Journal of Engineering Mechanics

This paper presents a hybrid system for controlling wind-induced flexural vibration of a frame structure in any vertical plan. The system was implemented and tested in a prototype reduced-scale two-floor building, which had steel decks supported by four columns of aluminum. The actuator consisted of a direct current motor that slid on a rail placed on top of the structure. The displacement of the motor was synchronized with lateral displacements of the structure obtained from the deformations of the columns, which, in turn, were measured by strain gages. A proposed system to automatically adjust direction was incorporated to the actuator to position it at the plan in which the structure oscillates, thus enabling a single mass to be used to absorb vibration in any vertical plan. The fuzzy control technique was employed in this control system, which was shown to be adequate for attenuating vibration.

The dynamics of slab tracks and floating slab tracks are analyzed by multibeam models for the track and by integration in the wave-number domain for the soil, which is modeled as a layered half-space. Frequency-dependent compliances and force transfers are calculated for a great variety of track and soil parameters. The distribution of the load and the displacements along the track is investigated as well as the wave propagation perpendicular to the track and the ground vibration amplitudes. The floating slab track has a dominating plate-mat resonance and a strong high-frequency reduction. A track-soil resonance can also be recognized for an unisolated slab track in the case of layered soils. Generally, there is a strong damping of the track by the soil. The reduction effect of the slab mat is mainly owing to the elimination of this strong damping. The continuous soil yields slightly different rules for the displacements and force densities than those of a Winkler support. The total force transfer from the rail to the soil is the best criterion to judge the effectiveness of a floating slab track in reducing the ground vibration at some distance from the railway line. The total force transfer is easier to calculate than the double Fourier integrals of the ground vibration amplitudes, namely in the far field, and it has the best correlation with the reduction of the ground vibration.

An innovative design for an adaptive configuration tuned mass damper (ACTMD) is proposed. An ACTMD is a semiactive dynamic vibration absorber by which the undesirable rotational vibrations of a structure can be greatly suppressed. It can also be used to attenuate translational vibrations that are converted into rotation by means of an appropriate mechanism. Retuning the absorber with the instantaneous excitation frequency is accomplished by changing the configuration of the ACTMD. The device consists of both fixed and moving parts. To readjust the absorber with the new condition, the position of the moving parts should change. As a result, the device’s mass moment of inertia (MMI) alters and the ACTMD adapts to the new condition in real time. However, the device may not cover all frequency bands, because the moving parts cannot be located in all desirable places. After determining the governing equations, the other effects of alternation in the device’s configuration, such as the attenuation-amplification coefficient, are interpreted. Then, the performance of the absorber is evaluated by controlling a transient rotational vibration through numerical simulation. Finally, a sensitivity analysis is carried out to identify a suitable range of MMI for designing an ACTMD.

Green’s functions for the continuous system of a beam with overhangs are constructed in this paper. Green’s functions for the corresponding mathematically transformed system are proven to be of oscillating kernels. The basic oscillating properties with respect to the natural frequencies and modes of the corresponding systems are revealed and proven. The number of the nodes of the flexural moment modes of the system is determined by analyzing its conjugated system. Furthermore, some qualitative properties of its displacement modes, rotational modes, moment modes, and shearing force modes are also obtained.

Cellular beams are expanded I-sections with circular web voids that have been used extensively in Europe, and are currently gaining popularity in the United States. For these expanded I-sections, stresses within the web void projection are the manifestation of primary bending and shear-induced Vierendeel bending. The circular shape of the web void and corresponding interaction between primary and Vierendeel bending results in a stress distribution where the critical stress occurs at a location where neither stress component is at its respective maximum. In this paper, the stress distribution in cellular beams at the service limit state is explored using closed-form equilibrium methods, finite-element analysis, and experimental testing. Two different cellular sections are studied, with four identical experimental samples per section type tested in the laboratory under simple support and uniform load conditions. Experimental data are compared with both finite-element results and closed-form predictions, and are used to establish the accuracy of the analytical methods considered. Cartesian and principal stresses are considered in the investigation. The study concludes that critical stress magnitude and location calculated using the closed-form and finite-element methods are in good agreement with experimentally measured data.

Numerous existing structures exhibit rocking behavior during earthquakes, and there is a continuing need to retrofit these structures to prevent collapse. In addition, while rocking behavior is typically prevented instead of utilized, an increasing number of structures are being designed or retrofitted to allow rocking motion as a means of seismic isolation. This paper investigates the use of viscous damping to limit the rocking motion by characterizing the fundamental behavior of damped rocking structures through analytical modeling. A single rocking block analytical model is used to determine the viscous damping characteristics, which exploit the beneficial aspects of the rocking motion, while dissipating energy and preventing overturning collapse. To clarify the benefits of damping, overturning envelopes for pulse-type ground accelerations are presented and compared with the pertinent envelopes of the free rocking block. A semianalytical solution to the linearized equations of motion enables rapid generation of collapse diagrams for pulse excitations, which provide insight into the overturning mechanisms of the damped rocking block and the sensitivity of the response to the parameters involved. In addition, through solution of the nonlinear equations of motion, bilateral and unilateral linear viscous dampers are shown to provide similar benefit toward preventing overturning, while nonlinear damping is found to provide relatively little and inconsistent benefit with respect to linear damping.

