Refined Solutions of Externally Induced Sloshing in Half-Full Spherical Containers

A mathematical model is developed for calculating liquid sloshing effects such as hydrodynamic pressures and forces in half-full spherical containers under arbitrary external excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the spherical configuration, the problem is not separable and the associated spatial functions are nonorthogonal. Application of the boundary conditions results in a system of coupled nonhomogeneous ordinary linear differential equations. The system is solved numerically, implementing a typical fourth-order Runge-Kutta integration scheme. The proposed simple methodology is capable of predicting sloshing effects in half-full spherical containers under arbitrary external excitation in an accurate manner. Hydrodynamic pressures and horizontal forces on the wall of a spherical container are calculated for real earthquake ground motion data. Dissipation effects are included in the present formulation, and their influence on the response is examined. Finally, it is shown that for the particular case of harmonic excitation, the system of ordinary differential equations results in a system of linear algebraic equations, which yields an elegant semianalytical solution.     

Dynamic Behavior of Reinforced Concrete Beams Strengthened with Composite Materials

The dynamic behavior of reinforced concrete (RC) beams strengthened with externally bonded composite materials is analytically investigated. The analytical model is based on dynamic equilibrium, compatibility of deformations between the structural components (RC beam, adhesive, composite material) and the concept of the high order approach. The equations of motion along with the boundary and continuity conditions are derived using Hamilton’s variational principle and the kinematic relations of small deformations. The mathematical formulation also includes the constitutive laws that are based on beam and lamination theories, and the two-dimensional elasticity representation of the adhesive layer including the closed form solution of its stress and displacement fields. The Newmark time integration method, which is directly applied to the resulting set of coupled partial differential equations, is adopted. This procedure yields a set of ordinary differential equations, which are analytically or numerically solved in every time step. The response of a strengthened beam to different dynamic loads that include impulse load, harmonic load, and seismic base excitation is numerically investigated. The numerical study highlights some of the phenomena associated with the dynamic response and explores the capabilities of the proposed model. The paper closes with a summary and conclusions.     

TLD Technique for Reducing Ice-Induced Vibration on Platforms

Tuned liquid damper (TLD) containers are designed to provide their sloshing forces in opposite directions against the inertia loads of the vibrating structure and thus to reduce the vibration. The sloshing forces that result from liquid motion may be determined either analytically or experimentally. The efficiency of the TLD in vibration reduction then can be estimated by attaching the TLD subsystem onto the dynamic equation of the vibrating structure. This paper describes investigations of the TLD system for an existing Bohai production jacket, which has routinely been excited by drifting ice during the winter seasons. In addition to a theoretical demonstration, a scaled model test and a full-scale field experiment were performed in this study. The technical strategy and main results of the investigation are presented in this paper.     

Random Vibration of Systems with Viscoelastic Memory

The equation of motion of linear dynamic systems with viscoelastic memory is usually expressed in a integrodifferential form, and its numerical solution is computationally heavy. In two recent papers, the writers suggested that the system memory be accounted for through the introduction of a number of additional internal variables. Following this approach, the motion of the system is governed by a set of first-order, linear differential equations, whose solution is quite easy. In this paper, the approach is extended to single-degree-of-freedom systems subjected to random, nonstationary excitation. The equations governing the time variation of the second-order statistics are derived, and an effective step-by-step solution procedure is proposed. Numerical example shows the accuracy of the procedure for white and nonwhite excitations.     

Simulation of re-entry in a piece of myocardial tissue: strong sensitivity to spatial and temporal conditions

A simple model for the simulation of re-entrant excitation was created. The model consists of a matrix of 15x15 compartments, where each compartment has its own action potential that depends dynamically on four ion currents (INa, ICa, Ik and Ib) having time and voltage-dependent activation and inactivation kinetics. The compartments were combined with resistors to simulate electrotonic interaction. At short excitation intervals the action potential was shortened in duration, and at even shorter coupling intervals decremental propagation occurred. Re-entry around an obstacle could be elicited in response to a properly timed extra stimulus. A time dependent unidirectional block was made by making some of the action potentials longer in duration. An obstacle was not a necessary substrate for re-entry, but the timing of the extra stimulus was critical. In the presence of an obstacle, the induction of re-entry was critically dependent on the shape of the obstacle. The most important result of the simulations is that the system is highly sensitive to the initial spatial and temporal conditions. These sensitivities are generic features of dynamic systems that are described by non-linear differential equations and are typical for chaotic systems. The system studied shows features associated with deterministic chaos.     

