Journal of Engineering Mechanics

Field experimentation on constructed systems demands consideration of many mechanisms of epistemic and aleatory uncertainties as well as human errors and subjectivity. This is especially true in operational modal analysis (OMA) applications that aim to identify the dynamic properties of a structure. Although statistics and probability theory are sufficient for quantifying aleatory uncertainty and bounding the resulting errors in OMA results, there is much debate as to whether the same tools may also be used to quantify epistemic uncertainty. This study explored a framework for better understanding the distinctions and impacts of these two types of uncertainties in OMA and how human errors and subjectivity may be classified. A physical laboratory model was designed to simulate four key sources of epistemic uncertainty that represented the primary test variables: structural complexity (changing boundary conditions, nonlinearity), ambient excitation characteristics (magnitude, directionality, and bandwidth), preprocessing approaches, and modal parameter identification algorithms. The experimental program employed these variables within a full-factorial design and was carried out independently by two experts. To quantify the impacts of epistemic uncertainty, an error function termed the uncertainty evaluation index (UEI) was formulated based on comparing the uniform load surfaces derived from OMA (using pseudomodal flexibility) and the ground truth flexibility obtained from both forced vibration and static testing. The advantage of the UEI is that it provides a physically meaningful approach to distinguish the importance of capturing various modes based on their contribution to the flexibility of the structure. The results demonstrated that proven and accepted data preprocessing techniques and modal parameter identification algorithms can significantly bias OMA results when used in certain combinations under different structural and excitation conditions. Although caution must be used when generalizing the results of this study, they do indicate that epistemic (or bias) uncertainty can be far more significant that aleatory (or random) uncertainty in the case of OMA.

New analytical solutions are derived for the frictional sliding of rigid blocks to idealized ground acceleration pulses. These excitations are indicative of near-fault earthquake motions affected by forward fault-rupture directivity, which may inflict large permanent displacements in the absence of substantial frictional resistance at the sliding interface. The scope of this study is threefold: (1) to derive analytical solutions for a wide set of idealized pulses; (2) to investigate the effects of symmetric and asymmetric sliding under both unilateral and bilateral excitation conditions; and (3) to explore alternative normalization schemes of peak sliding with reference to peak pulse acceleration, velocity, duration, and shape. A generalized exponential function, capable of simulating an infinite number of pulse waveforms based on a single parameter, is employed to this end. Results are presented in the form of dimensionless closed-form expressions and graphs that provide insight into the physics of the nonlinear problem.

The flow characteristics induced by a solitary wave propagating over a submerged and bottom-mounted structure were studied experimentally using time-resolved particle image velocimetry (PIV) and particle trajectory photography for flow visualization. The setup for time-resolved PIV consisted of a high-speed camera and an argon-ion laser. Image processing techniques were utilized to improve both the temporal and spatial resolutions of the PIV system. The main parameters were wave steepness $(H/h=0.16–0.38)$ and aspect ratios of the rectangular structures $(L/D=0.14–11.1)$. The vortex shedding process near the trailing edge was divided into the following phases: the formation of the separated shear layer, generation of the vortices, vortex motion, and breakdown of the vortices. The motions of the primary vortex may differ depending on experimental parameters. By analyzing these motions, flow patterns were categorized into Types A, B, and C, and the conditions for these types were investigated. In the formation of the shear layer, the similarity profile was determined by selecting the proper length and velocity scales. The relationship between characteristic scales and nondimensional experimental parameters were also investigated.

This paper presents a structural health monitoring methodology that uses acoustic emission (AE) features to predict crack growth in structural elements subjected to fatigue. This allows for the prediction of the failure of the structural element at the current load level. The methodology uses Bayesian inference to account for different sources of uncertainty such as uncertainty in the data (AE signal), unknown fracture mechanics parameters, and model inadequacy. The methodology is divided into two main components: a model updating component that uses available data to build a joint probability distribution of the different unknown fracture mechanics parameters, and a prognosis component in which this multivariable probability distribution is sampled to predict the stress intensity factor range at a future number of cycles. The application of the methodology does not require knowledge of the load amplitude nor the initial crack length. The methodology is validated using experimental data from a compact test specimen under cyclic loading.

