A method for quantifying pipe vibrations

Failures of piping due to vibration-induced fatigue are a serious problem in the chemical process industries (CPI) and a matter of concern for the safety and reliability of plant operations. Due to the complexity of flow-induced vibrations in pipes, no closed-form design solutions — those that can be expressed in terms of well-known functions — are available. In this article, we present a method for quantifying vibration forcing functions for the optimal design of metal piping systems in the CPI, as well as an example of its use. The method is an analytical technique based on the theory of vibrations in the frequency domain (Inverse Theory of vibrations). The method can be easily adopted by practicing engineers. Nomenclature L   Length of pipe span x   Distance along the span Differential operator ω   Circular frequency σ   Stress m   Mass per unit length U   Displacement of pipe Û Fourier transform of U k   Wave number FFT   Fast Fourier transform R    Reaction force EI   Bending modulus j   Square root of –1 ()T  Vector norm η   Loss factor Z   Section…