The Melnikov criterion of instability for random rocking dynamics of a rigid block with an attached secondary structure

In this paper we investigate the effect of structural flexibility on rocking motion of a system consisting of a free standing rigid block with an attached chain of uniaxially moving point masses. Motion is excited by random acceleration of the ground; instability is associated with overturning of the overall structure. The condition of instability is constructed by the stochastic Melnikov method. We demonstrate a twofold effect of structural flexibility on the rocking response. The attached structure may increase the critical angular displacement and velocity in comparison with the similar parameters of the single rigid block. At the same time, the enlargement of the domain of stability enhances the contribution of the random perturbation in the Melnikov process. As a result, a lower level of random forcing can result in overturning of the structure. As an example, an effect of a single-mass secondary structure on the dynamic behavior of the system is discussed. The paper is restricted to the consideration of seismic vulnerability of the structure. A similar approach can be applied to systems with wind or wave excitation.