Journal of Engineering Mechanics

This paper presents the development and application of a soft-computing technique in identification of forward and inverse dynamics of a self-sensing magnetorheological (MR) damper based on experimental measurements. This technique is developed by the synthesis of an NARX (nonlinear autoregressive with exogenous inputs) model structure and neural network within a Bayesian inference framework. The Bayesian inference procedures essentially eschew overfitting that could occur in network learning and improve generalization (prediction) capability by regularizing the complexity of learning. In applying the developed technique to the self-sensing MR damper, the present and past information of its input and output quantities, which contain the physical knowledge of the damper, is used to formulate its nonlinear dynamics. The NARX network architecture is then optimized to enhance modeling effectiveness, efficiency, and robustness. Experimental data of the damper subjected to both harmonic and random excitations are used for model identification and assessment. Assessment results show that the formulated Bayesian NARX network accurately emulates the nonlinear forward dynamics of the self-sensing MR damper. Improved generalization (prediction) capability of the NARX network model by the Bayesian regulation is observed by comparing the modeling results with and without considering regularization. An inverse dynamic model for the self-sensing MR damper is further formulated by the developed technique. The proposed soft-computing technique is viable to formulate dynamic models of the self-sensing MR damper for structural control applications.

Responses of elastic rods and shear beams with random field properties and also possibly under random field forcing are studied for random fields with linear, Matérn, Cauchy, and Dagum covariances. The latter two allow decoupling of the fractal dimension and Hurst effect. The authors find second order characteristics of the beam displacement under clamped–free boundary conditions. Overall, for a given variance, the variance of the output is strongest for linear, then Matérn, then Cauchy, and, finally, Dagum forcing. This is interesting and counterituitive because the Dagum and Cauchy models grasp the fractal characteristics and, additionally, the Hurst effect. In a number of (simpler) cases the results may be obtained in explicit analytical forms, but as Cauchy and Dagum models are introduced, one has to resort to numerics.

Unlike conventional seismic design, the columns of a rocking frame are designed to uplift and pivot during earthquake excitation. This paper investigates, analytically and numerically, the seismic response of a rocking frame with columns unequal in height (asymmetric), which are either freestanding or hybrid, i.e., enhanced with supplemental damping and recentering capacity. The paper establishes the equations of motion following the principles of analytical dynamics. Throughout the study, the deformation of the structural members is considered negligible. The analysis considers both pulse-type and non-pulse-type (historic) ground motions. It shows that the effect of asymmetry on the seismic stability of the rocking frame is marginal compared with the symmetric configuration, despite the very different kinematics of the corresponding rocking mechanisms. In contrast, the seismic stability of the hybrid rocking frame is very sensitive to fracture elongation of the supplemental restoring (tendons) and damping devices. The results confirm the high-performance seismic behavior of the planar rocking frame, thus illustrating its potential as an alternative seismic design paradigm.

In this paper, the dynamic response of a simply supported viscously damped double-beam system under moving harmonic loads is investigated. The double-beam system consists of two elastic homogeneous isotropic beams, which are identical, parallel, and connected continuously by a layer of elastic springs provided with viscous damping. Two coupled governing equations describing the vibration of those two beams are decoupled by a simple change of variables, so that the analytical solutions for the dynamic deflections of both beams can be given. Numerical examples are employed to investigate the effects of moving speed and frequency of load, as well as the damping and the elasticity of the layer, on the dynamic responses of the beams. The deflections for the double-beam system are also compared to these of a single-beam system.

Hybrid simulation is an experimental technique involving the integration of a physical system and a computational system with the use of actuators and sensors. This method has a long history in the experimental community and has been used for nearly 40 years. However, there is a distinct lack of theoretical research on the performance of this method. Hybrid simulation experiments are performed with the implicit assumption of an accurate result as long as sensor and actuator errors are minimized. However, no theoretical results confirm this intuition nor is it understood how minimal the error should be and what the essential controlling factors are. To address this deficit in knowledge, this study considers the problem as one of tracking the trajectory of a dynamical system in a suitably defined configuration space. To make progress, the study strictly considers a theoretical hybrid system. This allows for precise definitions of errors during hybrid simulation. As a model system, the study looks at an elastic beam as well as a viscoelastic beam. In both cases, systems with a continuous distribution of mass are considered as occur in real physical systems. Errors in the system are then tracked during harmonic excitation using space-time $L^2$-norms defined over the system’s configuration space. A parametric study is then presented of how magnitude and phase errors in the control system relate to the performance of hybrid simulation. It is seen that there are sharp sensitivities to control system errors. Further, the existence of unacceptably high errors whenever the excitations exceed the system’s fundamental frequency is shown to be present in hybrid simulation.