The localized effects and, particularly, the stress and deformation concentrations near edges, mortar joints, and irregular points in walls strengthened with externally bonded composite materials are studied. To quantify the structural behavior and to cope with the coupling of large-scale and localized-scale effects, a substructuring procedure that uses a specially tailored high-order finite element is developed. The specially tailored element accounts for the bidirectional behavior of the wall and for the interfacial interaction between the adhesively bonded components. The formulation uses a first-order shear deformation orthotropic plate theory for the independent modeling of the existing wall and the composite layers and a high-order theory for the modeling of the displacement fields of the adhesive layers. A static condensation-based substructuring procedure is used for the formulation of a superelement. The computational strength and the convergence characteristics of the high-order superelement formulation are demonstrated numerically. The superelement formulation is used to study the localized effects in a masonry assemblage strengthened with composite materials. This unique structural form is characterized by a vast dispersion of geometrical and elastic scales, presence of irregular regions, and concentrations of stresses. These localized three-dimensional (3D) stress fields are characterized and their sensitivity to various mechanical and geometrical properties is assessed. Conclusions regarding the impact of the localized effects are provided.

This research is directed toward an understanding of the high-speed interaction effects that two bodies have on each other. The experimental high-speed test track at Holloman AFB has undergone many design innovations over 50 years. One of the problems that remains in the modern era related to improving the speed characteristics of a rocket test sled is the wear that the interconnecting device, called the slipper, undergoes as it slides down the rail and impacts local asperities. The research is separated into two main areas. The first is the metallurgical investigation in which the material change is brought about by the surface friction through surface collision, and characteristics are determined that lead to a numerical model. The second is the development of a finite-element model using the commercial code ABAQUS, which is used in an attempt to capture the physics involved in the overall phenomenon. It became evident that the wear is not uniform, but is dictated by the evolving aerodynamics of a sled moving at close to 1,500 m/s, the speed considered in this research, creating an uneven wear surface at the interface of the slipper and rail. The finite-element analysis is separated into two models, one related to the global effects of movement using a predefined velocity versus time function, and the other defining a microlocal collision with a surface asperity. The Johnson-Cook flow equation is used to establish a von Mises maximum stress failure criterion within ABAQUS to arrive at the results. A method has been developed that allows the prediction of wear for a time-dependent forcing function obtained through a structural dynamics approach. Results indicate that the method is sufficiently robust that the physics of the wear process at high speeds is reasonably modeled. The metallurgical investigation is accomplished by testing component parts of a slipper recovered after a January 2008 sled test run, and this is used as the evidence of wear.

Seismic analysis, design, and performance assessment of buildings, bridges, and safety-related nuclear structures is based on two or three translational components of earthquake ground motion. Although rotational components (rocking and torsional) may contribute significantly to translational and torsional response and damage, they are not considered in design and assessment because their intensity and frequency content are not measured by accelerograms deployed in the free field. A method for developing rotational time series by first deconstructing the three translational time series of a ground motion recorded at one station into body waves is presented in this paper. The body waves are then reassembled to generate rotational time series. Point and line source representations of the fault rupture are considered. Results of the single station procedure are presented using rotational acceleration spectra and compared with the multiple-station-based geodetic method. The spectra are similar at periods greater than 1 s. The spectral ordinates computed using the geodetic method are significantly smaller at shorter periods, which is attributed to the underlying assumption of a plane surface for the recorded data at any time instant in the method.

