Propagation of Axisymmetric Waves in an Unlimited Elastic Shell

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Abstract
This investigation is concerned with the propagation of axisymmetric stress waves in unlimited thin shallow elastic spherical shells. In particular, a solution is obtained for an unlimited shallow spherical shell subjected to a harmonically oscillating concentrated load at the apex. This solution, exact within the scope of the linear theory of shallow shells, has an outward propagating wave character in the entire range of forcing frequency. Appropriate expressions for the mechanical impedance and the energy input are derived, and numerical results are obtained for the axial displacement corresponding to various forcing frequencies.

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