Journal of Engineering Mechanics

This paper presents a data-driven approach to damage detection and prognosis in the context of structural health monitoring. One of the main issues in dealing with structural damage and degradation is its hidden stochastic nature, which could be gradual or accompanied by sudden changes resulting from shock events. Although gradual degradation could be related to age and operating conditions, shocks could arise from loss of stiffness/connectivity or from impact, resulting in a subsequent change in degradation path. In this paper, a unified degradation modeling approach is presented based on a gamma process, where both gradual degradation and change points caused by shock events are identified in a unified formulation. Because the exact degradation path depends upon both operating and loading conditions, the model parameters are estimated directly from the sensory data using Bayesian inference. In the first step, a degradation indicator is calculated based on time-series modeling, which is then used together with a multivariate Hotelling’s $p$ control chart for damage detection. In the next step, the degradation indicator forms an input to a gamma process degradation model (single- or two-phase gamma process), which enables damage prognosis using time-series model parameters as surrogates. The advantage of this approach is the ability to detect change points and changes to the degradation path using a purely data-driven approach without the need for experimental failure data. The model parameters and prognosis estimates can be updated with the availability of monitoring data, which makes it a powerful tool for damage detection and prognosis in long-term condition-monitoring settings. A numerical example is presented to illustrate the overall process using simulated vibration data and highlight the potential advantages of using this methodology.

This study proposes a vibration control system consisting of a swing story subsystem, a lateral force resisting subsystem, and connecting dampers. The swing story subsystem comprising hinged columns connected to continuous beams is employed to resist the gravity load, and perimeter moment-resisting frames the lateral force. Dampers are adopted to transfer lateral forces between the two subsystems and are used to dissipate seismic energy. The main characteristic of the system is that both the fundamental and higher-mode responses can be reduced remarkably compared with conventional moment-resisting frame structures. This paper establishes equations of motion of the proposed swing story control system, and the dampers are optimally designed by a multiobjective optimization algorithm with the combination of the stability maximization and ${\mathrm{H}}_2$ criteria. To avoid instability of the flexible swing stories, sufficient stiffness is required for the dampers, and buckling analysis is thus conducted to determine the required minimum stiffness. Excellent vibration control effects of the proposed system are verified through numerical analyses of three-story and nine-story benchmark structures.

This paper presents a model capable of providing estimates of the apparent permeability directly from the pore-size distribution and from the properties of the fluid to be considered. The model is based on a hierarchical assembly of capillaries with decreasing diameter, generated randomly. The technique yields a porous network, which mimics the pore space measured experimentally by mercury intrusion. The intrinsic permeability and the evolution of the apparent permeability with mean pressure are provided by equating Darcy’s law and a combination of Poiseuille’s and Knudsen’s laws. Comparisons with experimental data on mortar specimens show that the model provides the intrinsic permeability and its evolution when the material is subjected to mechanical loads. For a given pore-size distribution, the evolution of the apparent permeability is also provided and test data with several types of gases compare quite well with the model.

In this paper, a new design approach based on the principles of energy and momentum conservation is proposed for the design of free-standing rigid barriers subject to point impact. The novelty of this approach lies in the fact that the mass inertia effect of the barriers and the coefficient of restitution for the impact are considered. With the new design approach, it is shown that for the same impact scenario, a taller barrier actually has a higher factor of safety due to the increased mass inertia—a result that could not have been obtained in a force-based calculation. The new approach has been verified by results from systematic physical and simulated impact experimentation. This paper presents full details of the derivation of the analytical expressions, their experimental verification, and illustration by a worked example. A design chart is also presented to make the proposed methodology easier to implement.

