An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification

Vassiliou, Michalis F.; Truniger, Rico; Stojadinović, Božidar

doi:10.1002/eqe.2608

Cited by 89 publications

(169 citation statements)

References 43 publications

(87 reference statements)

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“…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. Similarly, Vassilou et al 11 extended previous models for flexible rocking structures to account for the distributed mass of the column and foundation. In these models, the authors derived expressions for the energy dissipation at impact for a rigid interface, similar to previous studies.…”

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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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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“…Uplift of the podium structure affects the vibration properties of the SDOF superstructure [7,27,58]. An eigenfrequency analysis reveals that there are two distinct mode shapes of the podium structure: one is overturning of the rocking frame structure with a natural frequency of 0 Hz, and the other is the vibration of the SDOF system when the rocking frame structure is uplifted.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Model for Dynamic Response of an Elastic Sdof System Fixed on Top of a Rocking Single-Story Frame Structure: Experimental Validation

Bachmann¹,

Jost²,

Studemann³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…without tendons) taking advantage of the well-studied dynamic behavior of rocking structures. Indeed, a simple freestanding rocking block has been systematically studied for more than five decades both when the block is assumed rigid [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and when it assumed deformable [27][28][29][30][31][32][33][34][35][36][37]. Small scale experiments have been also performed [38][39][40][41][42][43][44][45][46][47][48][49][50][51].…”

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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An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification

Cited by 89 publications

References 43 publications

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

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

An Analytical Model for Dynamic Response of an Elastic Sdof System Fixed on Top of a Rocking Single-Story Frame Structure: Experimental Validation

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

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