Conference Paper

A Novel Snap-through Buckling Behavior of Axisymmetric Shallow Shells with Possible Application in Transducer Design.

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The behavior of spherical caps under radial dynamic edge loading in theform of step loading of infinite duration in the time domain has beeninvestigated. The aim here is to present a mathematical model of shallowshells of revolution which may undergo snap-through buckling as a resultof the radial displacement of the circular boundary. The snap-throughbuckling under such a loading condition is contrary to intuition and itseems not to have been previously observed. In this search it isobserved that snap-through buckling is also possible under peripheraldynamic loading conditions. The amount of snapping is remarkable whenthe cap has an opening around the apex. A technological application ofthe peripheral type of loading is seen in metal-ceramic compositetransducers achieved by installing a piezoelectric ceramic disk betweentwo metal end caps. The radial motion of the ceramic is converted into aflex-tensional motion in the spherical caps. As a result, a largedisplacement is obtained in the perpendicular direction, which mayresult in snap-through buckling. For the numerical solution of theproblem a computer program, using a linearized finite elementincremental-iterative approach based on updated Lagrangian formulationis developed, and the whole process is accomplished using the Newmarkmethod as the time integration scheme.
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