Abstract
General systems of cylindrical and toroidal shells enclosing an acoustic medium are studied by their response to acoustic excitation by a plane wave with harmonic time dependence. Noteworthy features are: (i) at frequencies low compared to the fundamental the torus’ cross section deforms as an ogive due to meridional curvature, (ii) coupled elastic resonances lag resonances of the empty system, (iii) additional circumferential harmonics appear besides 0 and 1 when the exciting frequency is closest to resonances of the shell’s cross section, (iv) longitudinal acoustic resonances lag resonances of the system with rigid walls, and (v) nonresonant response peaks occur at coincidence. The present analysis demonstrates the inadequacy of beam theory to model the response of short and thin shell configurations at frequencies above the fundamental elastic resonance.
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