Decoupling Criteria for Inelastic Irregular Primary/Secondary Structural Systems Subject to Seismic Excitation

The present work deals with the dynamic response of structures that are irregular in height, consisting of two parts, a lower part made of concrete and an upper part made of steel. Irregularity is due to different dynamic responses of the two parts, here expressed by their different damping ratios and inelastic material laws. The seismic design of such structures is not satisfactorily covered by current design codes, especially if a decoupled procedure is chosen for the analysis, where the lower part is excited first and its response is used as excitation for the upper part. The present paper aims at contributing toward better understanding of the interaction between the two parts and at proposing improved decoupling criteria for the seismic analysis of inelastic primary-secondary systems. Toward that goal, each part is modeled as a one-degree-of-freedom system, and the maximum responses of coupled and decoupled inelastic time history analyses are compared over a wide range of dynamic characteristics and strength levels of the two parts. The results are presented in the form of error levels between the two alternative analysis procedures.     

Dynamic Behavior of Nonlinear Cable System. IV

A suitable filter response is defined that allows studies of the effects of excitation bandwidth on the responses of geometrically nonlinear dynamic systems. For such a random excitation, as the bandwidth approaches zero, the mean square displacement response of a linear single-degree-of-freedom (SDOF) system approaches the mean square response to harmonic excitation. Studies of mean square responses of a nonlinear SDOF model of a cable system are presented. The set of nonlinear equations for the response moments are truncated using Gaussian closure and solved using continuation techniques as implemented in the program AUTO. Surfaces of turning point loci are computed in the parameter space of excitation bandwidth, excitation central frequency, and system damping. These surfaces provide values of the three parameters that separate regions with multiple mean square responses from regions with unique mean square responses. Response time histories are computed by simulation to illustrate system behavior in regions with multiple stable mean square responses.     

Double Modal Transformation and Wind Engineering Applications

Modal transformation techniques are usually adopted in structural dynamics with the aim of decoupling the equations of motion. They are based on the search for an abstract space in which the solution of the problem results simplified. Analogous transformation techniques have recently been developed with the aim of defining a space where a multivariate stochastic process is expressed by a linear combination of one-variate uncorrelated processes. This paper proposes a method, called double modal transformation, by which the dynamic analysis of a linear structure is carried out through the simultaneous transformation of the equations of motion and the loading process. By adopting this technique, the structural response is obtained through a double series expansion in which structural and loading modal contributions are superimposed. Its effectiveness and application are discussed with reference to two classic wind engineering problems—the alongwind response and the vortex-induced crosswind response of slender structures—which provide a wide panorama of the most relevant properties of this procedure.     

Extreme Value of Response to Nonstationary Excitation

An efficient method is presented for approximate computation of extreme value characteristics of the response of a linear structure subjected to nonstationary Gaussian excitation. The characteristics considered are the mean and standard deviation of the extreme value and fractile levels having specific probabilities of not being exceeded by the random process within a specified time interval. The approximate procedure can significantly facilitate the utilization of nonstationary models in engineering practice, since it avoids computational difficulties associated with direct application of extreme value theory. The method is based on the approximation of the cumulative distribution function (CDF) of the extreme value of a nonstationary process by the CDF of a corresponding “equivalent” stationary process. Approximate procedures are developed for both the Poisson and Vanmarcke approaches to the extreme value problem, and numerical results are obtained for an example problem. These results demonstrate that the simple approximate method agrees quite well with the direct application of extreme value theory, while avoiding the difficulties associated with solution of nonlinear equations containing complicated time integrals.     

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.     

