Journal of Engineering Mechanics

A closed-loop complete-feedback control algorithm is proposed for the control of a building modeled as a single-degree-of-freedom (SDOF) system using an active tuned mass damper (ATMD). The control force is calculated from the acceleration, velocity, and displacement feedbacks of the SDOF system and the active mass damper. The passive-control-device properties, including the stiffness and damping constants of the tuned mass damper and the three gain coefficients of the actuator, are derived by minimizing the displacement variance of the SDOF system. Simulations are performed to evaluate the performance of the active-tuned-mass-damper design on the examples of a SDOF system and a 10-story three-bay building frame. The results show that the control efficiency of the ATMD based on velocity feedback depends on the passive-control-device properties assumed. Also, the ATMD with optimal passive properties using complete feedback results in further reduction in the structural displacement. The results also show that for the same level of reduction in structural displacements, the control force required is smaller using complete feedback.

An approximate approach that transforms an analytical solution for uniform flow past two circular cylinders into a solution for uniform flow past two cylinders of arbitrary shape is proposed in this study. This approximate approach is a combination of the analytical solution, which is obtained in bipolar cylindrical coordinates, and the numerical pseudoconformal transformation. The method applied in this study is not only simpler than conventional numerical methods, but also considers the Kutta condition. The numerical transformation is examined by the Joukowski transformation. The streamlines of uniform flow past a symmetric Joukowski airfoil with an ellipse in front of it shows good agreement with the Hele-Shaw cell experiment. The lift force on the airfoil is also compared with the lift force of a single airfoil.

A new analytical solution is developed for steady-state lateral response of earth and rockfill dams built in semielliptical canyons and subjected to obliquely incident harmonic SH waves. The dam is idealized as a linearly hysteretic elastic body deforming only in shear, while the supporting canyon is modeled as an elastic rock half-space. The solution accounts in a rigorous way for the wave reflection and diffraction phenomena associated with the presence of the dam-filled canyon. The response of the dam and the canyon is expressed in terms of prolate radial and angular wave spheroidal functions. Representative results elucidate the importance of the effects of the dam-to-canyon material impedance, the canyon geometry, the angle of incidence, and the excitation frequency on the dam response. Comparisons are made with the response of the dam to “rigid-base” synchronous excitation. The developed solution offers a useful practical tool for parametric studies and preliminary design calculations, as the semielliptical shape can approximate reasonably well the geometry of several actual canyons.

This paper presents a new theoretical formulation of coupled heat, moisture, and air transfer in unsaturated soil. A mechanistic approach is adopted that extends a previous potential-based formulation of coupled heat and moisture transfer at constant air pressure. An assessment of the accuracy of the research is presented via comparisons with experimental work for isothermal moisture/air transfer and coupled heat/moisture transfer at constant pressure. Excellent correlation was achieved. Furthermore, verification of the complete new formulation has been achieved by satisfactory comparison of results with those obtained from an independent alternative numerical model. An application of the model to an example test problem is then presented, making use of thermophysical soil parameters that have been independently established for a range of the soil properties specified in the formulation. A number of features of interest related to the interaction between elevated temperatures, induced increased air pressure, and infiltration rates are described. The importance of including the air phase is thus identified, particularly in relation to its effect on the hydration process.

The Wentzel, Kramers, and Brillouin (WKB) asymptotic approximation is used to produce an analytical solution for the bounded, gravity-driven flow of smooth, uniform disks in the limit where the wall-form roughness is small and slip is large. A unique, steady solution is obtained for all channel slopes, in contrast with previous experiments. However, this apparent contrast can be explained by the fact that the large travel distances required to develop the very rapid flows predicted may exceed the practical limits for experimental observation. The slip speed governs the rate of mass transport, and is shown to be inversely proportional to the wall roughness, and directly proportional to the square root of the channel slope and channel width. The spatial variation in fluctuation speed is primarily governed by the energy dissipative characteristics of the disks. However, the ratio of slip speed to fluctuation speed at the wall is inversely related to both the wall elasticity and wall-form roughness.

This paper proposes a failure path approach for time-variant system reliability estimation of brittle structures. The significant failure sequences are identified by the branch-and-bound method, and the damage states in these sequences are grouped together into discrete damage levels ranging from intact structure to system collapse. The grouping is based on the number of degrees of redundancy in the structure as it accumulates different amounts of damage. The Markov chain assumption is used to model the cumulative damage under time-varying loads. The expressions for transition probabilities from one damage level to another are derived. The effect of load overlapping under multiple load processes is investigated. The method is applicable to large structures due to the systematic failure sequence identification strategy employed. The resultant probability transition matrix is found to be more compact and to represent the accumulation of damage better than existing methods. Two numerical examples are used to illustrate and examine the proposed method.

A time-domain equation error estimator is proposed for the problem of estimating constitutive parameters of a complex linear structure. We have assumed that the geometry and topology of the model are known and have measured the history of applied loads, and the accelerations at certain locations. For the proposed parameter estimation algorithm, we first estimate the displacement and velocity at the locations where accelerations have been measured by standard integration/filtering techniques. We recast the equations of motion as a discrete multistep method in terms of the displacements at the unmeasured degrees of freedom, and establish our measure of error as the weighted sum of residual forces at adjacent time points. We estimate the unknown constitutive parameters by solving a constrained nonlinear optimization problem, and take the parameter estimate to be the average of estimates over several time windows. We advocate the use of the recursive quadratic programming method to solve the optimization problem. The proposed time-domain estimator can accommodate response sampled incompletely in time, state, and space and is amenable to identification of complex structural systems.

