International Journal of Structural Stability and Dynamics

In this research, the frequency comparison function (FCF) method is proposed and studied to realize high-sensitive real-time crack identification at the welding joint area for a beam-type structure. This method is derived from the frequency response function (FRF). During FCF, we use the response signal collected from the designated point of the structure instead of the excitation. The standard deviation of the FCF amplitude curve is calculated to detect and evaluate the possible crack and its induced vibration perturbations afterward. Vibration responses are simulated in ANSYS by the use of the finite element analysis of a welded beam structure, and these signals are then analyzed with the FCF algorithm. It is concluded that FCF is an efficient method for breathing crack identification and can be easily applied under different excitation conditions, including harmonic and random ones. Meanwhile, FCF can be applied without any pre-processing algorithms such as filtering and smoothing. So, it can be used for real-time crack identification. By combining the FCF with the smart coating sensor composed of piezoelectric layers, the crack identification with high sensitivity is realized. The crack is detectable at its very early stage (starting from 3% of the beam thickness). Experimental studies under harmonic and random excitations are processed, and the results prove high sensitivity and feasibility of the proposed crack detection method.

Modal analysis of bridge under high-speed trains is essential to the design and health monitoring of bridge, but it is difficult to be implemented since the vehicle–bridge interaction (VBI) effect is involved. In this paper, the time–frequency analysis technique is performed on the non-stationary train-induced bridge responses to estimate the frequency variations. To suppress the interference terms in time–frequency analysis but preserve the time-variant characteristics of responses, the enhanced variational mode decomposition (VMD) is proposed, which is used to decompose the train-induced dynamic response into many of envelope-normalized intrinsic mode functions (IMFs). Then the short-time Fourier transform is applied to observe the time–frequency energy distribution of each IMF. The train-induced bridge signals measured from a large-scale high-speed railway bridge are analyzed in this paper. The IMFs associated with the pseudo-frequencies caused by train or the resonant frequencies of bridge are distinguished. And, frequency variations are captured from the time–frequency energy distributions of envelope-normalized IMFs. The results show the proposed method can extract the frequency variations of low-energy IMFs effectively, which are hard to be observed from the time–frequency energy distribution of train-induced bridge response. The instantaneous frequency characteristics extracted from the train-induced bridge response could be the important support for investigating the VBI effect of train–bridge system.

In this paper, a number of recently proposed implicit and explicit composite time integration schemes are reviewed and critically evaluated. To give suitable guidelines of using them in practical transient analyses of structural problems, numerical performances of these schemes are compared through illustrative examples. Meaningful insights into computational aspects of the composite schemes are also provided. In the discussion, the role of the splitting ratio of the recent composite schemes is also investigated through a different point of view, and similarities and differences of various composite schemes are also studied. It is shown that the explicit composite scheme proposed recently by the authors can noticeably increase the efficiency and the accuracy of linear and nonlinear transient analyses when compared with other well-known composite schemes.

The vehicle scanning method (VSM), an indirect approach for bridge measurement, has attracted intensive attention since it was proposed. By this method, a moving test vehicle is employed to detect the “mechanical” properties of the bridge, e.g. frequencies, mode shapes, damages, etc., utilizing the interaction between the two substructures. Compared with the conventional direct approach that requires quite a few sensors and data loggers to be fitted on the bridge, the advantage of the VSM is obvious: mobility, economy, and efficiency. As for railways, the broader vehicle-based techniques have long been used to detect the “geometrical” properties of the track, such as track profiles and rail conditions. Relatively little use has been made of the interaction between the moving vehicle/train and the track/bridge. This paper is a state-of-the-art report of the VSM’s applications to highway bridges and the vehicle-based techniques to railway tracks. It starts with a summary of the pioneering works by Yang and co-workers on the VSM. Then, the applications of the techniques to highway bridges and railway tracks will be separately reviewed. Conclusions will be made, along with future research directions, at the end of the paper.

