Finite-Amplitude Motion of a Piston in a Shallow, Fluid-Filled Cavity

A theoretical treatment of the motion of a piston in a fluid-filled cavity is presented. Emphasis is on the steady-state response of the piston to a sinusoidal driving force. Effects of finite amplitude and finite length of the cavity are taken into account; frictional damping is also considered. It is found that if the piston is driven hard enough in the neighborhood of resonance, the motion is markedly influenced by the nonlinearity of the equation of state (pressure-density relation) of the fluid. The fluid-filled cavity behaves as a nonlinear spring. The theoretical results show how measurements of the piston motion might be used to obtain data on the coefficients of the most important nonlinear terms in the equation of state of the fluid. Push-pull as well as single-sided piston-cavity systems are analyzed.