In this study, the scattering focused hydrodynamic interaction between linear waves and a proposed structural system with a floating body and two attached vertical porous walls was investigated analytically and experimentally. By the application of two sets of orthogonal eigenfunctions and matching conditions, the velocity potential and associated unknown coefficients in each fluid region were theoretically derived. The free-surface elevations and wave loads, including the force components and moment, were also formulated. Additionally, wavetank tests were performed to confirm the derived solutions, especially the transmitted waves. The present solutions of the limiting cases in terms of reflection/transmission coefficients and hydrodynamic forces and moments were found to match well the other published results. To evaluate the performance of the proposed floating-body system, the variations of the reflection and transmission coefficients versus the relative water depth, the porous-effect parameters, and the relative size of the structure were investigated. The results, which show the role played by the porous walls on the hydrodynamic forces and moments, are presented and discussed.

Servo-hydraulic actuators exhibit frequency-dependent variations of amplitude and delay during real-time hybrid simulation (RTHS). Effective compensation techniques to overcome these variations is a crucial component for the successful implementation of RTHS. Most of the existing compensation techniques have demonstrated effective performance under excitations with relatively low frequency bandwidth. To further advance the servo-hydraulic compensation for broader frequency bandwidth, this paper presents the design and performance evaluation of an optimal discrete-time model-based feedforward controller under inputs with broader frequency bandwidth as high as 0–30 Hz. As a compensation technique has not been fully explored in RTHS, the model-based design of discrete-time domain compensation techniques introduces the new technical challenge of inverting nonminimum phase systems. This paper identifies this new challenge by providing detailed supporting derivation, and explains the use of a digital filtering technique—a finite impulse response (FIR) filter—to address this new challenge, and the development process of the proposed FIR compensator using different optimization schemes. Furthermore, this paper demonstrates the compensation performance of the proposed FIR compensator, both numerically and experimentally, under reference inputs with various bandwidths, including bandlimited white noises with frequency bandwidth as high as 0–30 Hz. For comparison purposes, several existing feedforward compensation techniques are also implemented and compared with the proposed FIR compensator. Based on this study, it is found that the proposed FIR compensator technique not only provides excellent compensation performance under various bandwidths, but also offers great flexibility in its formulation by varying the model order with desired compensation performance and computational demands.

The paper deals with the generalization of Fourier-type relations in the context of fractional-order calculus. The instantaneous temperature-flux equation of the Fourier-type diffusion is generalized, introducing a self-similar, fractal-type mass clustering at the micro scale. In this setting, the resulting conduction equation at the macro scale yields a Caputo’s fractional derivative with order $\beta \in [0,1]$ of temperature gradient that generalizes the Fourier conduction equation. The order of the fractional-derivative has been related to the fractal assembly of the microstructure and some preliminary observations about the thermodynamical restrictions of the coefficients and the state functions related to the fractional-order Fourier equation have been introduced. The distribution and temperature increase in simple rigid conductors have also been reported to investigate the influence of the derivation order in the temperature field.

This work aims to shed light on the “thermally-anomalous” coupled behavior of slightly deformable bodies, in which the strain is additively decomposed in an elastic contribution and in a thermal part. The macroscopic heat flux turns out to depend upon the time history of the corresponding temperature gradient, and this is the result of a multiscale rheological model developed in Part I of the present study, thereby resembling a long-tail memory behavior governed by a Caputo’s fractional operator. The macroscopic constitutive equation between the heat flux and the time history of the temperature gradient does involve a power law kernel, resulting in the “anomaly” mentioned previously. The interplay between such a thermal flux and elastic and thermal deformability are investigated for a pinned-pinned truss. This allows a focus on the effects of the deviation from Fourier’s law on the thermoelastic coupling. Indeed, the interactions in the presented system are fully coupled because the temperature and displacement field mutually influence one another.

