Oscillations of a rocking block with an added pendulum

2015 ◽  
Vol 230 (2) ◽  
pp. 104-114 ◽  
Author(s):  
Luca Collini ◽  
Rinaldo Garziera ◽  
Aleksander V Karapetyan ◽  
Maria A Munitsyna ◽  
Alessandro Tasora
Keyword(s):  
Rocking Block

scholarly journals Closed-form rocking overturning conditions for a family of pulse ground motions

2016 ◽  
Vol 472 (2196) ◽  
pp. 20160662 ◽  
Author(s):  
Elias G. Dimitrakopoulos ◽  
Edwin Dat Win Fung
Keyword(s):  
Lower Bound ◽  
Finite Number ◽  
Closed Form ◽  
Physical Mechanism ◽  
Ground Motions ◽  
Critical Conditions ◽  
Rocking Block ◽  
Approximate Analytical Solutions ◽  
The Stability

This paper characterizes the stability of a rigid rocking block subjected to a family of multi-lobe pulse ground motions. It unveils a counter to intuition plurality of overturning (OT) modes despite the short duration and bounded energy of the examined ground motions. Accordingly, it describes with original closed-form expressions the critical conditions of all OT modes involving a finite number of impacts. It also proposes pertinent semi-analytical, exact analytical and approximate analytical solutions with respect to the determination of the (unknown) times of impact, as appropriate. The analysis reveals that the first , or lower bound , critical OT mode is in most cases toppling during free rocking after one impact specifically before the end of the pulse. For this case, it elucidates the physical mechanism behind the timing of impact that produces minimum amplitude and maximum amplitude critical OT, respectively, and proposes pertinent closed-form approximations. Finally, the study derives, in ‘universal’ terms, global ‘safety walls’ against rocking OT considering a large number of different pulse shapes.

scholarly journals Study of the Planar Rocking-Block Dynamics With Coulomb Friction: Critical Kinetic Angles

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Hongjian Zhang ◽  
Bernard Brogliato ◽  
Caishan Liu
Keyword(s):  
Numerical Simulations ◽  
Coulomb Friction ◽  
Numerical Scheme ◽  
Numerical Results ◽  
Experimental Results ◽  
Restitution Coefficient ◽  
Rocking Block ◽  
Kinetic Angle ◽  
Multiple Impact ◽  
Impact With Friction

The objective of this paper is to show, through the planar rocking block example, that kinetic angles play a fundamental role in multiple impact with friction. Even in the presence of Coulomb friction, a critical kinetic angle θcr is exhibited that allows one to split the blocks into two main classes: slender blocks with a kinetic angle larger than θcr, and flat blocks with a kinetic angle smaller than θcr. The value of θcr varies with the friction value, but it is independent of the restitution coefficient (normal dissipation). Numerical results are obtained using a multiple impact law recently introduced by the authors. Some comparisons between numerical and experimental results that validate the used model and numerical scheme are presented. However, this paper is mainly based on numerical simulations.

The Rocking and Stability of Spent Fuel Casks

2014 ◽  
Author(s):  
Raju Ananth ◽  
Shari Day ◽  
Mrinal Bose
Keyword(s):  
Classical Solution ◽  
Inverted Pendulum ◽  
Numerical Study ◽  
Viscous Damping ◽  
Base Excitation ◽  
Spent Fuel ◽  
Governing Equations ◽  
Acceleration Pulse ◽  
Rocking Block ◽  
The Stability

This paper describes an analytical and numerical study performed to benchmark LS-DYNA computer analysis of the response of a stacked spent fuel cask system to seismic base excitation. The LS-DYNA solution of the rocking block problem and stability of the block under the action of a base acceleration pulse are compared to the inverted pendulum solution first published by George W. Housner in 1963. Housner’s work has been cited by a number of subsequent investigations exploring the physics behind the rocking block problem, including Yim and Chopra [2]. The analytical formulation of the rocking block problem is derived in 2D in this paper. As is the case in many of the previous formulations, the solutions are provided after linearization of the governing equations. The stability of the unanchored block subjected to an acceleration pulse is solved using the energy method. The solution displays key differences relative to Housner’s minimum acceleration required to overturn. An alternate equation for effective viscous damping is also presented, which differs from the formulation given in Appendix A of ASCE 43-05 [9]. Simulation of the rocking block problem using LS-DYNA is shown to faithfully reproduce the classical solution, albeit at lower levels of energy loss. Effective damping and minimum acceleration to overturn from the LS-DYNA benchmark agree with predictions of the classical solution even after linearization.

TRANSIENT MOTION AND OVERTURNING OF A ROCKING BLOCK ON A SEESAWING FOUNDATION

1996 ◽  
Vol 191 (1) ◽  
pp. 177-187 ◽  
Author(s):  
L.N. Virgin ◽  
W.T. Fielder ◽  
R.H. Plaut
Keyword(s):  
Transient Motion ◽  
Rocking Block

LYAPUNOV'S EXPONENTS FOR NONSMOOTH DYNAMICS WITH IMPACTS: STABILITY ANALYSIS OF THE ROCKING BLOCK

2005 ◽  
Vol 15 (06) ◽  
pp. 2015-2039 ◽  
Author(s):  
ALESSIO AGENO ◽  
ANNA SINOPOLI
Keyword(s):  
Stability Analysis ◽  
Coulomb Friction ◽  
Equations Of Motion ◽  
Nonsmooth Dynamics ◽  
Rocking Block ◽  
Fundamental Solution Matrix ◽  
Unilateral Contacts ◽  
Discontinuous Nature ◽  
The Subject ◽  
Solution Matrix

The plane dynamics of a rigid block simply supported on a harmonically moving rigid ground is a problem which still needs investigating, although the matter has been the subject of much research since the last century. Unilateral contacts, Coulomb friction and impacts make the system hybrid as it reveals a mixed continuous and discontinuous nature. Thus, stability analysis requires the extension and adaptation of concepts with regard to variational-perturbative procedures. In particular, discontinuous systems exhibit discontinuities or "saltations" in the fundamental solution matrix which must be analyzed carefully. In this paper, the adaptation of numerical methods that permit us to obtain characteristic multipliers and Lyapunov's exponents for the rocking mode of the block will be tackled. Analytical methods are used for the linearized equations of motion; the results are compared with those in the scientific literature.

scholarly journals Oscillations Control of Rocking-Block-Type Buildings by the Addition of a Tuned Pendulum

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Luca Collini ◽  
Rinaldo Garziera ◽  
Kseniia Riabova ◽  
Mariya Munitsyna ◽  
Alessandro Tasora
Keyword(s):  
Numerical Simulations ◽  
Approximation Method ◽  
Dry Friction ◽  
Mechanical Model ◽  
Horizontal Plane ◽  
Galerkin Approximation ◽  
Block Type ◽  
Theoretical Part ◽  
Lagrange Formulation ◽  
Rocking Block

This study deals with the dynamical evolutions exhibited by a simple mechanical model of building, comprising a parallelepiped standing on a horizontal plane. The main goal is the introduction of a pendulum in order to reduce oscillations. The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method, and dry friction has also been considered. From the analytical/numerical simulations, we derive some important conclusions, providing us with the tools suitable for the design of absorbers in practical cases.

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