Interlaminar stresses near free edges in composite laminates were analyzed by considering interface modeling. Previous regular analytical solutions for free edge stress are not rigorous in their linear elastic modeling with dissimilar interfaces between homogeneous plies of laminated composites. Singular stress is not practical in reality at the free edge because it nearly never occurs in real situations. Until now, the analytical nonsingular approximate solutions have been accepted even though they cannot show the rigorous singular behavior at the free edges; this shortcoming is corrected within linear elasticity dissimilar interface modeling. In this study, a regular analytical solution is provided, which is rigorous within the linear elastic model featuring smoothly varying material properties through the thickness of the laminates. This interface modeling provides not only nonsingular stresses but concentrated finite interlaminar stresses using the principle of complementary virtual work and the stresses that satisfy the traction-free conditions not only at the free edges but also at the top and bottom surfaces of laminates are obtained. Significant reductions in stresses at the free edge were observed compared with the results without interface modeling. Various stress analyses were performed and the results demonstrate the usefulness of the proposed interface modeling.

Membranes, such as geosynthetic tubes, have been widely used in civil construction and as storage tanks. Estimation of the shape, structural tension, and internal pressure are essential for effective and safe use of these structures. Motivated by a numerical study on the case of a partially liquid-filled membrane, this study presents a novel general mathematical static analysis of a fully liquid-filled geosynthetic-tube membrane section anchored on an incline. The membrane problem can be modeled analytically as a set of simultaneous nonlinear ordinary differential equations with some undetermined boundary conditions. A close examination of possible analytical solutions for increasing the cross-sectional area of the membrane identifies that the membrane sections have four similarity (or canonical) shapes. Integration of the curvature expression results in a similarity solution of the canonical shape, expressed in terms of analytical elliptic integrals. Using the analysis method developed, the range of the characteristic parameters of each canonical shape and the associated pressure and tension of membrane sections of arbitrary sizes can be determined. The analytical results developed provide an efficient tool to identify the canonical shapes and transition points and are valuable in interpreting the physics.

Many theoretical and experimental studies of complex path-dependent dynamic systems lead to restoring forces expressed as piecewise nonlinear algebraic equations. Examples include, but are not limited to, bilinear hysteretic, Ramberg-Osgood, Masing, generalized Masing, Clough, and Takeda models, which are popular in engineering mechanics applications. These models relate restoring force to displacement and velocity by means of piecewise relations having only $C^0$ continuity, which leads to two sorts of challenges in numerical simulation. First, the equations of motion may not simply be a set of ordinary differential equations, rather they may fall within the framework of differential-algebraic equations (DAEs). Second, there are unknown locations of discontinuities of low-order derivatives of the solution. This study seeks accurate and efficient numerical solutions of the DAEs with $C^0$ continuity, enabling robust simulation of these complex nonlinear dynamic systems. This study focuses on explicit time integration for single degree-of-freedom problems, while presenting a suitable problem formulation, detailed guidelines, case studies, and convincing insights, while exploiting two built-in MATLAB functions (ode45.m and the Events option). User-defined options are carefully examined, and recommendations are made based on a systematic study of approximation accuracy and computational efficiency, particularly as they relate to global error and tolerance proportionality when using an explicit, adaptive Runge-Kutta (RK) solver. Obtaining accurate values of state event locations results in a robust approach to solving the identified class of problems. This work initiates the possibility of treating many similar models by using the proposed programming module and, more importantly, by applying and further advancing the underlying theoretical concepts.

In this paper a general solution to the geometrically nonlinear analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary monosymmetric cross sections with a deformable connection subjected to arbitrary loading is presented. The plate-beam structure is assumed to undergo moderate large deflections and the nonlinear analysis is carried out by retaining the nonlinear terms in the kinematical relationships. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate under the hypothesis that the plate and the beams can slip in all directions of the connection without separation, while the arising tractions in all directions at the fictitious interfaces are taken into account. These tractions are integrated with respect to each half of the interface width, yielding two interface lines along which the loading of the beams as well as the additional loading of the plate are defined. Their unknown distribution is established by applying continuity conditions at the interfaces in all directions, taking into account their relationship with the interface slip through the shear connectors’ stiffness. Any distribution of connectors in each direction of the interfaces can be handled. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account. Six boundary value problems are formulated and solved using the analog equation method, a boundary element-based method. Application of the boundary element technique leads to a system of nonlinear and coupled algebraic equations that is solved using iterative numerical methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions; the knowledge of which is very important in the design of prefabricated ribbed plates.

This paper presents an analytical solution for a steady two-dimensional planar flow of incompressible, inviscid fluid between a nonsinusoidal periodic wavy surface and a plane surface. Equations and graphs for the surface topography, the streamlines, and the resulting pressure distribution are presented. In addition to its esthetic merits, this solution furnishes a series of progressively more severe benchmark solutions for the verification of Euler solvers.

An analytical solution for the space-time variation of contaminant concentration in one-dimensional uniform groundwater flow in a homogenous semi-infinite porous formation (e.g., aquifer) subjected to time-dependent source contamination is derived. The temporally dependent dispersion in the aquifer is investigated under two conditions. First, the temporally dependent dispersion distribution in the aquifer is considered as a sinusoidally varying function and, second, the temporally dependent dispersion distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free; i.e., the aquifer is not clean and the initial concentration is an exponentially decreasing function of the space variable and is tending to zero toward infinity. The concept that dispersion is directly proportional to the seepage velocity is employed. The analytical solution is illustrated using an example and may help benchmark a numerical code and solution.