Journal of Engineering Mechanics

A new output-only system identification (SI) scheme composed of a virtual dynamic shaker (VDS) is proposed. The concept of the VDS is analogous to a secondary system such as a tuned mass damper (TMD), but it is a virtual device that is attached virtually to a primary structure. The SI technique is based on the dynamics of the combined primary structure and the VDS for the estimation of structural modal parameters. The dynamic response of the VDS is amplified around the natural frequency of the primary structure and depends on the level of damping ratio of the VDS. In this manner, the natural frequency of the primary structure can be determined as it represents the frequency at which the variance of the VDS response reaches its maximum. The structural damping ratio can be identified through the derived ratio of the response variances of VDSs attached individually to the primary structure with different damping ratios. The proposed VDS scheme is validated in detail through extensive examples of building structures under wind loads using numerical simulations and full-scale records obtained through full-scale measurements, with emphasis on the damping estimation. In addition, a comparison with other popular output-only SI schemes is made to examine the efficacy of the proposed VDS-based scheme. On the basis of the extensive examples used in this study, the damping estimates by the VDS are overall accurate, comparable with those by other popular schemes, which corroborates the efficacy of the proposed VDS as an easy-to-use approach for the output-only SI.

Material nonlinearity analyses are widely used to determine the safety of structural components or engineering structures. Although advanced computer hardware technology has considerably improved the computational performance of such analyses, large and complex emerging structures and expensive computational process still attract the attention of researchers toward finding more efficient and accurate numerical solution methods. This paper combines an inelasticity-separated (IS) concept with the finite-element method (FEM) to establish a novel and efficient framework (IS-FEM) for structures with material nonlinear behavior that only occurs within certain small local domains. The IS concept presented in this paper begins by decomposing the strain on a nonlinear material into its linear-elastic and inelastic components and runs through the whole framework. Based on the principle of virtual work, a novel governing equation for structures with an IS form is derived by treating the decomposed inelastic strain as additional degrees of freedom. Moreover, the changing stiffness matrix in the classical FEM is expressed as the sum of the invariant global linear elastic stiffness matrix and another changing inelastic stiffness matrix with a small rank, and it represents the material nonlinearity of local domains so that the efficient solution method can be applied to perform nonlinear analyses via the mathematical Sherman–-Morrison–Woodbury (SMW) formula. Because the unchanging global stiffness matrix is used throughout the whole nonlinear analysis and the computational effort only focuses on a small dimension matrix that represents the local inelastic behavior, the efficiency of the proposed IS-FEM is improved greatly. The proposed method is validated against the results of classical FEM via three separate numerical examples and its value and potential for use in any material nonlinearity analyses are also demonstrated.

This paper proposes a new symplectic method for obtaining the natural frequencies and modes of beams resting on elastic foundations. A generalized Hamiltonian functional is first derived via the Lagrange multiplier method, and the first-order dual equation of motion in the time domain and its corresponding boundary conditions are obtained. The time coordinate is separated from the dual equation to yield the natural-frequency-related eigenvalue equation and the first-order dual equation in the frequency domain. Then, the spatial coordinate is separated from the newly derived dual equation to yield the natural-mode-related eigenvalue equation. According to the eigenvalue analyses, this paper obtains a series of eigenvalue spectra: the continuous and discrete eigenvalue spectra that represent the relationships of the two types of dimensionless eigenvalues for infinite and finite beams, respectively; these eigenvalue spectra help to understand the connection between structural vibration and wave propagation. For a finite beam with a specific boundary condition, its mode vectors are composed of transverse deflection, bending rotation, shear force, and bending moment, and they are called the full mode shape vectors (FMSVs) in this paper. These FMSVs were verified to be orthogonal according to the property of the Hamilton matrix. A simply supported and a cantilever beam were used as examples to validate the accuracy and applicability of the symplectic method. Their vibration properties, mainly the discrete eigenvalue spectra and FMSVs, are comprehensively analyzed, and some significant conclusions are drawn.