Laboratory tests on sand–marine clay mixtures reveal that the effect of sand mass fraction on the overall consolidation behavior is negligible for a sand mass fraction of 20% or less. Further increase of the sand fraction significantly affects the overall consolidation process. To describe this behavior, a consolidation model is proposed within a homogenization framework. The sand–marine clay mixture is divided into two systems: a clay matrix system consisting of the silts, clay particles, and void space in the marine clay matrix; and an inclusion system consisting of sand particles. The volume fraction of sand particles is adopted as the structure variable, representing the intergranular structure evolution of the sand-clay mixtures. Based on some reasonable assumptions, the governing equations are formulated and the consolidation problem is solved using Galerkin’s weighted residual method within the finite-element framework. The proposed consolidation model has five principal parameters: four intrinsic ones depending on the behavior of the pure clay matrix and one structure parameter related to the intergranular structure. Only two conventional oedometer tests are needed for the calibration of these model parameters. Comparison between the test data and the model prediction reveals that the model can well reproduce the effect of sand fraction on the overall consolidation behavior of the tested sand–marine clay mixtures.

Frequency-domain methods are usually more efficient computationally than time-domain methods to compute the responses of linear dynamic systems. However, a common drawback of frequency-domain methods is that computed responses are merely the steady-state response, not the total response. It appears that no analytical solution has been derived for the transient response of a multiple-degree-of-freedom (MDOF) dynamic system to arbitrary periodic loading. An analytical contribution of this article is deriving a closed-form solution for the transient responses of linear MDOF systems to arbitrary periodic excitations. Together with the fast Fourier transform (FFT) algorithm, a very efficient numerical method is developed to compute the transient and total responses of MDOF systems, suitable for both damped and undamped systems. In the newly developed method, the computational time required for obtaining the transient response is much less than that for the steady-state response. Three numerical examples are provided in this paper to verify the correctness, and demonstrate the effectiveness as well, of the newly developed method.

Homogenization of a representative volume element (RVE) is often used as the basis for defining the effective properties of a composite material. Although this is a powerful and useful approach for predicting global response, it does not capture the inherent variability of the material. Homogenization of statistical volume elements (SVEs), which are partitions of the RVE, provide a population of apparent properties that can be used to statistically characterize this local variability. The challenge to using these models lies in choosing a partitioning scheme and appropriate mesoscale to define the SVEs. In this work, two partitioning schemes are examined, a traditional square grid and polygon cells generated using Voronoi tessellation. Each scheme is used with a range of mesolength scales, i.e., partition sizes, and applied to composites with varied phase contrast ratios and differing microstructures. The resulting distributions of properties, described by probability density functions and generated using the principle of maximum entropy, are used to compare partitioning schemes. The results show consistent advantages to using Voronoi tessellation. This method reduces the impact of contrast ratio on property bounds, makes the choice of partition size less critical to a mesoscale model, and is able to better distinguish between subtle microstructural differences.

This paper presents isogeometric analysis of a hygro-thermo-chemo-mechanical concrete model at early age and beyond. Balance equations are introduced at the microscale and averaged to obtain balance equations at the macroscale. Constitutive laws are then applied directly at the macroscale. The final balance equations are mass, momentum, and energy based. These are written as a function of five primary variables in two dimensions: gas pressure, capillary pressure, temperature, and displacements. The standard finite-element shape functions are replaced by non-uniform rational B-splines that are used in isogeometric analysis. These basis functions possess a higher degree of continuity and can be used to construct an exact geometry when compared with their finite-element counterparts. Also, local mesh refinement at the mesh boundary is achieved easily with isogeometric basis functions. These properties make the isogeometric basis functions very suitable for describing the many transient processes that occur, especially in concrete at an early age. Isogeometric basis functions are implemented directly into an existing finite-element model. The accuracy of the isogeometric concept is compared and validated against the finite-element-based approach. The examples show that the isogeometric model is more accurate than the finite-element model on a per-degree-of-freedom basis.

A numerical method is presented to accurately simulate paddle-generated impulse waves. An order-one implicit splitting scheme allows advection and diffusion phenomena to be decoupled. Advection is solved using a semi-Lagrangian scheme implemented on a dynamic adaptive octree. This method enables the use of Courant numbers larger than one while the octree is refined at the liquid–air interface. Diffusion is solved on a fixed, unstructured finite-element tetrahedral mesh. Interpolation between octree and finite elements is discussed. Numerical results pertaining to paddle-generated waves in a tilted cavity are successfully compared with experimental data.

