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Previous studies of precariously balanced objects in seismically activeregions provide important information for aseismatic engineering andtheoretical seismology. They are almost founded on an oversimplifiedassumption: any 3-dimensional (3D) actual object with special symmetry could beregarded as a 2D finite object in light of the corresponding symmetry. To gainan actual evolution of precariously balanced objects subjected to variouslevels of ground accelerations, a 3D investigation should be performed. Invirtue of some reasonable works from a number of mechanicians, we derive threeresultant second-order ordinary differential equations determine the evolutionof 3D responses. The new dynamic analysis is following the 3D rotation of arigid body around a fixed point. A computer program for numerical solution ofthese equations is also developed to simulate the rocking and rolling responseof axisymmetric objects to various levels of ground accelerations. It is shownthat the 2D and 3D estimates on the minimum overturning acceleration of acylinder under the same sets of half- and full-sine-wave pulses are almostconsistent except at several frequency bonds. However, we find that the 2D and3D responses using the actual seismic excitation have distinct differences,especially to north-south (NS) and up-down (UD) components. In this work thechosen seismic wave is the El Centro recording of the 18 May 1940 ImperialValley Earthquake. The 3D outcome does not seem to support the 2D previousresult that the vertical component of the ground acceleration is less importantthan the horizontal ones. We conclude that the 2D dynamic modeling is notalways reliable.

Response of 3D Free Axisymmetric Rigid Objects under Seismic Excitations