Elastic wave propagation in high-rise buildings is studied using a Timoshenko beam model with rigid floor slabs, with the objective of gaining insight into the effects of their repeatable arrangement. The propagator of the composite beam was derived in the frequency domain and used to compute the state vector for input base translation and rocking. Further, the dispersion relation was derived for Bragg scattering from the slabs for an infinite, periodic beam. Results are shown for the dispersion and beam transfer functions and impulse response functions for properties typical for buildings. The results, extrapolated for illustrative purposes beyond the range of validity of simple beam models, reveal the banded nature of the dispersion and response with real phase velocity in the pass and imaginary in the stop bands. The latter act as mechanical filters of higher frequency waves and vibrations, and represent a possible attenuation mechanism in buildings. While real structures would have more complex banded spectra, the selective nature of the filtering could be exploited for passive higher frequency vibration control to protect sensitive equipment from vibrations created, e.g., by high-speed trains, traffic, explosions, or smaller but near seismic events.

The present paper proposes an analytical solution of the four points bend end-notched flexure test (4ENF) with frictional contact between the delamination surfaces. The analytical solution was developed in the framework of the classic Euler-Bernoulli bending beam theory with orthotropic linear elastic constitutive behavior. The frictional contact was modeled as rigid–perfectly plastic with the Mohr-Coulomb activation function and the nonassociative flow rule. The elastic solution of the partially cracked beam subjected to the four points bending test with frictional contact was developed, and the Mode II delamination toughness was analytically determined by means of the Griffith approach, as a function of the delamination load, geometry specimen, and frictional coefficient. The 4ENF delamination test was also numerically solved by two-dimensional (2D) finite-element analysis with a cohesive-frictional interface, and the results were compared with the analytical beam solutions. The comparison showed a very good accuracy of the analytical solution, even though it was based on the simple beam theory.

This paper investigates the nonlinear elastic in-plane dynamic buckling of a fixed shallow circular arch that was subjected to an arbitrarily located step radial point load, which has not been previously reported in the literature. The arbitrary step load produced unsymmetrical deformations of the arch and unsymmetrical internal forces in the arch and caused the arch to oscillate unsymmetrically. Because the unsymmetrical equilibrium path was nonlinear and consisted of a primary stable branch, an unstable branch, and a remote stable branch, when the step load reached a critical value, the arch could oscillate to reach the unstable equilibrium branch and subsequently lose its in-plane stability in a dynamic buckling mode. Hence, the first condition for dynamic buckling of the arch was that the load could induce oscillation of the arch sufficiently large to reach an unstable equilibrium position. The second condition was derived on the basis of the principle of the conservation of energy: the total potential energy of the system needed to vanish for its possible dynamic buckling. This condition could be used in conjunction with the nonlinear equilibrium path to derive the analytical solution for the dynamic buckling load of shallow arches under an arbitrary step radial point load. The unsymmetrical effects of the load position on the dynamic buckling load were found to be significant. First, if the load was not applied at the crown of the arch, there was only one dynamic buckling load. This was different from the case of a fixed arch subjected to a step point load at its crown, in which an upper and a lower dynamic buckling load exist. Second, the dynamic buckling load first decreased and then increased as the point of the application of the load moved away from the crown. Third, when the load position exceeded a specific value from the crown, the arch did not experience dynamic buckling but oscillated around a stable equilibrium point under the step load. The effects of the modified slenderness on the dynamic buckling were also investigated, and it was found that the dynamic buckling load increased with an increase of the modified slenderness. Finally, the comparisons with the nonlinear elastic static in-plane buckling showed that the nonlinear elastic dynamic buckling load of an arch was lower than its static counterpart.

The safety of cars and trucks crossing gapped road surfaces can be affected by their operational speed, mass, and the tire and road surface characteristics. As part of a research on the safety of road vehicles crossing discontinuous road surfaces, the dynamic behavior of a single tire passing a gap has been examined as reported in this paper. First, the kinematics of a tire crossing the gap in the road surface is analytically formulated. The formulation has shown that the tire exhibits three distinct (single-point, two-point, and flying) modes of travel depending on its operational speed. The dynamics of the tire are larger in single-point mode that exhibits two critical velocities, which have been validated using a nonlinear arbitrary Lagrangian Eulerian method in the finite-element framework. The validated analytical model has shown that the critical velocity is mainly affected by the mass of the overburden.