For the simulation of fluctuating wind velocity field with $n$ processes, the existing spectral representation method requires a total of $n(n+1)/2$ executions of the fast Fourier transform (FFT) algorithm. This requirement is found to be computationally expensive for large structures where the number of processes $n$ becomes very large. An efficient spectral-representation-based method is proposed for the simulation of stochastic wind velocity field using Fourier-Stieltjes integral and polynomial decomposition of order $q$. The proposed approach is very efficient because only $q\times n$ executions of the FFT algorithm are required. Numerical investigations involving the simulation of stochastic wind velocities along the deck of a bridge show that the order of the polynomial decomposition $q$ is very small compared to the number of processes $n$, and more than 50% of computation time can be saved for the simulation of 100 processes.

Estimating the peak value of wind load effects is an important task for engineers of structural and cladding design. Because of the various sources of uncertainties, such as the aerodynamic effect, model selection, and calibration errors, the peak wind load effects may have large variations. This study evaluates the uncertainty of the peak value of wind load effects across multiple samples from a wind tunnel. The Hermite polynomial model (HPM)-based translation process method is adopted to estimate the peak wind load effect. An empirical formula is proposed to estimate the parameters of peak value distribution. Two analytical approaches to model the uncertainty of the peak value at any fractile are proposed based on the probability function and the Gaussianity inference of the peak value. Numerical examples including the wind pressure coefficient and wind-induced response illustrate the performance of the proposed approaches.

A novel stochastic averaging technique based on a Hilbert transform definition of the oscillator response displacement amplitude is developed. Specifically, a critical step in the conventional stochastic averaging treatment involves the selection of an appropriate period of oscillation over which temporal averaging can be performed. Clearly, for oscillators with nonlinear stiffness defining such a period is not an obvious task. To this aim, an intermediate step is often introduced relating to the linearization of the nonlinear stiffness element, i.e., treating it as response amplitude dependent. Obviously, this additional approximation can potentially decrease the overall accuracy of the technique. Thus, to circumvent some of the aforementioned limitations an alternative definition of the amplitude process is considered herein based on the Hilbert transform. In comparison to a standard definition of the response displacement amplitude, the amplitude definition used herein does not require the a priori selection of an equivalent natural frequency. Notably, this feature provides enhanced flexibility in the ensuing stochastic averaging treatment, and it can potentially result in higher accuracy. Further, an extension of the Hilbert transform–based stochastic averaging is developed to account for oscillators endowed with fractional derivative terms as well. The hardening Duffing oscillator both with and without fractional derivative terms, as well as the bilinear stiffness oscillator, are considered in the numerical examples section for demonstrating the reliability of the technique. For all cases the analytical results are compared with pertinent Monte Carlo simulation data.

High performance control systems (HPCS), including semiactive, active, and hybrid damping systems, are effective solutions to increase structural performance versus multihazard excitations. However, the implementation of HPCS within structural systems is still in its infancy, because of the complexity in designing a robust closed-loop control system that can ensure reliable and high mitigation performance. To overcome this challenge, a new type of controller with high adaptive capabilities is proposed. The control algorithm is based on real-time embedding of measurements to minimally represent the essential dynamics of the controlled system, therefore providing adaptive input space capabilities. This type of controller is termed an input-space dependent controller. In this paper, a specialized case of input-space dependent controller is investigated, where the embedding dimension is fixed, but the time delay used in the construction of the embedding varies with time. This constitutes a variable multidelay controller (VMDC), which includes an algorithm enabling the online selection of a time delay based on information theory. Here, optimal time delay selection is first studied and its applicability of the VMDC algorithm demonstrated. Numerical simulations are conducted on a single-degree-of-freedom (SDOF) system to study the performance of the VMDC versus different control strategies. Results show a significant gain in performance from the inclusion of an adaptive input space, and that the algorithm was robust with respect to noise. Simulations also demonstrate that critical gains in performance could be obtained from added knowledge in the system’s dynamics by comparing mitigation results with a linear quadratic regulator (LQR) controller. Additional simulations are conducted on a three degrees-of-freedom (3DOF) system, which consists of a model structure equipped with an actuator and subjected to nonsimultaneous multihazards. Results show enhanced mitigation performance of the VMDC versus LQR strategies when using limited-state feedback, validating the capability of the controller at mitigating vibrations based on limited knowledge and limited measurements, and thus its promise at multihazard applications.

