永岗,吕英民,张进国.波纹管力学性能研究水平述评[J].石油机械,1999,27(12):47-50.
[8] NOVOZHILOVVV .FoundationsoftheNonlinearTheoryofElasticity[M ].Rochester,NewYork:GraylockPress,Inc,1953.
[9] GUYANRJ.Reductionofstiffnessandmassmatrices[J].AIAAJ ,1965,3(2):380-391.
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