Journal of Engineering Mechanics

The method of superposition is used to achieve a free-vibration analysis of orthotropic cantilever plates resting on point supports. In the initial development of the analysis it is assumed that the supports are symmetrically distributed about the plate centerline running normal to the clamped edge. Delineation is then made between modes that are symmetric, or antisymmetric, with respect to this centerline. It is shown how a small modification to the theory permits the obtaining of solutions for the case where supports are located at the plate outer corners. Modifications required to handle the case where support points do not have a symmetric distribution are also described. Free-vibration eigenvalues are provided for square plates with a pair of symmetrically distributed support points and various combinations of orthotropic property ratios. The problem under study is one that may occur, for example, in cantilevered mezzanine floors in buildings. It is expected that the tabulated eigenvalues will also provide useful reference points for other researchers. This appears to be the first analytical-type solution developed for this realistic industrial problem.

The active vibration control of a moving flexible member was studied in this work. The equation of motion of flexible members could be expressed as a continuous time-varying state equation in the state space. The matrix of state transition was approximated stepwise by the matrix exponential; in addition, the state equation was discretized to a difference equation to improve the computing efficiency. Furthermore, an optimal control of time-varying procedure system based on the minimization of a quadratic performance index for state vectors and control forces was developed. Active vibration control of a rotating beam was selected as a numerical example in making a comparison with other methods. Active vibration control of a rotating beam using the piezoelectric actuators was carried out as an experiment example.

A numerical technique for integrating the fully elliptic Reynolds-averaged Navier-Stokes and diffusion equations has been used to investigate the effect of ambient density stratification on the flow characteristics of a vertical force plume in a cross-flow of a stably linear stratified environment. A two-equation k -ε turbulence model is employed to simulate the turbulent transport quantities and to close the solving problem. Some basic flow features and a structure for the interaction of the buoyant jets with a density-stratified cross-flow are obtained. The results show that the ambient stratification tends to inhibit the flow development of the buoyant source and to encourage the formation of secondary and third vortex pairs in the jet cross section as a plume flowing downstream. It then results in causing the jet-flow oscillation from its maximum height-of-rise.

A class of hybrid inverse eigenmode problems is formulated such that a set of stiffnesses of a structure supported by a prescribed shear-type foundation system at an interface is determined for a specified lowest eigenvalue and a specified set of lowest-mode deformation-quantity ratios in the structure. The key point of the hybrid inverse eigenmode formulation is to take full advantage of the dynamic equilibrium of the whole superstructure, including the interface, and to express the lowest-mode interstory-drift components in the foundation system in terms of the specified lowest eigenvalue and the specified lowest-mode deformation quantities in the superstructure. A property on signs of the lowest-mode components is clarified for a general finite-element model supported by a shear-type foundation system. A systematic procedure for determining the stiffnesses of the superstructure is devised. The condition for uniqueness of the stiffnesses is then disclosed. Finally an example of application of this formulation is presented for a finite-element beam model supported by a shear-type foundation system.

A theoretical model is constructed for a large-deflection analysis of a rigid, perfectly-plastic cantilever with a tip mass loaded by a transverse follower force pulse. The purpose of building and analyzing such a model is to provide an analytical basis for studying unconstrained motions of a whipping pipe. Such motion can arise from the failure of high-pressure piping systems and is consequently a safety-related phenomenon. A guillotine break in the pipe leads to the expulsion of a jet of high-pressure fluid, and the reaction force pulse exerted on the pipe causes it to accelerate and deform. Generally, the motion of the pipe consists of an initial transient phase and a modal, root rotation phase. The equations for the initial traveling hinge phase and root rotation phase are derived and solved numerically. Pipe kinematics and deformations are deduced and comparisons are made with observations from pipe-whip tests. Finally, the model is used to give indications of the variation in the zone of influence (i.e., the region where the whipping pipe could strike another pipe or other components) for different ratios of tip mass to pipe mass.

In a companion paper, the effects of large deflections were evaluated for plastic deformation of a cantilever beam under a transverse force pulse applied at its tip. Here, the effect of material elasticity is introduced in addition to the large deflections through a simple model. The beam is assumed to be rigid and perfectly-plastic, but instead of the usual fully clamped constraint at its root, an elastic, perfectly-plastic rotational spring is incorporated there so that the beam-spring system has a certain capacity to store elastic energy. Compared with the rigid, perfectly-plastic model, the present beam-spring model shows differences in the initial plastic hinge position and in the minimum magnitude of the force needed to produce plastic collapse. It is also shown that a range of different responses may occur as the remaining plastic hinge travels along the beam segment toward the root, rather than the unique response mode in the rigid, perfectly-plastic analysis.