The use of viscous dampers to mitigate cable vibrations on cable-stayed bridges is very popular. A viscous damper attached to a stay cable results in complex mode shapes. Such complexity could affect the dynamic stability of the cable under wind action, yet it is neglected in conventional galloping analysis. A general framework to investigate the problem of galloping of a stay cable with an attached viscous damper is therefore developed. Aerodynamic forces on the complex modes are considered, including aeroelastic coupling between the modes. A numerical example for an ice-accreted stay cable with a damper shows that conventional galloping analysis overestimates the critical wind speed for galloping occurrence. The complexity of the mode shapes gives rise to the cable being more unstable than ignoring it by treating the mode shapes as real.

This paper presents a time-dependent reliability method for the assessment of corrosion-affected metal pipe failures. Two nonlinear limit state functions are proposed for brittle and ductile pipes with mixed mode fracture. For brittle materials, a general failure criterion taking into account all three fracture modes is adopted, whereas for ductile materials, the criterion of stress intensity factor is used, based on a newly developed model of elastic fracture toughness. Stochastic models of corresponding load effects are developed and an upcrossing method is used to quantify the probability of failure and predict the remaining service life. A case study is presented to illustrate the proposed method, followed by a sensitivity analysis to investigate the effects of key variables on the probability of pipe failure. The use of Mode I fracture toughness rather than mixed-mode fracture toughness of the pipe is found to underestimate the probability of its failure. The corrosion and internal pressure have the most influence on the probability of failure for both brittle and ductile pipes, whereas pipe internal radius has the least effect. The method presented in this paper can assist pipe engineers and asset managers in developing a risk-informed and cost-effective strategy for better management of corrosion-affected metal pipelines.

An unusual overshooting behavior might be experienced in the forced response of a high-frequency mode for a structure-dependent integration method. This unusual overshooting is different from that found in the free vibration response and can be detected by examining an alternative form of the local truncation error derived from a forced vibration response rather than a free vibration response. In addition, this local truncation error can be applied to develop an effective remedy to remove the adverse overshoot behavior. This remedy can be obtained by introducing a load-dependent term into the difference equation for displacement increment for structure-dependent integration methods, such as the first and second Chang family methods. All the analytical findings are numerically verified.

Dynamic modal testing is an economical method of evaluating structural key stiffness, the accuracy of which relies on the determination of selected target modes. Pretension deviations are usually inevitable in cable domes; their stiffness, however, depends highly on the pretensions in the system. The target modes thus cannot be determined effectively based only on idealized numerical models regardless of pretension deviations. A method is proposed to select the target modes based on the idealized numerical model and to accomplish its expansion based on perturbed structural models considering the randomness of pretension deviations. The sensitivity relationships between member length errors and their effect on eigenvalues and mode shapes are established. For the prescribed error limits on member lengths, the possible variations of target modes obtained based on the idealized numerical model can be distinguished. To monitor the key stiffness, a two-step strategy for expanding the assembly of target modes is suggested by considering the mode shape change and mode jumping. An illustrative Geiger cable dome is employed to investigate the validity of the target mode determination method put forward in this paper.

