Nonlinear resonant oscillations of a gas in a tube of varying cross-section

Abstract

An investigation is made of the oscillations produced in a gas contained in a tube closed at one end by a rigid barrier and at the other by a piston vibrating at near resonant frequencies. For a tube of uniform cross-section this problem is now well documented. The purpose of this investigation is to demonstrate that a tube of varying cross-section can produce significant changes in the solution for quite small variations. In particular a complicated Duffing like response is possible, with solutions that are not unique for certain frequencies. A significant increase in amplitude occurs relative to non-resonant oscillations and relative to resonant oscillations in a tube of uniform cross-section. This increase can be further enhanced by suitable choice of the variations in cross-section.