Dynamics of a sliding‐rocking block considering impact with an adjacent wall

Abstract

Summary A freestanding rigid block subjected to base excitation can exhibit complicated motion described by five response modes: rest, pure rocking, pure sliding, combined sliding‐rocking, and free flight. Previous studies on the dynamics of a rocking block have assumed that the block does not interact with neighboring objects. However, there are many applications in which the block may start or come in contact with an adjacent boundary during its motion, for example, a bookcase or cabinet colliding with a partition wall in an earthquake. This paper investigates the dynamics of a sliding‐rocking block considering impact with an adjacent wall. A model is developed in which the base and wall are assumed rigid, and impact is treated using the classical impulse and momentum principle. The model is verified by comparing its predictions in numerical simulations against those of an existing general‐purpose rigid‐body model in which impact is treated using a viscoelastic impact model. The developed model is used to investigate the effects of different parameters on the stability of a block subjected to analytical pulse excitations. It is found that wall placement (left or right) has a dominant effect on the shape of the overturning acceleration spectra for pulse excitations. In general, decreasing the gap distance, base friction coefficient, and wall coefficient of restitution enhance the stability of the block. Similar observations are made when evaluating the overturning probability of a block using earthquake floor motions.

Shake table testing of a rocking podium: Results of a blind prediction contest

“…Both figures are adapted from Ref. 31. because it can also describe the seismic behavior of nonanchored equipment, [2][3][4][5][6][7][8][9][10][11][12] masonry structures, [13][14][15][16][17][18][19][20][21] and ancient Greco-Roman and Chinese temples. [22][23][24][25][26] Motivated by the increasing stability of larger rocking blocks with identical aspect ratios, researchers have suggested using rocking as a seismic design strategy because the uplift of the block acts as a mechanical fuse and limits the design forces of both the superstructure and the foundation.…”

“…Such structures attracted the attention of the research community after the powerful 1960 Valdivia (Chile) earthquakes, when Housner presented his seminal work 1 on the dynamics of the archetype rocking block (Figure 1). The rocking block dynamic model is useful because it can also describe the seismic behavior of nonanchored equipment, 2–12 masonry structures, 13–21 and ancient Greco‐Roman and Chinese temples 22–26 …”

Demands on nonstructural components in buildings with controlled rocking braced frames

“…The seismic demands on unanchored slender contents were computed using the model of a pure‐rocking rigid block proposed by Housner 44 . Although unanchored components may exhibit a combination of sliding and rocking, 45 the consideration of this coupled response is beyond the scope of this study. As such, it was assumed that for slender components, the interface between the floor and the block had sufficient friction to prevent sliding.…”

Simplified analysis of bilinear elastic systems exhibiting negative stiffness behavior

“…Several researchers have used a stiff tendon to keep the post‐uplift stiffness positive 23‐32 . However, in an attempt to further decrease the design moments, this paper focuses on negative stiffness systems that are designed to sustain rocking motion without sliding 33–38 . In particular, this paper focuses on negative stiffness systems that do not exhibit hysteretic damping, thus, load and unload on the same branch.…”

“…[23][24][25][26][27][28][29][30][31][32] However, in an attempt to further decrease the design moments, this paper focuses on negative stiffness systems that are designed to sustain rocking motion without sliding. [33][34][35][36][37][38] In particular, this paper focuses on negative stiffness systems that do not exhibit hysteretic damping, thus, load and unload on the same branch. These systems do not accumulate displacements as negative stiffness hysteretic systems would.…”