This contribution addresses the estimation of exceedance probabilities of the dynamic random response of railway bridges subjected to high-speed trains in the presence of random rail irregularities. The random nature of the irregular rail track is described by a spatial ergodic stochastic process, and consequently the dynamic bridge response becomes a stochastic process in time with generally unknown distributions. Using numerical simulation methods, the response thresholds for bridge deflection and acceleration are estimated to obtain small exceedance probabilities. Combining these limits with the response at perfect rail geometry provides an estimate of the dynamic response amplification due to random rail irregularities. This is in line with the semi-probabilistic safety concept of modern civil engineering, where critical response thresholds for structures are associated with small exceedance probabilities. It is shown that modeling the maximum bridge deflection as a normally distributed random variable with parameters fitted to the results of a Monte Carlo simulation with small sample size is a computationally efficient approach for estimating the amplified deflection. In contrast, the random maximum bridge acceleration is better captured by a lognormal distribution. As an efficient alternative, the subset simulation method provides accurate predictions for very small exceedance probabilities. If the amplitudes of the rail irregularities at discrete spatial coordinates along the rail axis are considered as random variables, the stability of subset simulation increases.

This paper investigates the dynamic properties of an inhomogeneous, Bernoulli–Euler multi-segment beam composed of different materials. To the best of knowledge of the authors, the problem of random vibrations of beams composing of different chunks of the beams, namely, strong and weak parts, has not been studied in the literature. In this paper, exact solution of the natural frequencies and associated mode shapes of the multi-segment Bernoulli–Euler beam are obtained using Krylov–Duncan functions, followed by free, forced, and random vibration analyses using the normal mode method. Special emphasis is placed on two special configurations of multi-segment beam, namely, the ‘rigid-soft-rigid beam’ (RSR beam) and ‘soft-rigid-soft beam’ (SRS beam) as simplest manifestations of the multi-chunked structures. Some remarkable properties exhibited by the dynamic response of multi-segment beam are demonstrated through this work, which may be of considerable engineering significance, and could not have been anticipated in advance, especially quantitatively.

This paper reports the most recent developments concerning Generalized Beam Theory (GBT) formulations, and corresponding finite element implementations, for steel-concrete composite beams. These formulations are able to perform the following types of analysis: (i) materially nonlinear analysis, to calculate the beam load-displacement response, up to collapse, including steel plasticity, concrete cracking/crushing and shear lag effects, (ii) bifurcation (linear stability) analysis, to obtain local/distortional bifurcation loads and buckling mode shapes of beams subjected to negative (hogging) bending, accounting for shear lag and concrete cracking effects and (iii) long-term service analysis including creep, cracking and arbitrary cross-section deformation (which includes shear lag) effects. The potential (computational efficiency and accuracy) of the proposed GBT-based finite elements is illustrated through several numerical examples. For comparison purposes, results obtained with standard finite strip and shell/brick finite element models are provided.

The importance of allowing for the many different types of structural interaction that have an effect on the performance of light gauge members when used in practical situations is emphasized. A distinction is drawn between internal interactions involving the various plate elements of the steel profiles and external interactions involving the other components in the system. Although full-scale testing of representative systems can capture this behavior, the costs involved make this an impractical general basis for design; codified methods generally consider only isolated plates within members and isolated members within systems, thereby neglecting the potentially beneficial effects of both forms of interaction. Properly used, modern methods of numerical analysis offer the potential to systematically allow for both forms of interaction — provided the numerical models used have been adequately validated against suitable tests. The use of such an approach is explained and illustrated for three commonly used structural systems: roof purlins, floor beams, and columns in stud walls. In each case, it is shown that, provided sufficient care is taken, the numerical approach can yield accurate predictions of the observed test behavior. The subsequently generated large portfolio of numerical results can then provide clear insights into the exact nature of the various interactions and, thus, form the basis for more realistic design approaches that are both more accurate in their predictions and which lead to more economic designs. Building on this, modifying existing arrangements so as to yield superior performance through specific modifications is now possible. Two such examples, one in which improved interconnection between the components in a system is investigated and a second in which prestressing is shown to provide substantial enhancement for relatively small and simple changes, are presented.

Medium-frequency (mid-frequency) vibration analysis of complex structures plays an important role in automotive, aerospace, mechanical, and civil engineering. Flexible beam structures modeled by the classical Euler–Bernoulli beam theory have been widely used in various engineering problems. A kinematic hypothesis made in the Euler–Bernoulli beam theory is that the plane sections of a beam normal to its neutral axis remain planes after the beam experiences bending deformation, which neglects shear deformation. However, previous investigations found out that the shear deformation of a beam (even with a large slenderness ratio) becomes noticeable in high-frequency vibrations. The Timoshenko beam theory, which describes both bending deformation and shear deformation, would naturally be more suitable for medium-frequency vibration analysis. Nevertheless, vibrations of Timoshenko beam structures in a medium frequency region have not been well studied in the literature. This paper presents a new method for mid-frequency vibration analysis of two-dimensional Timoshenko beam structures. The proposed method, which is called the augmented Distributed Transfer Function Method (DTFM), models a Timoshenko beam structure by a spatial state-space formulation in the $s$-domain. The augmented DTFM determines the frequency response of a beam structure in an exact and analytical form, in any frequency region covering low, middle, or high frequencies. Meanwhile, the proposed method provides the local information of a beam structure, such as displacement, shear deformation, bending moment and shear force at any location, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated in numerical examples, where the efficiency and accuracy of the proposed method is demonstrated. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are examined through comparison of the Timoshenko beam and Euler–Bernoulli beam theories.

