Study of coupled waves of cylinder walls and internal liquid based on cylindrical shell theory and wave equation

In the present study, we focus on coupled waves of cylinder walls and an internal liquid, one of the important issues in various fluid machinery including nuclear reactors. The main objective of this study is to propose a novel method to predict coupled wave frequencies based on the cylindrical shell theory and wave equation with the consideration of the fluid added mass. First, we introduce the fluid added mass to consider the effects of the liquid mass. Second, we discuss the vibration behavior of cylinder walls and sound propagation of an internal liquid separately to describe the coupled wave theoretically. In this discussion, we derive dispersion relations of the cylinder walls and internal liquid based on the Flugge's cylindrical shell theory and wave equation in the cylindrical coordinates, respectively. To validate our proposed theory, we conduct an experiment on the coupled waves using a SUS304 pipe as a cylinder and water as an internal liquid. As a result of frequency analysis based on the power spectral density (PSD), we confirm that the coupled waves occur without any external vibration sources, and the vibration modes and the most prominent vibration mode vary with the flow rate of the internal water. Also, theoretical values of coupled wave frequencies consistently agree with experimental values. This result demonstrates that coupled wave frequencies can be predicted correctly using dispersion relations of cylinder walls and an internal liquid derived based on the cylindrical shell theory and wave equation with the consideration of the fluid added mass. The prediction of coupled wave frequencies for liquid-filled structures by our proposed method leads to the prevention of significant levels of vibrations and noises by making a difference between coupled wave frequencies and mechanical vibration frequencies.