It is still an open problem to develop a model with a uniform theoretical treatment under various loading conditions. This paper aims to formulate such a model for describing both monotonic and cyclic behaviors of granular materials. An exponential function was adopted to reproduce the stress-strain relation. Within the framework of endochronic models, the shear strain component was enriched with an absolute term to account for a reverse loading effect during shearing. The capacity of the basic model with four parameters for reproducing the basic features of granular materials was examined. Three numerical schemes for simulating undrained triaxial tests, drained triaxial tests under constant $p^{\prime }$ or under constant confining stress, and under both monotonic and cyclic loadings were established. Then, three modifications were carried out to enhance the model by introducing a nonlinear elasticity, a nonlinear stress dilatancy, and the critical state concept with four additional parameters. The enhanced version of the model showed good performances in simulating triaxial tests on Toyoura sand under various loading conditions: drained, undrained, constant $p^{\prime }$, constant confining stress, and monotonic and cyclic loadings.

Almost all engineering systems are not only uncertain, but also time-variant. As such, it is most appropriate to use a time-dependent reliability method, e.g., first passage probability, in the prediction of their failures. Mathematically, this problem can be modeled as an upcrossing (or outcrossing) of a stochastic process from a safe domain. A thorough examination of published literature suggests that there are very limited analytical solutions for the calculation of the upcrossing rate. This paper attempts to derive an efficient analytical solution for calculation of upcrossing of a nonstationary Gaussian process. The merit of the derived solution is that the upcrossing rate for nonstationary Gaussian processes can be calculated in a simple and computationally efficient procedure. The application of the derived solution is demonstrated with an example of a cast-iron pipe in which internal pressure is modeled as a nonstationary Gaussian load process. It is found that smaller values of correlation length, i.e., higher cycle rate of the process, would increase the upcrossing rate. The paper concludes that the derived new solution performs very well in calculation of upcrossing of a nonstationary Gaussian process in terms of accuracy and efficiency.

In order to study the time- and temperature-dependent long-term behavior of metal seals, experimental investigations on special metal seals have been carried out at five different temperatures in a temperature range between 20 and 150°C for more than 7 years. Experimental results indicate a noticeable change of relevant sealing properties like seal force and usable resilience depending on time and temperature. In this study, the metal seals are treated as a homogeneous material block so that the identified decrease in seal force can be treated as a material relaxation effect. For the time-dependent behavior of seal force, an enhanced power-law model is introduced for the first time and is compared with the currently used power-law model. Additionally, regarding the influence of temperature, the time-temperature superposition principle is applied to metal seals for the first time with a clearly defined process. Thus, possible mistakes in the application of principle could be avoided. The introduced method is widely available for different applications regarding effects the principle with time and temperature.

Anchored by the theory of extreme value statistics, Weibull distribution is the most widely used mathematical model for strength distribution of brittle structures. In a series of recent studies, a finite weakest-link model was developed for strength distribution of quasi-brittle structures, and the classical Weibull distribution was shown to represent the large-size asymptote of the model. By employing a length scale, the finite weakest-link model is capable of capturing correctly the size effects on both the probability distribution and the mean value of structural strength. However, the connection of this length scale with the basic material properties is still missing. This study investigates the relationship between the length scale of the finite weakest-link model and the material length scales by analyzing the size effect on the mean structural strength. The mathematical form of this relationship is derived through dimensional analysis. To validate the model, a set of mean size effect curves is obtained through stochastic simulations, which use a nonlinear constitutive model involving both the Irwin characteristic length and the crack band width. The internal length scale of the weakest-link model is determined by optimum fitting of the benchmark size effect curves in the small-size range. Furthermore, the effect of stress field on this internal length scale is studied by considering three different loading configurations. The present analysis reveals the importance of the mean size effect analysis for the calibration of finite weakest-link model.