Behavior of Inverted Pendulum Cylindrical Structures That Rock and Wobble During Earthquakes

Abstract eng:
The in-plane (2d) response of rigid rocking blocks has been extensively studied. In order to use rocking as a seismic response modification strategy for large structures (such as bridges and chimneys), the rocking motion of bodies in two orthogonal planes (3d rocking) needs to be explored first. Dynamic models of systems allowed to step out or roll out of their initial position and rocking plane have received attention. However, under earthquake excitation such systems may remain stable, but often end their motion with significant residual displacements with respect to their starting position. Such behavior is not acceptable for real structures. This paper studies the 3d motion of a rigid cylinder that is allowed to uplift and sustain rocking and wobbling motion without sliding or rolling-out of its initial position. Like a rectangular body in 2d rocking motion, the cylinder has zero residual displacement at the end of its 3d motion. The 3d dynamic model of the cylinder has two degrees of freedom, making it the simplest 3d extension of Housner’s classical rocking model. The development of the 3d cylinder model is presented first. This model is computationally inexpensive and simple enough to perform extensive parametric analyses to understand the roles of the dominant parameters of the 3d rocking and wobbling (unsteady rolling) motion. Modes of motion of the cylinder are identified and presented. Finally, 3d rocking and wobbling spectra are constructed and compared with the classical 2d rocking spectra, to indicate that, in many cases, the 2d approach may lead to unconservative estimates of 3d rocking and wobbling response.

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