Practical Tutorial on cylindrical structure vibro-acoustics Part 1 - Vibrations

Abstract

The mathematics which describe the vibroacoustic behavior of cylindrical structures are imposing to say the least. Part 1 of this practical tutorial demystifies cylindrical shell vibration theory by using measured data from actual shells and pipes to explain key concepts. For any shell, you can estimate frequency ranges where shells behave like simple beams and flat plates, greatly simplifying calculations of modes of vibration and mobilities. The key is first calculating the ring frequency - the frequency where membrane waves can propagate fully around the shell circumference. Simple infinite structure theory may then be used to compute mean mobilities for beam, shell, and flat plate behavior. Modes of vibration for a cylinder depend on both longitudinal and circumferential harmonics, or a helical wavenumber. Cremer's simple approximate resonance frequency formula is used to show examples for a large diameter short shell and a small diameter long shell (a pipe). Finally, the measured modal densities of an elbowed pipe are compared to estimates from an empirical expression for modal density of a shell. In all cases in this tutorial, measurements and simple estimates agree well, showing that cylindrical shell vibrations may be estimated without difficult math or complex computer models.