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This paper reinvestigates the classic problem of the dispersion relations of a cylindrical shell by obtaining a complete set of analytical solutions, based on Flügge’s theory, for all orders of circular harmonics, n=0,1,2,…,∞. The traditional numerical root search process, which requires considerable computational effort, is no longer needed. Solutions of the modal patterns (eigenvectors) for all propagating (and nonpropagating) modes are particularly emphasized, because a complete set of properly normalized eigenvectors are crucial for solving the vibration problem of a finite shell under various admissible boundary conditions. The dispersion relations and the associated eigenvectors are also the means by which to construct transfer matrices used to analyze the vibroacoustic transmission in cylindrical shell structures or pipe-hose systems. The eigenvectors obtained from the conventional method in shell analysis are not as conveniently normalized as those commonly used in mathematical physics. The present research proposes a new alternative method to find eigenvectors that are normalized such that their norms equal unity. A parallel display of the dispersion curves and the associated modal patterns has been used in the discussion and shown to provide a more insightful understanding of the wave phenomena in a cylindrical shell.

An overview of the vibro-acoustic behavior of fluid-filled piping systems is given, summarizing noise sources, how piping structures and fluids accept energy from noise sources, and how the energy is then transmitted and exchanged by wavetypes throughout the piping. Discrete and broad-band frequency noise sources from active components, such as pumps, and passive components, such as valves and flow over piping, are described, and scale on flow velocities and operating speeds. The turbulence in the fluid flow contributes to piping system noise and vibration. The turbulence in the core flow impinges on both active and passive devices, causing discrete and broad-band noise sources. Turbulence near pipe walls excites structural piping modes. Techniques for quantifying the turbulence and its effects are described. An overview of the mechanisms of acoustic and vibrational energy propagation in piping walls and fluids is given, along with a discussion of various tools used to model the propagation, such as finite element (FE) and boundary element (BE) analysis, transfer matrix (TM) analysis, and statistical energy analysis (SEA). FE and BE models may be used to model high levels of complexity in both structural-acoustic systems and noise sources, but require large model sizes at high frequencies. TM and SEA models sacrifice modeling generality, but can represent high frequency behavior at low computational cost. Finally, means of mitigating acoustic and vibration energy transmission, such as narrow-band acoustic attenuation devices (quarter wavelength silencers and Quincke tubes), broad-band acoustic attenuation devices (mufflers and acoustic filters), and broad-band structural vibration attenuation devices (isolators and rubber piping), are outlined.