Monte Carlo simulation is used to study the statistical behavior of the time-domain parameter estimator presented in the companion paper, using a bridge truss as a model problem. The effects of the estimation time step, the initial parameter values, and the quality and quantity of information on the outcome of parameter estimation are investigated. The paper demonstrates that the time step must be sufficiently small to control the errors inherent in the numerical integration scheme, but should be large enough to provide new information for the estimator. As expected for this type of problem, the estimates are biased in the presence of noise in the measurements. However, for practical amplitudes of noise, the estimated parameters are sufficiently reliable. The estimator has the desirable characteristic that, when the noise amplitude is sufficiently small, the accuracy of the estimates can be increased by presenting more information to the algorithm.

Construction and maintenance of engineering structures in arctic regions demands an understanding of and the ability to cope with environmental problems produced by permafrost. Where thawing of the permafrost cannot be prevented, the range, amount, and extent of degradation are factors that must be taken into account in the design of engineering structures. Predictions of these factors are facilitated by the use of a mathematical model designed to predict the physical system under consideration. This study addresses the problem by developing a predictive model to describe permafrost thaw subsidence based upon a complete formulation of the problem. This problem is one of multiphase (air, ice, water, and solid) transport and deformation in a porous medium. The conservation of mass equations for liquid water, ice with phase change, and deforming soil solids are developed. Darcy's law is extended to include moisture movement due to thermal gradients. The quasi-static equilibrium equations and stress-strain relations that assume a perfectly elastic solid matrix are also employed. Simultaneous variations of moisture retention and phase-composition curves with temperature and pore pressure are also incorporated in the model. The energy-conservation equation, which includes terms due to viscous dissipation and compression effects, along with the other equations expressed, is found to satisfactorily represent the physical processes occurring in thawing permafrost soils. Approximations to simulate the thawing of a one-dimensional soil column are then developed from the general model.

In this paper, we develop a numerical solution to equations derived in the first part of this study to simulate the thaw subsidence of an unsaturated frozen soil due to surface heating. Solutions obtained in terms of pore pressure, temperature, degree of unfrozen water content, ice content, and porosity provide the spatial and temporal variations of these quantities in a thawing soil column. A one-dimensional form of governing equations is discretized by employing a Crank-Nicolson finite-difference scheme. These highly nonlinear equations are then solved by an iterative procedure at every time step for predescribed positive surface temperatures that produce thawing. The numerical solutions are obtained for a 1-m silt column. Results show that, above the frozen region, unfrozen water saturation increases due to low hydraulic conductivity, which prevents the melting ice from draining, thus causing accumulation of water above it. It has also been observed that most of the settlement at the surface is due to thaw consolidation rather than settlement due to drainage. The former is completed in seven days of a 12-day simulation period. Furthermore, a sensitivity analysis was carried out to determine the response of the simulation to deviations in the values of certain parameters. It is found that the settlement estimations are very sensitive to the thaw-settlement parameter and phase-composition curve, thus requiring accurate determination of these parameters for a reliable simulation of the thaw-consolidation process.

This technical note shows that the injudicious addition of area to the cross secion of a beam in bending may reduce the minimum elastic section modulus. Simple expressions are derived, which give the locations within a section where this occurs. For initially symmetrical standard beam sections these locations extend from the neutral axis for distances of between 12% of the section depth for round bars, to 35% for I-beams. An expression is derived for the location at which any added area will give the maximum reduction in minimum section modulus and another expression from which the magnitude of this maximum reduction may be calculated. The theoretical worst case is an idealized I-beam with a negligible web area for which any added area except at the neutral axis or flanges will reduce the section modulus; and the theoretically possible maximum reduction is 16.7%, corresponding with a 20% increase in stress. The results obtained in this paper should be particularly useful in the design of built-up sections such as box-girder bridges, aircrafts, and ship hulls in which fatigue and/or fracture may be a limiting constraint.

The Mohr diagram is a graphical technique that is well known and widely used in stress analysis. Mohr's graphical construction enables the determination of the magnitude of the normal stress component for a given oblique plane. On the other hand, it only gives the magnitude of the total shearing stress, thus failing to provide its components. This paper is an extension of Mohr's work to overcome this shortcoming. A proposed method, based on the utilization of Cauchy's formula, along with vector analysis of both the stress vector and the normal stress component, is suggested. It allows full representation of the shearing stress components in Mohr space. This present technique is mathematically derived and graphically depicted.

Propagation of surface waves of oblique incidence across infilled trenches is considered. An analytical approach based on the Green's function technique is developed to estimate the reflection and transmission of surface waves across a layer inserted between two homogeneous quarter-spaces. For the transmission of surface waves across the layer, a differential matrix operator is constructed by using Taylor series expansion in order to relate field quantities on each side of the layer. Reflection and transmission coefficients of the Rayleigh wave across the layer are then integrated by using the representation theorem. After validating the method against experimental data, influence of the material contrast and the angle of incidence on the efficiency of an in-filled trench is examined.