Response analysis of rigid structures rocking on viscoelastic foundation

Palmeri, Alessandro; Makris, Nicos

doi:10.1002/eqe.800

Cited by 64 publications

(43 citation statements)

References 29 publications

(31 reference statements)

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“…An alternative formulation is however proposed by [8], also on the base of the Housner theory, that can in the present case be further simplified according to the specific expression of I O :…”

Section: Restitution Coefficientmentioning

confidence: 99%

Shaking Table Tests on Unreinforced Load-Bearing Masonry Walls – Comparison With Simple Rocking Models.

Mordant¹,

Dietz²,

Degée³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Section: Restitution Coefficientmentioning

confidence: 99%

Shaking Table Tests on Unreinforced Load-Bearing Masonry Walls – Comparison With Simple Rocking Models.

Mordant¹,

Dietz²,

Degée³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…In equation (13), T is the kinetic energy of the system and Q is the generalized force acting on the system…”

Section: Equation Of Motion Of the Rocking Framementioning

confidence: 99%

“…The substitution of equations (17) and (21) into Lagrange's equation given by (13) results to the equation of motion of the rocking frame for θ(t)<0. …”

Section: Equation Of Motion Of the Rocking Framementioning

confidence: 99%

“…The fundamental differences between the response of a rocking rigid column (inverted pendulum) and the response of the linear elastic oscillator (regular pendulum) led to the development of the rocking spectrum (Makris and Konstantinidis [10]). More recent studies pertinent to the rocking response of rigid columns have focused on more practical issues such as representation of the impact (Prieto et al [11]), the effect of the flexibility-yielding of the supporting base (Apostolou et al [12], Palmeri and Makris [13]) or the effect of seismic isolation (Vassiliou and Makris [14]). …”

Section: Introductionmentioning

confidence: 99%

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Rocking Response and Stability Analysis of an Array of Free-Standing Columns Capped With a Free-Standing Rigid Beam

Makris¹,

Vassiliou²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This paper investigates the planar rocking response of an array of free-standing columns capped with a freely supported rigid beam in an effort INTRODUCTIONUnder base shaking slender objects and tall rigid structures may enter into rocking motion that occasionally results in overturning. Early studies on the seismic response of a slender rigid block were presented by Milne [1]; however, it was Housner [2] who uncovered a sizefrequency scale effect which explained why: (a) the larger of two geometrically similar blocks can survive the excitation that will topple the smaller block; and (b) out of two same acceleration amplitude pulses, the one with the longer duration is more capable to induce overturning. Following Housner's seminal paper a number of studies have been presented to address the complex dynamics of one of the simplest man-made structures-the free standing rigid column.Yim et al. [3] conducted numerical studies by adopting a probabilistic approach, Aslam et al. [4] confirmed with experimental studies that the rocking response of rigid blocks is sensitive to system parameters; while Psycharis and Jennings [5] examined the uplift of rigid bodies supported on viscoelastic foundation. Subsequent studies by Spanos and Koh [6] investigated the rocking response due to harmonic steady-state loading and identified "safe" and "unsafe" regions together with the fundamental and suharmonic modes of the system. Their study was extended by Hogan [7], [8] who further elucidated the mathematical structure of the problem by introducing the concepts of orbital stability and Poincare sections. The transient rocking response of free-standing rigid blocks was examined in depth by Zhang and Makris [9] who showed that there exist two modes of overturning: (a) by exhibiting one or more impacts; and (b) without exhibiting any impact. The existence of the second mode of overturning results in a safe region that is located on the acceleration-frequency plane above the minimum overturning acceleration spectrum. The fundamental differences between the response of a rocking rigid column (inverted pendulum) and the response of the linear elastic oscillator (regular pendulum) led to the development of the rocking spectrum (Makris and Konstantinidis In this paper we investigate the planar rocking response of an array of free-standing columns capped with a freely supported rigid beam as shown schematically in Figure 1. Herein we use the term "rocking frame" for the one degree of freedom structure shown in Figure 1. Sliding does not occur either at the pivot points at the base or at the pivot points at the capbeam. Our interest to this problem was partly motivated from the need to explain the remarkable seismic stability of ancient free-standing columns which support heavy free standing epistyles together with the even heavier frieze atop. As an example, Figure 2 shows the entrance view of the late archaic temple of Aphaia in the island of Aegina nearby Athens, Greece. Dates ranging from 510BC to 470BC have been proposed fo...

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“…They concluded that both solutions were equivalent, allowing the use of the simple one. The former solution was also studied in [9], whilst the latter was used in [10,11]. ElGawady et al [12] investigated the influence of the material constituting the interface through experimental tests and Vassilou and Makris [13] examined the benefits of different types of isolated base thanks to numerical simulations.…”

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

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Response analysis of rigid structures rocking on viscoelastic foundation

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Cited by 64 publications

References 29 publications

Shaking Table Tests on Unreinforced Load-Bearing Masonry Walls – Comparison With Simple Rocking Models.

Shaking Table Tests on Unreinforced Load-Bearing Masonry Walls – Comparison With Simple Rocking Models.

Rocking Response and Stability Analysis of an Array of Free-Standing Columns Capped With a Free-Standing Rigid Beam

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

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