The classic split-Hopkinson pressure bar (SHPB) data reduction methodology is revisited. A complete one-dimensional analysis of the SHPB system is presented for linear-elastic and viscoelastic specimens, for which the specimen and bar diameters are equal. In general, the assumptions inherent in the classic SHPB data reduction method are found to be inconsistent. However, the classic SHPB data reduction scheme is applicable in the case of acoustically soft materials. These analyses are extended to explain major issues in the general linear elastic case, including materials with regular and singular memory. Exact expressions for the average stress and strain in the specimen and Fourier transform of the memory kernel function in terms of experimental parameters in the quasi-static limit are formulated. Dynamic adjustments associated with elastic and viscous relaxation processes are also derived.

A Monte Carlo–based methodology is introduced as a generalization of the variability response function (VRF) concept, applicable to both statically determinate and indeterminate beam structures with possibly large stochastic variations of parameters (bending stiffness or flexibility). This new methodology overcomes all limitations associated with the Taylor expansion-based VRFs used in the past. Two generalized VRFs (GVRFs) result from this methodology: a deflection GVRF and a bending moment GVRF. Numerical evidence indicates that these GVRFs are neither unique nor completely independent of the probabilistic characteristics of the random field modeling the variations of the bending flexibility. The GVRFs are found to be mildly sensitive to the non-Gaussian marginal distribution of this field, but are minimally dependent on its spectral density function. Taking advantage of this finding, a fast Monte Carlo–based methodology for estimating representative GVRFs is also introduced, significantly reducing the computational effort.

In this research, the concept of continuum damage mechanics (CDM) was implemented to evaluate damage initiation and evolution in structural steel rebars at low and intermediate loading rates. The work was divided into experimental and theoretical phases to evaluate the ductile damage behavior. The experimental part involved uniaxial tensile tests for steel bars at the ambient temperature over a range of strain rates between $3.0\times {10}^{-4}\text{and}0.1{\text{s}}^{-1}$. Scanning electron microscopy (SEM), coupled with image processing techniques, was utilized to characterize the damage at several loading stages. The theoretical part of this paper introduced a new energy-based isotropic damage model capable of capturing the evolution of damage throughout the deformation process. The proposed damage model was verified via comparisons with the present SEM results and with other data available in the literature. The comparisons showed good agreement, and results from both approaches indicated that cracks and voids intensified significantly with the increase of plastic strain and strain rates. Results proved that the new procedure was satisfactory for damage characterization and offered good simplifications.

An illustrative fracture mechanics–based design paradigm is proposed for unbonded concrete overlays (UBCOs), an increasingly popular pavement rehabilitation system, with the ultimate goal of establishing a more rational design procedure than those currently available. To illustrate the advantages of the fracture mechanics–based approach to design, specific attention is paid to one type of failure associated with pavement structures, reflection cracking. The design formulas derived from the results of a large number of crack propagation simulations of both the UBCO composite and a reference single-layer new pavement quantify the dependence of the required overlay thickness and load-carrying capacity on all relevant material and geometric parameters. Preliminary comparisons of the results with field observations suggest that the fracture mechanics paradigm offers a promising procedure for improved design of UBCOs.

A relatively simple technique is presented for estimating the first-passage probability of any stationary Gaussian process. In particular, the technique is shown to give meaningful results for the troublesome case of a process with a bimodal spectral density that cannot be truly classified as either narrowband or broadband. Mathematically, the technique is only a seemingly minor revision of a long-known method for narrowband processes. What is new here is the demonstration of its applicability not only to narrowband processes but also to other spectral densities, including challenging bimodal situations. The fundamental idea is that of a Markovian point process in which the probability of the process never having crossed a given level $u$ is approximated as the probability that all members of the set of amplitude (or envelope) values at a discrete set of time values are below $u$, along with the assumption that the set of amplitude values has Markovian conditioning. The critical parameter that must be determined is a correlation coefficient that appears in the jointly Rayleigh distribution of the amplitude at two time values. A method involving simple numerical integration (or a series solution) is shown to give an appropriate value for this parameter for a given spectral density and a given value of $u$. The model is shown to give generally good agreement with simulation results for processes in which the commonly used Vanmarcke approximation is inadequate.