Space-Time Analysis of the Flow-Induced Vibration of a Solid Containing anEmbedded Cylindrical Shell

摘要

This report develops a model of a viscoelastic solid that contains an embeddedcylindrical shell through which fluid flows at low Mach number. The model output corresponds to the displacement that a beamformed, steered array of sensors would measure in wavenumber and frequency. The solid and the shell are modeled using elasticity equations of isotropic mediums. The fluid is modeled with two pressure terms: one that represents the acoustic pressure field and one that represents the normal forces of the turbulent boundary layer on the inner wall of the cylindrical shell. The fluid equations are coupled to the solid equations by conservation of momentum. The spatial (or wave number) response of the array and the array elements are also included in the model. All the model terms are assembled in an integral equation and numerically evaluated at various frequencies. The work is verified with an experiment in which gravity-fed water is passed through a piece of surgical tubing that is contained in the block. Displacement measurements of the free surface of the block are made with an eight-element array, and the results are compared to the theoretical model. It is shown that the model and the experiment are in good agreement. (MM).