Seismic response analysis of multidrum classical columns

This paper presents a numerical investigation on the seismic response of multidrum classical columns. The motivation for this study originates from the need to understand: (a) the level of ground shaking that classical multidrum columns can survive, and (b) the possible advantages or disadvantages of retrofitting multidrum columns with metallic shear links that replace the wooden poles that were installed in ancient times. The numerical study presented in this paper is conducted with the commercially available software Working Model 2D?, which can capture with fidelity the sliding, rocking, and slide‐rocking response of rigid‐body assemblies. This paper validates the software Working Model by comparing selected computed responses with scarce analytical solutions and the results from in‐house numerical codes initially developed at the University of California, Berkeley, to study the seismic response of electrical transformers and heavy laboratory equipment. The study reveals that relative sliding between drums happens even when the g‐value of the ground acceleration is less than the coefficient of friction, µ, of the sliding interfaces and concludes that: (a) typical multidrum classical columns can survive the ground shaking from strong ground motions recorded near the causative faults of earthquakes with magnitudes M_w=6.0–7.4; (b) in most cases multidrum classical columns free to dislocate at the drum interfaces exhibit more controlled seismic response than the monolithic columns with same size and slenderness; (c) the shear strength of the wooden poles has a marginal effect on the sliding response of the drums; and (d) stiff metallic shear links in‐between column drums may have an undesirable role on the seismic stability of classical columns and should be avoided. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic response of pile groups under oblique-shear and Rayleigh waves

A simple analytical solution is presented to calculate the pile-soil-pile interaction and eventually the dynamic response of pile groups when excited by the passage of Rayleigh waves and obliquely incident SH-waves. A dynamic Winkler model, with realistic frequency-dependent ‘springs’ and ‘dashpots’ in conjunction with physically motivated approximations is utilized to compute the wave field radiating from an oscillating pile and the effect of this field on an adjacent pile. The coupled rocking motion of the pile group resulting from Rayleigh waves and the torsional motion of the pile group resulting from SH-waves is accurately predicted by a simple mathematical expression. The results of the presented method can be obtained with ‘hand calculations’ and are in excellent agreement with results from ‘rigorous’ solutions based on integral equation formulations. It is found that the group response is primarily affected from the phase difference of the input seismic motion at the location of each pile (wave-passage effect). Pile-soil-pile interaction has insignificant effect and can be neglected.     

Nonlinear response of single piles under lateral inertial and seismic loads

A macroscopic model that consists of distributed hysteretic springs and frequency dependent -pots is utilized to model the lateral soil reaction and a practical method based on one-dimensional finite element formulation is developed to compute the nonlinear response of single piles under dynamic lateral loads. The model is physically motivated, adequate for cohesive and cohesionless soils, and involves standard geotechnical parameters. Only two parameters have to be calibrated by fitting experimental data. Hysteretic and radiation damping are modeled realistically within the practical range of amplitudes and frequencies. The model is calibrated and validated against five well instrumented full-scale experiments and typical values for the range of the model-parameters are provided. Subsequently, the developed model is utilized to study the nonlinear seismic response of single piles. Finally, the developed method and the calibrated model are used to predict the inertial and seismic response of one of the piles used in the foundation of the Ohba bridge near Tokyo, Japan.     

Axisymmetric galactic models in spherical potentials

We study projected kinematic characteristics of a class of axisymmetric models for the luminous components of galaxies. Models of this class are known as extended Osipkov-Merritt models and have been studied first by Arnold (1990). The line-of-sight velocity dispersions are given and the profiles of the projected velocity distribution are described using their Gauss-Hermite moments.     

Effect of viscous,viscoplastic and friction damping on the response of seismic isolated structures

In this paper the efficiency of various dissipative mechanisms to protect structures from pulse‐type and near‐source ground motions is examined. Physically realizable cycloidal pulses are introduced, and their resemblance to recorded near‐source ground motions is illustrated. The study uncovers the coherent component of some near‐source acceleration records, and the shaking potential of these records is examined. It is found that the response of structures with relatively low isolation periods is substantially affected by the high‐frequency fluctuations that override the long duration pulse. Therefore, the concept of seismic isolation is beneficial even for motions that contain a long duration pulse which generates most of the unusually large recorded displacements and velocities. Dissipation forces of the plastic (friction) type are very efficient in reducing displacement demands although occasionally they are responsible for substantial permanent displacements. It is found that the benefits by hysteretic dissipation are nearly indifferent to the level of the yield displacement of the hysteretic mechanism and that they depend primarily on the level of the plastic (friction) force. The study concludes that a combination of relatively low friction and viscous forces is attractive since base displacements are substantially reduced without appreciably increasing base shears and superstructure accelerations. Copyright © 2000 John Wiley & Sons, Ltd.     