In this paper, an indirect and numerical time integration approach is proposed for dynamic analysis of space structures by using comprehensive wavelet functions. For this purpose, the proposed scheme is implemented on the second-ordered differential equation of motion governing single-degree-of-freedom (SDOF) systems and subsequently for multi-degrees-of-freedom (MDOF) systems. In this way, two different types of free-scaled wavelet functions have been utilized, namely the simple Haar wavelet functions and the complex Chebyshev wavelet functions. Accordingly, for the proposed procedure, a simple formulation has been derived from the adaptive approximation of external loadings and responses by free-scaled wavelet functions. It is deduced that the proposed method lies on unconditionally stable scheme. From an optimization point of view, the error and computation time involved have been comparatively evaluated. Finally, it is demonstrated that the time history analysis of space structures is optimally accomplished by lesser computational time and high accuracy of responses, particularly in the large-scaled systems for broad-frequency content loadings.

An energy approach within the framework of thermodynamics is used to model the fatigue process in plain concrete. Fatigue crack growth is an irreversible process associated with an irreversible entropy gain. A closed-form expression for entropy generated during fatigue in terms of energy dissipated is derived using principles of dimensional analysis and self-similarity. An increase in compliance is considered as a measure of damage accumulated during fatigue. The entropy at final fatigue failure is shown to be independent of loading and geometry and is proposed as a material property. A relationship between energy dissipated and number of cycles of fatigue loading is obtained.

Unreinforced portland-cement concrete exhibits a nonlinear relationship between applied stress and observed strain, even though the strains are at magnitudes that warrant the infinitesimal strain approximation (i.e., the norm of the displacement gradient is appropriately small). Previous efforts to model this nonlinear response of concrete express a dependence of stress on the deformation gradient (via the infinitesimal strain). However, models derived from the class of Cauchy elastic bodies do not allow a nonlinear relationship between the stress and linearized strain. Nonlinear constitutive relations that are implicit relations between the stress and a proper measure of strain, or nonlinear expressions of an appropriate measure of strain as a function of stress, lead to a logical linearization procedure wherein the linearized strain can be a nonlinear function of the stress. Using such a constitutive model, the authors accurately characterize both axial strain and circumferential strain in concrete that occurs under axial compression, up to the peak compressive stress (i.e., the failure stress). The phenomenological coefficients of the constitutive models are given predictive power via correlation with compressive strength and the air content of the ten concrete mixtures (comprising 23 concrete cylinders) that were experimentally tested under unconfined uniaxial compression.

This paper proposes an approximate method for estimating the extreme value responses of nonlinear dynamic systems to random excitations. The method focuses on the mean zero responses with the unimodal and symmetrical distributions and uses, respectively, the generalized Gaussian distributions (GGDs) and the Nataf distribution to model the marginal distributions of the displacement and velocity responses and the joint distribution of them. By using an effective parameter estimation method and empirical formula, the parameters in the GGD models and Nataf model are estimated, respectively, from the response statistics obtained from stochastic simulation. Under the Poisson assumption of the upcrossing events of the response of interest, the extreme value estimate is obtained from the analysis of the first passage probabilities of the response. The proposed method is suitable for both hardening and softening responses and, moreover, has a high enough efficiency and accuracy for practical applications. Numerical examples demonstrate the efficiency, accuracy, and utility of the method in the extreme value response estimates.

Super-large hyperbolic cooling towers (SCT) are typical cylinder-like structures and feature spatial, three-dimensional (3D), circumferential motion characteristics, wherein the non-Gaussian probability distribution characteristics of local fluctuating wind pressures involved with vortex shedding or reattachment phenomena are excessive compared with the traditional wind load theoretical system based on Gaussian assumption. In this paper, the stochastic distribution characteristics of fluctuating wind pressures for the SCT ($H=215\mathrm{m}$) in the Jiangxi nuclear power plant with aeroelastic effect based on synchronous pressure and vibration wind tunnel test were investigated, then the formation mechanism of non-Gaussian fluctuating wind pressures was further revealed. According to the formation mechanism, the probability distribution characteristics, spatial correlation, criterion, and division of non-Gaussian fluctuating wind pressures were discussed in detail. Finally, the prediction method and distribution characteristics of extreme value distribution of wind pressures on the basis of guaranteed rate and correlation were proposed. Herein, some useful conclusions can be used for reference in the design of wind-resistant SCT.

Bodies are prestressed with the intention to enhance the load-carrying capacity of the body. The primary objective of this study is to understand the effect of prestressing the constituents in composite bodies on the overall mechanical performance of the composites. This paper considers composites having linearized viscoelastic constituents that can exhibit fluidlike and solidlike behavior. It also examines the effect of stress relaxation in a component of the prestressed composite on the overall load-carrying capacity of the composite. The properties of the composite, whether a brittle inclusion embedded in ductile matrix or a ductile inclusion in brittle matrix, are greatly influenced by the ratio of the induced prestress with respect to the external load and thereby influence the load-carrying capacity of the composite.

