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Nonlinear Dynamics of Shallow Spherical Caps Subjected to Peripheral Loading

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Abstract

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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Authors and Affiliations

  1. Department of Civil Engineering, Eastern Mediterranean University, Gazimagusa, T.R.N.C. Via Mersin 10, Turkey

    Ghassan Odeh

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  1. Ghassan Odeh
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Odeh, G. Nonlinear Dynamics of Shallow Spherical Caps Subjected to Peripheral Loading. Nonlinear Dynamics 33, 155–164 (2003). https://doi.org/10.1023/A:1026043624118

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