Dimensionality reduction of the 3D inverted pendulum cylindrical oscillator and applications on sustainable seismic design of bridges

The simplest 3D extension of Housner's planar rocking model is a (wobbling) cylinder allowed to uplift and roll on its circumference, but constrained not out initial position. useful for the description bridges that use as seismic isolation technique, in an effort save material by reducing design moment size foundations. This paper shows describing wobbling motion terms displacements rather than rotations more useful. It unveils remarkable property bodies extends motion: A small large same slenderness will sustain roughly equal top displacement, long they are close overturning. allows using response infinitely ? proxy compute all cylinders having slenderness, irrespectively their size. Thus, dimensionality problem reduced one. Moreover, this median sets ground motions can be described approximate function only two non-dimensional parameters, namely or where u displacement body.