A novel procedure for structural health assessment, denoted as unscented Kalman filter with unknown input (UKF-UI), is proposed using the nonlinear system identification concept. To increase its implementation potential, a substructure concept is introduced, producing a two-stage approach. It integrates the unscented Kalman filter concept and an iterative least-squares technique. The two most important features of the method are that it does not need the information on the time history of the excitation to identify structural systems represented by finite elements, and that it can identify defects in them using only a limited amount of noise-contaminated nonlinear response information. The proposed method is robust enough to detect the locations and severity of defects at different locations in the structure. The defect detection capability increases significantly if the defective member is in the substructure or close to it. The method is conclusively verified with the help of two examples using impulsive and seismic excitations. The superiority of UKF-UI over extended Kalman filter-based procedures is documented. The proposed UKF-UI procedure has high implementation potential and can be used for health assessment of large structural systems.

The full-scale data measured from tall buildings and long-span bridges are usually nonstationary due to transient earthquake ground motion, sudden changes in wind speed and/or direction, or time-varying motion of vehicles. The dynamic properties (i.e., frequency, damping, etc.) of these structures during nonstationary events closely relate to their operational safety, so their accurate identification is critical. Traditional system identification methods may fail to provide reliable results (especially for damping estimation) in these situations due to a lack of long segments of stationary data. In addition, these methods are not able to track the time-varying system properties caused by large amplitude response due to strong earthquakes or winds. This highlights the necessity of developing system identification methods suitable for nonstationary/transient data. In response to this need, this paper proposes a new nonstationary system identification scheme which first utilizes the wavelet transform (WT) to uncover the time-varying features of nonstationary data. Then the transformed singular value decomposition (TSVD) is introduced in tandem to automate the identification of analysis regions in the time-frequency domain. Subsequently, Laplace wavelet filtering is adopted to extract impulse-type signals from the WT coefficients in the identified analysis regions, thus enabling a reliable damping estimation from transient nonstationary data. Finally, the frequency and damping ratio are reliably identified from the extracted impulse-type signals by the wavelet modulus decay (WMD) or from the parameters of the Laplace wavelet, whereas mode shapes can be easily identified using SVD. Thanks to the automatic identification of the analysis regions by the TSVD, the proposed scheme can be readily used to conduct online nonstationary system identification from a set of streaming signals, which can be extremely advantageous for a quick structural condition assessment under extreme events. The efficacy of the proposed scheme is first evaluated using simulated nonstationary data with and without noise and compared with the existing approaches in the literature. Then, its ability in handling closely spaced modes is compared with the second order blind identification (SOBI) method. Finally, the performance of the proposed scheme for full-scale nonstationary data is investigated and compared with other methods in the literature.

This study aims to propose a new model for clay behavior by incorporating physical–chemical effects acting between clay clusters using the Chang and Hicher micromechanical approach. Local mechanisms are thus introduced through repulsive and attractive forces similar to double-layer van der Waals forces, which are obtained from the derivation of energy potentials. A specific study of local parameters and their evolution is conducted using experimental data from the mineralogy variation provoked by the variation of a remolded saturated reconstituted clayey mixture consisting of kaolinite and montmorillonite ranging from 0 to 100% montmorillonite. Using scale transition, the results of micro–macrocalculations under an isotropic loading path show a very good agreement with experimental results.

The classic spectral representation method (SRM)-based nonstationary process simulation algorithm is used extensively in the engineering community. However, it is less efficient owing to the unavailability of fast Fourier transform (FFT). In this paper, an efficient, almost accurate, and straightforward algorithm is developed for the simulation of the multivariate nonstationary process. In this method, an evolutionary spectral matrix is decomposed via Cholesky method, and then proper orthogonal decomposition (POD) is used to factorize decomposed spectra as the summation of the products of time and frequency functions. Because original time-dependent decomposed spectra are decoupled via factorization, FFT can be used to significantly expedite the simulation efficiency. This POD-based factorization is totally data-driven and optimal, and fewer items are required in matching decomposed spectra. Therefore, the accuracy and efficiency of the factorization can be guaranteed at the same time. Another attractive feature of this factorization is straightforwardness, because only regular eigenvector decomposition is involved. Numerical examples of nonstationary processes are used to demonstrate the effectiveness and accuracy of the proposed approach. Results show that the factorization and simulation agree with the targets very well. In addition, the speed at which sample functions are generated is significantly improved over classic SRM, in which the full summation of sine/cosine terms is needed.