Soft materials possess magnificent properties which could be harnessed for different potential applications. Compared to other soft materials, hydrogels have some unique advantages which can be used in the shape deformation or shape transformation of structures. This paper aims to investigate the deformation mechanisms of hydrogel-based bi-material beam structures and study the non-uniform geometric effects on the shape transformation including programmable scroll and helical deformations. With a sloped thickness design, the structures could be transformed from an initial quasi-2D beam configuration into some other 2D self-scroll and 3D self-helical configurations. From the hydrogel material model, a modified deformation formula for bi-material beam structures based on the framework of the classical beam theory has been developed to predict the shape morphing behaviors. The relationship between the curvature and the mismatch strain is derived in its explicit form and the theoretical results are verified through several numerical simulations. Furthermore, experiments are carried out to demonstrate the design principles for reconfigurable bi-material beam structures and the experiments show that the structures tend to deform similarly to that predicted by the analytical models. The presented work could provide guidance for future applications of responsive hydrogel-based bi-material beam structures such as in soft actuators and soft robots.

In this paper, we analyze the restrictions on the coefficients in the constitutive equations of linear Viscoelasticity that follow from the Second Law of Thermodynamics under isothermal conditions. Especially, we analyze the constitutive equations in which fractional derivatives of real and complex order appear. We present the conditions that follow after application of the Bochner–Schwartz theorem. Conditions derived here, representing in certain cases a weak form of the Second law of Thermodynamics, are more general (weaker) than the classical Bagley–Torvik conditions widely used in Viscoelasticity Theory. Several examples that illustrate the theory are presented.

Uncertainties in structural parameters and measurements can be accounted for by incorporating interval analysis into the updating scheme of finite element models using a response-surface function. To facilitate the interval arithmetic operation, two different strategies are proposed in this paper to transform the response-surface function into a corresponding interval response-surface function. These strategies minimize the inherent interval overestimation that can arise from the variable dependency of the surrogate model. In the first strategy, the natural extension and centered-form extension methods are used to mitigate the interval overestimation of the surrogate model, which may or may not contain interaction terms. In the second strategy, the natural extensión method is also adopted to realize the interval transformation of the surrogate model containing interaction terms but an affine arithmetic is further introduced to minimize the interval overestimation. To demonstrate the efficacy of the proposed method, model parameters are determined from an instrumented model of a cable-stayed bridge tested on a shaking table. Results show that the proposed updating method is feasible and effective for applications to finite element models of complex bridge structures.

Investigating the nonlinear dynamic response of reinforced concrete (RC) structures is of significant importance in understanding the expected behavior of these structures under dynamic loading. This becomes more crucial during the design of new or the assessment of the existing RC structures that are located in seismically active areas. The numerical simulation of this problem through the use of detailed 3D modeling is still a subject that has not been investigated thoroughly due to the significant challenges related to numerical instabilities and excessive computational demand, especially when the soil–structure interaction (SSI) phenomenon is accounted for. This study aims at presenting a nonlinear simulation tool to investigate this numerically cumbersome problem in order to provide further inside into the SSI effect on RC structures under nonlinear dynamic loading conditions. A detailed 3D numerical model of full-scale RC structures considering the SSI effect through modeling the nonlinear frame and soil domain is performed and discussed herein. The constructed models are subjected to dynamic loading conditions and an elaborate investigation is presented considering different type of structures, material properties of soil domains and depths. The RC structures and the soil domains are modeled through 8-noded hexahedral isoparametric elements, where the steel bar reinforcement of concrete is modeled as embedded beam and truss finite elements. The Ramberg–Osgood constitutive law was used for modeling the soil domain. It was shown that the SSI effect can significantly increase the flexibility of the system, altering the nonlinear dynamic response of the RC frames causing local damages that are not observed when the fixed-base model is analyzed. Furthermore, it was found that the structures founded on soft soil developed larger base-shear compared to the fixed-base model which is attributed to resonance phenomena connected to the SSI effect and the imposed accelerograms.