河谷地形对土层地震反应的影响

为了分析河谷对土层地震反应的影响,采用二维有限元法,对跨度500m的某河谷地形的土层进行地震反应分析.为研究地震波传播过程对土层地震反应的影响,分析比较了一致地震输入和行波地震输入作用下土层线性和等效线性化地震反应的差异.同时将有限元计算结果与层状土层的一维波动分析结果相比较,讨论河谷地形对土层地震反应的影响.数值计算的结果表明:在水平地震输入作用下,由于河谷的存在,在河谷附近将会激起较大的竖向运动;与一致地震输入相比,在行波地震输入作用下,土层表面水平加速度反应减小,竖向加速度反应增大.     

Effects of Space Distribution of Excitation on Seismic Response of Arch Dams

The effects of the ground motion spatial variation and of the canyon geometry on the dynamic response of arch dams during the event of an earthquake is studied in this paper. The seismic response of a dam subject to time harmonic longitudinal, shear, and Rayleigh waves impinging the dam site from different directions is analyzed. Several canyon and reservoir geometries are considered. A three-dimensional boundary element model which allows for the rigorous representation of the dynamic interaction between the dam, the foundation rock, and the water is used. The foundation rock is modeled as a uniform viscoelastic boundless domain where the incident traveling wave field is defined by its analytical expression, which may include any spatial variation. The obtained results show the importance of three-dimensional effects which are many times neglected.     

Seismic Fragility Analysis of Structural Systems

A method is presented for the evaluation of the seismic fragility function of realistic structural systems. The method is based on a preliminary, limited, simulation involving nonlinear dynamic analyses performed to establish the probabilistic characterization of the demands on the structure, followed by the solution of a general system reliability problem with correlated demands and capacities. The results compare favorably with the fragility obtained by plain Monte Carlo simulation, while the associated computational effort is orders of magnitude lower. The method is demonstrated with two applications, a steel-concrete box girder viaduct with RC piers subjected to both uniform and nonuniform excitations, and a three-dimensional RC building structure subjected to bidirectional excitation.     

Stochastic Response of an Inclined Shallow Cable with Linear Viscous Dampers under Stochastic Excitation

Considering the coupling between the in-plane and out-of-plane vibration, the stochastic response of an inclined shallow cable with linear viscous dampers subjected to Gaussian white noise excitation is investigated in this paper. Selecting the static deflection shape due to a concentrated force at the dampers location and the first sine term as shape functions, a reduced four-degree-of-freedom system of nonlinear stochastic ordinary differential equations are derived to describe dynamic response of the cable. Since only polynomial-type terms are contained, the fourth-order cumulant-neglect closure together with the C-type Gram-Charlier expansion with a fourth-order closure are applied to obtain statistical moments, power spectral density and probabilistic density function of the cable response, whose availability is verified by Monte Carlo method. Taking a typical cable as an example, the influence of several factors, which include excitation level and direction as well as damper size, on the dynamic response of the cable is extensively investigated. It is found that the sum of mean square in-plane and out-of-plane displacement is primarily independent of the load direction when the excitation level and viscous coefficient of the damper are fixed. Moreover, the peak frequency and half-band width of the spectra of both the in-plane and the out-of-plane displacements are increasing with excitation level when the damper size is constant. It is also observed that, even though the actual optimal damper size is slightly greater than the one obtained by the complex modal theory, the difference of statistical moment of the cable caused by these two damper size is negligible, so the vibration reduction effect provided by the theoretical optimal viscous coefficient is satisfactory.     

Contaminant Transport in Fissured Soils by Three-Dimensional Boundary Elements

A boundary element method for the solution of contaminant transport equations in three-dimensional (3D) fissured soils with non-equilibrium exchange is proposed. Fast transport is assumed to take place through a network of fissures which can be one-dimensional, two-dimensional or 3D space. Soil-matrix blocks act as storage sites for the contaminant, combining with sorption in the fissures, to increase retardation. The 3D boundary element method is formulated in the Laplace domain, where equations are linearized with respect to time, and the need for time stepping is hence removed. Solution is inverted back into time domain using a numerical technique. The numerical solution is validated and the scope of the method is illustrated by applying it to the study of cylindrical, rectangular, and spherical waste repositories in a fissured clay. The effects on contamination patterns of various fissure configurations as well as the shapes, dimensions, and number of repositories are assessed.     

