NONSMOOTH MODELLING OF IMPACTS IN ROCKING STRUCTURES WITH POISSON’S LAW

Abstract eng:
Rocking action offers a favorable seismic isolation effect that relieves the structure from deformation and damage during strong earthquakes. A complete description of the dynamics of a rocking structure requires, apart from the equation of motion, an appropriate treatment of the contact phenomenon. During rocking, when rotation reverses, the smooth motion of the structure is interrupted by nonsmooth impacts. To date, most analytical and numerical investigations on the rocking behavior treat impacts adopting the ‘classical’ model of the angular coefficient of restitution or with ad-hoc assumptions. This paper revisits the contact process encountered in two archetypal rocking structures: the rigid rocking block and the flexible rocking oscillator from a nonsmooth dynamics perspective. It considers impact as an instantaneous event and treats it through a system of inequalities known as the linear complementarity problem (LCP). This study models contact behavior with a set-valued Poisson’s law in the normal direction and assumes sticking behavior in the tangential direction. The analysis demonstrates the ability of the proposed methodology to capture the impact behavior of different structures rocking on a rigid base. The results show that the proposed LCPs verify corresponding analytical results of other methodologies. Specifically, regarding the rocking block, comparisons of the nonsmooth model with the ‘classical’ impact model reveal perfect agreement. This study further unveils the substantial role of the Poisson’s coefficient of restitution in capturing the experimental response of the flexible rocking oscillator in cases where other analytical models fail. Most importantly, the nonsmooth dynamics approach captures all physically feasible postimpact states, which can be solved both analytically and numerically. Finally, the proposed approach offers a more concise description of the impact problem in rocking structures and it contributes to a more realistic treatment and better understanding of the contact phenomenon during rocking.

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