The moment-based Hermite transformation models are widely used in extreme-value prediction and fatigue estimation of non-Gaussian processes. However, when only higher-order ordinary central moments (C-moments) are involved in the transformation, the Hermite model would lead to statistical uncertainty. Furthermore, the application of moment-based Hermite models to measured time series is restricted if accurate moments cannot be retrieved from data. In this paper, the respective virtues of C-moments and linear moments (L-moments) are exploited to formulate a new style of nonlinear transformation. Combinations of these two types of moments are sought with various strategies in terms of the accuracy in extreme-value prediction of non-Gaussian processes. It is found that for a process of very strong non-Gaussianity, the quartic C-moment model renders best accuracy when the sampling data are rich, while two of hybrid C- and L-moment (C/L) models work most nicely when data size is limited.

In this study, the weak-form finite-element model has been developed for bending of plates considering the rotation gradient–dependent potential energy along with the conventional strain energy in the case of moderate rotation for Cosserat solid. The microrotation of the material point is considered to be constrained with the macrorotation of the continua. First, the governing equations are obtained from the principle of virtual displacements considering the displacement field as general power (Taylor) series expansion about the displacement of the midplane of the plate, and then the formulations are specialized for the general third-order, first-order, and the classical plate theory. The nonlinear finite-element models have been developed for all the plate theories considered. Further, the analytical solution for a simply supported linear plate is presented. In the numerical examples, the stiffening and anisotropic effects in response to oriented microstructures in the continuum of a microplate are illustrated. The parametric effect of the material length scale on the various components of stress is also studied.

The effective in-plane elastic moduli of different types of honeycomb cores with thick walls are studied using analytical and numerical approaches. Analytical equations derived in this paper take a proposed jointed rectangle into consideration. The analytical results under plane stress and plane strain conditions are also obtained. The effective in-plane elastic moduli are studied as a function of their own relative densities because of the different methods of describing the geometrical shapes of honeycomb cores. The results are quantitatively compared with the available experimental results in this paper. It indicates that the present model can better predict the elastic properties in $x$-direction but are less suitable in $y$-direction. The proposed jointed rectangle has significant effect at high relative density. Moreover, the effective in-plane modulus increases with the relative height of honeycomb cores because of the Poisson effect of the material, and the results under plane stress and plane strain conditions are the lower and upper bounds, respectively.

This technical note presents a model formulation that can be used for analyzing the in-plane free vibration behaviors of a very large–sag extensible cable supported at the same and different levels. The formulation model developed in this study is based on a variational approach, which involves the virtual strain energy because of axial stretching, the virtual work done by cable self-weight, and by the inertia forces. The coupled equations of motion in the Cartesian coordinates are obtained by taking into account the difference of Euler’s equations between equilibrium and displaced states. The Galerkin finite element method is used to obtain the mass and stiffness matrices and then the eigenvalue problem is solved. The numerical analysis results are given to demonstrate the dynamic free vibration on natural frequencies and mode shapes of various characteristics of cables from very small–sag to very large–sag cable configurations, the special case of a very large–sag cable was investigated and compared with the natural frequencies and mode shapes of the simple hanging chain.

It is well established that the lateral bending stiffness of thin panels is considerably enhanced by judicious use of ribs or stiffeners. This increase in stiffness is primarily due to a disproportionate increase in the second moment of area, and because relatively little mass is added, stiffened panels are especially appealing in an aerospace engineering context. In experiments it is relatively straightforward to measure bending deflections (especially in a cantilever configuration) and natural frequencies using laser vibrometry and associated signal-processing tools. This paper reports on a parametric study in which bending stiffness and natural frequencies are measured for a set of rectangular panels, conveniently manufactured using a three-dimensional (3D) printer. Both isogrid (stiffeners in a triangular configuration) and orthogrid (stiffeners in a rectangular configuration) structures were made and tested, with certain nondimensional parameters held constant (for example, total mass and length-to-width ratio) to facilitate easier comparison. The boundary condition considered was one edge clamped and the other edges free (simple cantilever) with a consistent plan area aspect ratio, and with the height and arrangement of stiffening ribs providing the major parametric variation.