Dynamic Behavior of Presssure Loaded Metal-Rubber Laminate Bellows Structures

A rubber-metal laminate bellows structure was investigated to replace bellows used in thermoacoustic refrigerators; in these machines they convert reciprocating mechanical work produced by a transducer, into pressure oscillations in helium gas.  Such a seemingly mundane structure exhibits some unexpected results.   Timoshenko beam theory can be extended to model  the behavior of  such a structure, employing two observations most often credited to J. A. Haringx: First, an analogy exists between an axially loaded Euler beam and a pipe without axial loading but subject to internal pressure, and second, for this type of rubber-metal laminate structure, the transverse component of the axial load acts perpendicular to the bending slope, rather than the deflection slope, as recongized by Haringx and extended by Gent.   Dynamically, the theory for the rubber metal laminate predicts somewhat unexpected behavior:  first, shifts in the shape of the dispersion curves for the Timoshenko beam, producing regimes where propagation is possible at two phase speeds at arbitrarily low frequencies, and second, an unusual  “tuning curve” for transverse resonance frequencies—in effect, the transverse resonance frequency can be reduced via internal or external pressure.   When oscillatory pressure oscillations are present, this can lead to a fluid-structure interaction in which the bellows can be parametrically excited to instability.