Base Excitation of Rigid Bodies. I: Formulation

Shenton, Harry W.; Jones, Nicholas P.

doi:10.1061/(asce)0733-9399(1991)117:10(2286)

Cited by 174 publications

(91 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this model, planar impact was assumed, which could occur during any of these modes. Shenton and Jones 5 similarly derived the equations of motion for the multiple modes of the two-dimensional freestanding block. However, energy dissipation was treated as a singular coefficient of restitution at smooth, instantaneous point impacts.…”

Section: Introductionmentioning

confidence: 99%

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

Wittich

Hutchinson

2017

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

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

show abstract

Section: Introductionmentioning

confidence: 99%

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

Wittich

Hutchinson

2017

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

show abstract

“…Shenton III and Jones established criteria for the transition between the possible modes of response (sliding, rocking, etc.) and derived the corresponding governing equations [14]. A particular attention is given to the effects of the friction coefficients in [15].…”

Section: Introductionmentioning

confidence: 99%

Rocking Behaviour of Simple Unreinforced Load-Bearing Masonry Walls Including Soundproofing Rubber Layers

Mordant¹,

Denoël²,

Degée³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

View full text Add to dashboard Cite

show abstract

“…In the numerical simulations performed here, 0.8 ks    is always used as in [Shenton & Jones, 1991]; according to results found in [Caliò & Marletta, 2003] and , in this paper, it is always assumed 0.2.…”

Section: Seismic Excitationmentioning

confidence: 99%

“…In the past, several papers analyzed the behaviour of rigid blocks under different kind of excitations because many monolithic objects of art, such as statues, obelisks and fountains, subject to earthquake excitation, can be modelled as rigid blocks. In [Shenton & Jones, 1991] a general bi-dimensional formulation of the rigid block has been obtained and rocking and slide-rock approximated conditions have been written. More recently this model has been used to describe the behaviour of monolithic bodies subject to base excitations as a one-sine pulse excitation in [Zhang & Makris, 2001;Makris & Black, 2004, Kounadis 2010 and earthquake excitation in [Agbabian et al, 1988;Pompei et al, 1998;Taniguchi, 2002].…”

Section: Introductionmentioning

confidence: 99%

Seismic Protection of Monolithic Objects of Art Using a Constrained Oscillating Base

Contento¹,

Egidio²

2012

Advances in Geotechnical Earthquake Engineering - Soil Liquefaction and Seismic Safety of Dams and Monuments

View full text Add to dashboard Cite

Base Excitation of Rigid Bodies. I: Formulation

Cited by 174 publications

References 8 publications

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

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

Rocking Behaviour of Simple Unreinforced Load-Bearing Masonry Walls Including Soundproofing Rubber Layers

Seismic Protection of Monolithic Objects of Art Using a Constrained Oscillating Base

Contact Info

Product

Resources

About