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Axial vibrations of U-shaped bellows with elastically restrained end conditions

机译：具有最终约束的U型波纹管的轴向振动

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摘要

Previous work by Li et al. in the area of axial vibrations of bellows dealt with fixed end conditions. However, it is seen on several occasions that bellow ends are welded to a small pipe spool that has a lumped mass such as a valve or an instrument. Hence, the present paper aims at finding out the effect of elastically restrained ends on the axial natural frequencies. The analysis considers finite stiffness axial restraints on the bellows, i.e. solving the set of equations with non-homogeneous boundary conditions. Two bellow specimens are considered for comparison having the same dimensions as taken by Li in his analysis. The transcendental frequency equation deduced is accurate as the first, second and third mode frequencies computed are in close agreement to the ones obtained by Li.
机译：Li等人先前的工作。在固定端部条件下波纹管的轴向振动区域。但是，在几种情况下都可以看到，波纹管的末端被焊接到一个小的集管上，该集管具有集总的质量，例如阀门或仪器。因此，本论文旨在找出弹性约束端对轴向固有频率的影响。该分析考虑了波纹管上的有限刚度轴向约束，即求解具有非均匀边界条件的方程组。为了进行比较，考虑使用两个波纹管样本，它们的尺寸与Li在分析中所用的尺寸相同。推论的超越频率方程是准确的，因为计算的第一，第二和第三模式频率与Li所获得的频率非常一致。

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