The Melnikov criterion of instability for random rocking dynamics of a rigid block with an attached secondary structure
The author investigates the dynamic behavior of a structure consisting of a rectangular symmetric rigid block (or a frame) with an attached chain of point masses coupled by linear viscoelastic suspensions and moving along the vertical axis of symmetry of the block. Assuming rigid foundation, large friction to prevent sliding, and the Newton restitution law at impact, the only possible response of the structure is rocking about the corners of the block accompanied by relative oscillations of the secondary structure. The problem of rocking is nonlinear even for the simple case of the planar response of a slender rigid uniform rectangular block on a flat rigid horizontal foundation. The nonlinearity is due to the impact occurring when the corner of rotation switches from one side of the block to the other. It is shown that under some non-restrictive assumptions, the rigid model is acceptable, but the condition of stability depends on the parameters of the secondary structure. 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.
scientific article; zbMATH DE number 5656669