Transient fluid vibration in piping systems including non-proportional damping and mean flow: superposition of complex eigenmodes

Abstract

A complex modal superposition technique is advanced for the analysis of transient vibrations of compressible fluids in piping systems, thereby widening the range of application of the structural mechanics approach [1–3] to the most general linear systems. Real valued transient responses are calculated by use of complex valued eigenfrequencies, eigenmodes and modal Foss dampings of the vibrating fluid. Both transient pressures and transient accelerations can be prescribed. The piping systems studied may contain continuous and discrete fluid elements and also modal bodies describing three-dimensional components. The extension to complex modal superposition means that non-proportional damping and mean flow of the fluid can be accounted for. Transcendentally frequency-dependent complex valued non-symmetric mobility matrices are treated. In the calculation technique applied [4–6], the complex non-linear eigenproblem is replaced by a sequence of complex linear eigenproblems that are solved by using two-sided Ostrowski matrix iteration. Associated real valued eigenfrequencies are found by use of the Wittrick-Williams algorithm and are employed as starting values in the iterative procedure. Five numerical examples are given.