Abstract
The continuous small amplitude disturbances generated by the oscillations of a piston in a gas contained in a closed-ended tube are discussed. The coupled characteristic equations are integrated exactly for a model equation of state which approximates any stress–strain law with an error at
O
([strain]
3
). When the small amplitude limit is taken and the relative importance of amplitude dispersion and nonlinear interaction is assessed, the disturbances can be determined from solutions to a nonlinear functional equation. The motions are characterized by a similarity parameter,
A
, and a frequency parameter,
∆
. A simple algebraic scheme for constructing continuous periodic solutions of the functional equation is given, and the
A–∆
plane is divided by a transition curve. The various resonances are then evident.
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