Kinematic Pile Response to Vertical P-wave Seismic Excitation

An analytical solution based on a rod-on-dynamic-Winkler-foundation model is developed for the response of piles in a soil layer subjected to vertical seismic excitation consisting of harmonic compressional waves. Closed-form solutions are derived for: (1) the motion of the pile head; (2) the peak normal strain in the pile, and (3) the group effect between neighboring piles. The solutions are expressed in terms of a dimensionless kinematic response factor Iv, relating pile-head motion and free-field soil surface motion, a dimensionless strain transmissibility factor Iε, relating pile and soil peak normal strains, and a pile-to-pile interaction factor α measuring group effects. It is shown that a pile foundation may significantly reduce the vertical seismic excitation transmitted to the base of a structure.     

Frequency Response of Flag-Shaped Single Degree-of-Freedom Hysteretic Systems

Recognizing the importance of limiting residual deformations that are usually associated with the response of full hysteretic systems under seismic loading, a number of energy dissipating devices and innovative structural systems exhibiting a full recentering response have recently been developed. Although these systems encompass the highly desirable self-centering characteristic, they inherently have less energy dissipation capacity when compared to more traditional fuller hysteretic systems. Little information is available on the nonlinear dynamics of systems exhibiting this flag-shaped hysteresis. In this paper, the frequency response of single degree of freedom (SDOF) systems exhibiting the flag-shaped hysteresis is computed in a closed form using the method of slowly varying parameters. The solution is derived for two independent variables representing the postyielding stiffness and energy dissipation capacity that define all self-centering hysteretic systems. The hysteretic systems covered by this formulation range from bilinear elastic systems (with no energy dissipation) to full bilinear elastoplastic. The frequency response exhibits a softening branch with multiple solution regions. A relationship between the system properties and bounded response at resonance for a given amplitude of excitation is also derived. Further analysis is carried out to assess the stability of these multiple solution regions. It is found that both stable solution branches can be achieved depending on the nature of the excitation. An amplitude jump phenomenon is also present both in increasing frequency and decreasing frequency sweeps. The concept of theoretical versus likely response curve is discussed for less idealized excitation functions.     

Free Out-of-Plane Vibrations of Masonry Walls Strengthened with Composite Materials

The natural frequencies and the out-of-plane vibration modes of one-way masonry walls strengthened with composite materials are studied. Due to the inherent nonlinear behavior of the masonry wall, the dynamic characteristics depend on the level of out-of-plane load (mechanical load or forced out-of-plane deflections) and the resulting cracking, nonlinear behavior of the mortar material, and debonding of the composite system. In order to account for the nonlinearity and the accumulation of damage, a general nonlinear dynamic model of the strengthened wall is developed. The model is mathematically decomposed into a nonlinear static analysis phase, in which the static response and the corresponding residual mechanical properties are determined, and a free vibration analysis phase, in which the dynamic characteristics are determined. The governing nonlinear differential equations of the first phase, the linear differential eigenvalue problem corresponding to the second phase, and the solution strategies are derived. Two numerical examples that examine the capabilities of the model and study the dynamic properties of the strengthened wall are presented. The model is supported and verified through comparison with a step-by-step time integration analysis, and comparison with experimental results of a full-scale strengthened wall under impulse loading. The results show that the strengthening system significantly affects the natural frequencies of the wall, modifies its modes of vibration, and restrains the deterioration of the dynamic properties with the increase of load. The quantification of these effects contributes to the understanding of the performance of damaged strengthened walls under dynamic and seismic loads.     

Spatial constraints and regulatory functions in monkeys' (Cebus apella) search.

By means of an apparatus featuring a set of suspended baited containers, search abilities of 4 capuchin monkeys (Cebus apella) were evaluated. The experiment featured different spatial configurations of the search space. Results showed that monkeys exhaustively searched 9 containers spatially distributed as a 3?×?3 matrix, a cross, a line, or a circle. Search efficiency was higher when the search space featured either a linear or circular arrangement of containers. When faced with a linear arrangement of containers, the subjects developed principled search trajectories from 1 end to the other of the linear array. This behavioral regulation was independent from search efficiency as measured by the amount of visits to containers already explored. The data suggest that monkeys use either the travel distance or the cognitive costs associated with unprincipled travel trajectories as currency for regulation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)