Buckling loads of arches could be significantly affected by the assumptions made on the load behavior during buckling. For a funicular arch whose centerline coincides with the compression line, we may consider two types of load behaviors based on how the line of load action shifts during buckling. This paper presents the governing differential equations for the elastic in-plane buckling problem of funicular circular arches under uniform radial pressure based on the two different load behavior assumptions, as well as analytical and numerical methods for analysis. For the analytical method, buckling criteria of rotationally-restrained ended circular arches with an internal rotational spring are formulated by using the general solution of the governing differential equation. For the numerical method, the Hencky bar-chain model (HBM) and its simple matrix formulations for general funicular arches are established. The buckling loads and mode shapes of funicular circular arches are solved by using HBM and verified against exact solutions obtained from the analytical method. For funicular catenary arches and parabolic arches, the buckling load solutions by HBM with various number of segments are also obtained and compared with the solutions presented by the previous researchers.

Functionally graded porous structures (FGPSs), characterized by a continuous spatial gradient in both porosity and material properties, have been considered as the new generation lightweight structures. Research activities on FGPSs have grown rapidly in recent years. This paper is devoted to review the existing research works on FGPSs and to highlight the important advances in this emerging area. It consists of: (i) a brief introduction of porous materials and Functionally graded porous materials (FGPMs); (ii) an elaboration of the key factor and micromechanical models related to material properties of FGPMs; (iii) a comprehensive review of mechanical analysis of FGPSs; (iv) a detailed discussion of the main challenges and future research directions; (v) a conclusion.

This study addresses the analytical treatment of a closed-form buckling equation for lateral-torsional stability of thin web composite cantilever beams under mid-height tip force. The beam is composed of random ply fiber orientations. Classical lamination theory is embedded into the Vlasov plate formulation to make up the framework of the analytical treatment. A closed-form solution is realized when an innovative dimensional reduction is extended to the 3D constitutive stiffness matrix. This was made possible through a two-step process in which the shear strain, lateral curvature, and twisting curvature are retained first. By condensing the shear strain variable, effective lateral, torsional, and coupling stiffness terms were formulated. Applying the equilibrium conditions in the deformed configuration, two differential equations are obtained in terms of the lateral curvature and twisting angle. Eliminating the lateral curvature, the twisting angle differential equation with nonconstant coefficients is generated. This equation is solved using a hybrid numerical-analytical approach yielding an analytical buckling expression. Finite element results are generated to verify the accuracy of the buckling load predictions indicating very good correlation with the buckling equation results regardless of the random lamination applied.

For the seismic design of a mid-rise reinforced concrete (RC) building considering the damage control, the main purpose of this work is to propose a simplified method that can be used to estimate the damage index or damage state induced by the near-fault and far-fault earthquakes. In addition to the maximum deformation response, the hysteretic energy dissipation induced the earthquakes is also considered in the damage index quantification based on the modified equivalent linearization method (MELM). Based on the damage index model in terms of the maximum deformation response and hysteretic energy dissipation under an earthquake, this work provides a convenient method by which an engineer can determine the damage-controlling minimal ductility requirement to ensure that the damage index remains under a specified value. For a mid-rise RC building structure, an engineer can also apply the simplified formula proposed in this work to obtain the damage-controlling yielding strength for a specified ductility capacity.

Fatigue cracks generated by repeated loads cause structural failures. Such cracks grow continuously and at an increasing speed owing to the concentration of stresses near the crack tips. Therefore, the early detection of fatigue cracks is imperative in the field of structural-health monitoring for the safety of structures exposed to dynamic loading. In particular, the detection of those cracks subjected to compression is known as a challenging problem in the nondestructive inspection area. The nonlinear ultrasonic modulation technique is effective for the detection of microcracks smaller than the size of a wavelength because this technique uses the deformation of waves passing through the crack surfaces. However, the technique has not been thoroughly verified for detecting cracks subjected to external forces. In this study, nonlinear ultrasonic modulation tests are performed on two types of crack specimens under compressive forces. The results show that in fatigue-cracked specimens, the cracks can be detected using modulated waves even under strong compressions. With artificial cracks, buckling occurs at a relatively low compression, and the amounts of modulated waves rapidly increase due to the bending of the specimen before buckling failure takes place. In this study, the crack detection methodology under compression is proposed and experimentally verified. The proposed method might be beneficial to find cracks under compression in various structural components.