  Previous studies of precariously balanced objects in seismically active
regions provide important information for aseismatic engineering and
theoretical seismology. They are almost founded on an oversimplified
assumption: any 3-dimensional (3D) actual object with special symmetry could be
regarded as a 2D finite object in light of the corresponding symmetry. To gain
an actual evolution of precariously balanced objects subjected to various
levels of ground accelerations, a 3D investigation should be performed. In
virtue of some reasonable works from a number of mechanicians, we derive three
resultant second-order ordinary differential equations determine the evolution
of 3D responses. The new dynamic analysis is following the 3D rotation of a
rigid body around a fixed point. A computer program for numerical solution of
these equations is also developed to simulate the rocking and rolling response
of axisymmetric objects to various levels of ground accelerations. It is shown
that the 2D and 3D estimates on the minimum overturning acceleration of a
cylinder under the same sets of half- and full-sine-wave pulses are almost
consistent except at several frequency bonds. However, we find that the 2D and
3D responses using the actual seismic excitation have distinct differences,
especially to north-south (NS) and up-down (UD) components. In this work the
chosen seismic wave is the El Centro recording of the 18 May 1940 Imperial
Valley Earthquake. The 3D outcome does not seem to support the 2D previous
result that the vertical component of the ground acceleration is less important
than the horizontal ones. We conclude that the 2D dynamic modeling is not
always reliable.