An accurate pointwise equilibrating polynomial element with springs connected to its ends to model semirigid connections is derived. The formulated element and coded computer program for second-order nonlinear analysis of flexibly jointed steel frames is employed to study a variety of problems using one element per member, which is not possible by the conventional cubic Hermitian function and most of the currently available elements. When incorporated into a nonlinear-analysis computer program, the versatility of the program is greatly improved as the convergence rate is increased, and the modeling effort for accurate solution is reduced considerably because the element stiffness remains accurate under high axial load. The capability of the proposed element in handling a harsh benchmark problem is also verified in one of the examples.

A probabilistic-based micromechanical model has been developed for the postcracking behavior of a brittle matrix reinforced with short, randomly distributed fibers. The model that predicts the composite-bridging stress crack-opening displacement (COD) relationship, accounts for fiber pullout, fiber tensile rupture, and a local frictional effect called snubbing. However, it does not account for fiber bending rupture, and the possible effect of matrix spalling at the exit points of inclined fibers from the matrix. The model assumes a fiber/matrix interface that is controlled by a constant frictional bond stress. The model is used to predict the composite tensile strength and fracture energy. Comparisons of model-predicted bridging stress-COD relationship with experimental data, where fiber rupture has occurred, show reasonable agreement supporting the validity of the proposed model. The model is then used to perform a parametric study to evaluate the effect of the micromechanical parameters on the composite tensile strength and fracture energy. The study suggests that this model can be used to design the composite for optimum performance.

Based on an energy principle and a virtual crack extension technique, a practical finite-element modeling approach for the automatic mixed-mode two-dimensional (2D) linear elastic fracture mechanics (LEFM) crack-propagation analysis has been developed. By decomposing the displacement field obtained from a conventional finite-element analysis into symmetric and antisymmetric displacement fields with respect to the crack, Mode-I and Mode-II energy release rates can be determined using a generalization of the stiffness derivative method, and the corresponding stress intensity factors can then be calculated. The load at which a crack propagates and the propagation direction can be determined using one of the well-established mixed-mode crack-propagation criteria. Unlike the previously developed approaches to crack propagation, this approach does not require the use of symmetric crack-tip mesh, nor crack-tip singular elements, which greatly simplifies the subsequent remeshing process to allow for crack propagation. The automatic crack-propagation process is achieved by using a simple and efficient local 2D remeshing algorithm that can be easily programmed. Convergence studies, mesh sensitivity studies, and the practical use of the new approach are presented through various example problems.

The rigid block considered here represents an idealized model for a piece of equipment, a monument, a storage tank, or even a tall building, which may topple by rocking under intense ground shaking at its base during an earthquake. The base excitations consist of both horizontal and vertical ground accelerations, and they are assumed to be nonstationary processes with evolutionary broad-band spectra. The total energy of the rocking block is approximated as a Markov process, and a modified version of quasiconservative averaging is applied to obtain the governing Itô equation for the process. The reliability of the system (namely, the probability that toppling has not occurred up to a given time t ) is calculated by using the numerical procedure of path integration, on the basis that the transition probability density of the Markov process in a sufficiently short time interval is approximately Gaussian.

An image-analysis method developed to study granular flow, the accumulating particle trajectories (APT) method, is shown to be a versatile tool to study the movements of disks. The moving disks, which are provided with suitable dot patterns, are video-recorded and the recorded sequences are analyzed to provide trajectories of the disks and the dots, thus making it possible to study both translational and rotational movements. It is also possible to introduce time markers in the trajectories. Up to eight images per second can be analyzed. The filtering necessary to attenuate electronic noise in the video equipment is performed as time filtering between consecutive images and is very efficient. The method's demands for processing power are very moderate and, therefore, particle movements during time spans corresponding with thousands of video frames can be easily presented as analysis results. The method can be implemented at relatively low cost.

A reduction in the number of random variables carried in a structural-reliability analysis can be achieved by an orthogonal transformation of the basic random vector to a vector of independent standard normal variables, followed by a reduction procedure similar to that employed in modal analysis in structural dynamics. This paper investigates the error introduced by this reduction in the representation of random fields through orthogonal-series expansions. It is found that the error in the second-moment representation of a random field is bounded by the reduction error, which is easily computed, when the correlation length of the random field is short; this often is the case in stochastic finite-element analysis.