Simulation of Structural Deformations of Flexible Piping Systems by Acoustic Excitation Using Modal Controllabilities

Abstract

Valve action and pump fluctuation in piping systems can lead to undesired excitation of structural components by propagating sound waves in the fluid path. This vibro-acoustic problem is addressed by studying the dynamics as well as excitation mechanism. Fluid-structure interaction has a significant influence on both hydroacoustics and on structural deformation. Therefore, pipe models are generated in three dimensions by using Finite Elements to include higher-order deflection modes and fluid modes. The acoustic wave equation in the fluid is hereby fully coupled to the structural domain at the fluid-structure interface. These models are used for simulating transient response and for performing numerical modal analysis. Unfortunately, such 3D models are large and simulation runs turn out to be very time consuming. To overcome this limitation, reduced pipe models are needed for efficient simulations. The proposed model reduction is hereby based on a series of modal transformations and modal truncations, where focus is placed on the treatment of the nonsymmetric system matrices due to the coupling. Afterwards, dominant modes are selected based on controllability and observability considerations. Furthermore, modal controllabilities are used to quantify the excitation of vibration modes by white noise at the pipe inlet representing acoustic sources. The excitation of structural elements connected to the piping system can therefore be predicted without performing transient simulations. Numerical results are presented for spatially arranged complex piping systems including elbow pipes and joints connected to target structures to demonstrate the usefulness of the presented method for vibro-acoustic investigations. The method is to support the design and the analysis of fluid-filled elastic piping systems and its environment in the presence of acoustic sources such as in hydraulic systems.