Planar rocking response and stability analysis of an array of free‐standing columns capped with a freely supported rigid beam

This paper investigates the planar rocking response of an array of free‐standing columns capped with a freely supported rigid beam in an effort to explain the appreciable seismic stability of ancient free‐standing columns that support heavy epistyles together with the even heavier frieze atop. Following a variational formulation, the paper concludes to the remarkable result that the dynamic rocking response of an array of free‐standing columns capped with a rigid beam is identical to the rocking response of a single free‐standing column with the same slenderness yet with larger size, that is a more stable configuration. Most importantly, the study shows that the heavier the freely supported cap beam is (epistyles with frieze atop), the more stable is the rocking frame regardless of the rise of the center of gravity of the cap beam, concluding that top‐heavy rocking frames are more stable than when they are top light. This ‘counter intuitive’ finding renders rocking isolation a most attractive alternative for the seismic protection of bridges with tall piers, whereas its potential implementation shall remove several of the concerns associated with the seismic connections of prefabricated bridges. Copyright © 2012 John Wiley & Sons, Ltd.     

Dimensional analysis of the earthquake-induced pounding between inelastic structures

In this paper the seismic response of inelastic structures with unilateral contact is revisited with dimensional analysis. All physically realizable contact types are captured via a non-smooth complementarity approach. The implementation of formal dimensional analysis leads to a condensed presentation of the response and unveils remarkable order even though two different types of non-linearity coexist in the response: the boundary non-linearity of unilateral contact and the inelastic behaviour of the structure itself. It is shown that regardless the intensity and frequency content of the excitation, all response spectra become self-similar when expressed in the appropriate dimensionless terms. The proposed approach hinges upon the notion of the energetic length scale of an excitation which measures the persistence of ground shaking to impose deformation demands. Using the concept of persistency which is defined for excitations with or without distinct pulses, the response is scaled via meaningful novel intensity measures: the dimensionless gap and the dimensionless yield displacement. The study confirms that contact may have a different effect on the response displacements of inelastic structures depending on the spectral region. In adjacent inelastic structures, such as colliding buildings or interacting bridge segments, contact is likely to alter drastically the excitation frequencies’ at which the system is most vulnerable. Finally, it is shown that the proposed approach yields maximum response displacements which correlate very well with the persistency of real earthquakes for a bridge system with considerably complex behaviour.     

Multiplicity functions of dark matter haloes from fractional Brownian motion

We studied the formation of dark matter haloes assuming a Fractional Brownian Motion (FBM) of trajectories in the plane (S,δ). S is the variance of the smoothed overdensity δ. The values of δ are calculated using a filter of radius R that defines a mass scale M, and thus S is considered as a function of mass M. Focusing on a specific point of the initial Universe and calculating δ as a function of the radius R of the filter a random walk on the plane (S,δ) is established. If the above evolution is a FBM motion then there exist correlations between various mass scales. These correlations depend on a Hurst exponent H. Various mass scales are not correlated for H=1 and the evolution is reduced to the classical Brownian motion. Following Zhang and Hui (Astrophys. J. 641:641, 2006), we constructed a Volterra integral equation for the distribution of trajectories after a first crossing of an ellipsoidal barrier. The integral equation is solved numerically and multiplicity functions of dark matter haloes were derived and compared to the results of N-body simulations. Our results show that for H=1.05 the resulting multiplicity functions are in excellent agreement, much better than the agreement predicted by any other model, with the predictions of N-body simulations. This shows that FBM model is a very promising tool for the study of the formation of structures in the Universe.     

Non-parametric methods in density profile estimation of stellar systems

In this paper a specific inverse astronomical problem is treated. We study the problem of inferring the spatial density profile of a spherically symmetric stellar system from values of its surface density or from discrete data as the projected positions of its stars on the plane of sky. Non parametric techniques were used based on the least-squares method or on the maximum likelihood estimation. The smoothness of the resulting profiles is increased by the method of regularization.     

Inversions for axisymmetric galactic disks

We use two models for the distribution function to solve an inverse problem for axisymmetric disks. These systems may be considered - under certain assumptions - as galactic disks. In some cases the solutions of the resulting integral equations are simple, which allows the determination of the kinematic properties of self-consistent models for these systems. These properties for then = 1 Toomre disk are presented in this study.