Analysis, simulations, and experiments are performed for a piston in a vibrated liquid-filled cylinder, where the damping caused by forcing liquid through narrow gaps depends almost linearly on the piston position. Adding a little gas completely changes the dynamics of this spring-mass-damper system when it is subject to vibration. When no gas is present, the piston’s vibrational response is highly overdamped due to the viscous liquid being forced through the narrow gaps. When a small amount of gas is added, Bjerknes forces cause some gas to migrate below the piston. The resulting pneumatic spring enables the liquid to move with the piston so that little liquid is forced through the gaps. This “Couette mode” thus has low damping and a strong resonance near the frequency given by the pneumatic spring constant and the piston mass. Near this frequency, the piston response is large, and the nonlinearity from the varying gap length produces a net force on the piston. This “rectified” force can be many times the piston’s weight and can cause the piston to compress its supporting spring.
A surrogate system in which the gas regions are replaced by upper and lower bellows with similar compressibility is studied. A recently developed theory for the piston and bellows motions is compared to finite element simulations. The liquid obeys the unsteady incompressible Navier-Stokes equations, and the piston and the bellows obey Newton’s 2nd Law. Due to the large piston displacements near resonance, an Arbitrary Lagrangian Eulerian (ALE) technique with a sliding-mesh scheme is used to limit mesh distortion. Theory and simulation results for the piston motion are in good agreement.
Experiments are performed with liquid only, with gas present, and with upper and lower bellows replacing the gas. Liquid viscosity, bellows compressibility, vibration amplitude, and gap geometry are varied to determine their effects on the frequency at which the rectified force makes the piston move down. This critical frequency is found to depend on whether the frequency is increased or decreased with time.