Many electrically driven thermoacoustic refrigerators have employed corrugated metal bellows to couple work from an electro-mechanical transducer to the working fluid typically. An alternative bellows structure to mediate this power transfer is proposed: a laminated hollow cylinder comprised of alternating layers of rubber and metal ‘hoop-stack’.

Fatigue and visoelastic power dissipation in the rubber are critical considerations; strain energy density plays a role in both. Optimal aspect ratios for a rectangle corss-section in the rubber, for given values of bellows axial strain and oscillatory pressure loads are discussed. Comparisons of tearing energies estimated from known load cases and those obtained by finite element analysis for candidate dimensions are presented.

The metal layers of bellows are subject to an out-of-plane buckling instability for the case of external pressure loading; failure of this type was experimentally observed. The proposed structure also exhibits column instability when subject to internal pressure, as do metal bellows. For hoop-stack bellows, shear deflection cannot be ignored and this leads to column instability for both internal and external pressures, the latter being analogous to the case of tension buckling of a beam.

During prototype bellows testing, transverse modes of vibration are believed to have been excited parametrically as a consequence of the oscillatory pressures. Some operating frequencies of interest in this study lie above the cut-on frequency at which Timoshenko beam theory (TBT) predicts multiple phase speeds; it is shown that TBT fails to accurately predict both mode shapes and resonance frequencies in this regime. TBT is also shown to predict multiple phase speeds in the presence of axial tension, or external pressures, at magnitudes of interest in this study, over the entire frequency spectrum.

For modes below cut-on absent a pressure differential (or equivalently, axial load) TBT predicts decreasing resonance frequencies for both internal external static pressure, and converges on known, valid static buckling solutions. Parametric stability in the presence of oscillatory pressure is discussed for such modes; periodic solutions to the Whittaker-Hill equation are pursued to illustrate the shape of the parametric instability regions, and contrasted with results of the more well-known Mathieu equation.