SIMPLIFIED DISPERSION RELATIONSHIPS FOR IN-VACUO PIPES

The dispersion characteristics of a pipe offer a way to gain physical insight into its dynamic behaviour. Whilst these can be found in the literature they are generally calculated by numerically solving the characteristic equation. In this paper, a simplified characteristic equation of an in vacuo pipe is presented and from this analytical expressions for the wavenumbers for the circumferential modes below the ring frequency are derived. It is shown that before waves cut on and propagate, they change from being decaying standing waves at low frequencies to being nearfield waves. A simplified expression is also determined for the cut on frequencies of the n⩾2 circumferential modes. Simulations are presented to validate the results against some established theories of pipe vibration.