3D model of rigid block with a rectangular base subject to pulse-type excitation

Zulli, Daniele; Contento, Alessandro; Egidio, Angelo Di

doi:10.1016/j.ijnonlinmec.2011.11.004

Cited by 61 publications

(49 citation statements)

References 21 publications

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“…13(a) are illustrated in Figs. 67,68,69 in [63]. In particular, the number of impacts before the overturn event may be seen on the θ(t) curves (a), (b), (c) of these figures.…”

Section: Pulse-type Base Excitationmentioning

confidence: 99%

“…The conclusions to be drawn from all these works are that experimental results are not always easy to interpret, and kinematic restitution rules applied to planar models are too simplistic to correctly model the motion of a block rebounding on a ground, which may consist of complex stick/slip/impact/rebound phases. Recently, three-dimensional models have been developed [67], thus relaxing the assumption that the system is confined in a 2D motion.…”

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confidence: 99%

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Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data

2013

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This paper concerns the dynamics of planar rocking blocks, which are mechanical systems subject to two unilateral constraints with friction. A recently introduced multiple impact law that incorporates Coulomb friction is validated through comparisons between numerical simulations and experimental data obtained elsewhere by other authors. They concern the free-rocking motion with no base excitation, and motions with various base excitations for the study of the onset of rocking and of the overturning phenomenon. The comparisons made for free-rocking and for the onset of rocking demonstrate that the proposed impact model allows one to correctly predict the block motions. Especially the free-rocking experiments can be used to fit the impact law parameters (restitution and friction coefficients, block width). The free-rocking fitted parameters are then used in the excited-base cases.

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“…13(a) are illustrated in Figs. 67,68,69 in [63]. In particular, the number of impacts before the overturn event may be seen on the θ(t) curves (a), (b), (c) of these figures.…”

Section: Pulse-type Base Excitationmentioning

confidence: 99%

mentioning

confidence: 99%

Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data

2013

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“…For example, Konstantinidis and Makris 6 derived the equations of motion of a three-dimensional, rigid block for free rocking. This work was extended by Zulli et al 7 to account for dynamic base excitation as well as eccentricity of the mass atop a rectangular footprint. Mass eccentricity was further studied probabilistically in a two-dimensional formulation by Purvance et al 8 and with respect to minimum overturning acceleration by Shi et al 9 Related to flexibility of the block, Acikgoz and DeJong 10 derived the equations of motion for a linear elastic oscillator able to uplift at its rigid base.…”

Section: Introductionmentioning

confidence: 99%

Rocking bodies with arbitrary interface defects: Analytical development and experimental verification

Wittich

Hutchinson

2017

Earthq Engng Struct Dyn

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SummaryThe rocking response of a rigid, freestanding block in two dimensions typically assumes perfect contact at the base of the block with instantaneous impacts at two distinct, symmetric rocking points. This paper extends the classical two-dimensional rocking model to account for an arbitrary number of rocking points at the base representing geometric interface defects. The equations of motion of this modified rocking system are derived and presented in general terms. Energy dissipation is modeled assuming instantaneous point impacts, yielding a discrete angular velocity adjustment. Whereas this factor is always less than unity in the classical model, it is possible for this factor to exceed unity in the presented model, yielding a finite increase in the angular velocity at impact and a markedly different rotational response than the classical model predicts. The derived model and the classical model are numerically integrated and compared to the results of recent shake table tests. These comparisons show that the new model significantly enhances agreement in both peak angular displacement and motion decay. The equations of motion and the energy dissipation of the presented model are further investigated parametrically considering the size of the defect, the number of rocking points, and the aspect ratio and size of the block. | INTRODUCTIONThe original motivation for studying freestanding and rocking structures stems from the observed overturning of small, slender structures compared to the apparent stability of certain larger, slender structures following strong earthquake excitations. 1 More recently, motivation has shifted to the intentional design of rocking structures in an effort to harness their inherent energy dissipation and self-centering mechanisms (e.g., Ref [ 2 ], and references therein). Additionally, the class of freestanding and rocking structures includes water towers, gravestones, nuclear radiation shields, mechanical and electrical equipment, and culturally significant statues and columns. Since many of these components are critical to a facility's post-earthquake functionality or are culturally significant, accurate prediction of the seismic response is necessary.The well-known and broadly utilized classical rocking model was introduced in the pioneering work of Housner. 1 This rocking model considers a two-dimensional, symmetric, rectangular, rigid block that oscillates about two rocking points at its base atop a rigid foundation. The model further assumes that there is sufficient friction to prevent sliding and that the block transitions smoothly between rocking points through an inelastic impact with conservation of angular momentum. The response of this block is modeled as a set of piecewise equations of motion and an instantaneous reduction of angular velocity at the moment of impact. This velocity reduction is typically known as a coefficient of restitution and is strictly a function of geometry

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“…not constrained by tendons) 3d rocking motion was studied in the context of rocking structures [69,70] (and not of the protection of equipment [71][72][73][74][75][76]). The main difference between the unintentional rocking for equipment protection and intentional structural column rocking, is that structures need to return to their original position.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of a Rigid Slab Supported by Four Rigid Cylinrical Rocking and Wobbling Columns

Rajah¹,

Bachmann²,

Vassiliou³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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3D model of rigid block with a rectangular base subject to pulse-type excitation

Cited by 61 publications

References 21 publications

Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data

Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data

Rocking bodies with arbitrary interface defects: Analytical development and experimental verification

Dynamic Response of a Rigid Slab Supported by Four Rigid Cylinrical Rocking and Wobbling Columns

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