Journal of Engineering Mechanics

Systems of second-order linear ordinary differential equations (ODEs) to arbitrary input functions appear in many fields of physics and engineering. Numerical methods for solving these kinds of problems have been mainly performed in the time and frequency domains. In contrast, this paper develops an efficient, seminumerical pole-residue method implemented in the Laplace domain. In this article, a key concept and development is on how to compute the poles and residues of the output from those of the input and system transfer functions. Once the poles and residues of the output are known, the corresponding time history of the output is readily obtained. Even though the correctness of the new method has been verified by using a step-by-step time-domain solution, the accuracy of the new method in theory is higher than that of any time-domain approach, partially because the output obtained from the new method is a continuous function of time.

This paper revisits the nonlinear in-plane analysis of a shallow pin-ended circular arch under a central concentrated load. It is found that the arch may have multiple equilibrium branches and limit points, and a modified slenderness of the arch defined in the paper plays an important role in the number of the limit points and equilibrium branches. The analytical solution for the specific modified slendernesses that switch the number of equilibrium branches and limit points is derived. The analytical solutions for the load, axial force, and radial displacements corresponding to the specific modified slendernesses are also derived. This paper deepens the understanding for the geometric nonlinear analysis of circular arches and their geometric softening and stiffening behavior and provides useful benchmarks for the analyses of shallow arches. In addition, this paper extends the current solutions of nonlinear equilibrium of arches associated with axial compression to those associated with axial tension caused by large deformations.

This manuscript investigates some instability features in granular materials by considering an elementary grain arrangement on the intermediate scale. Although force chains have long been recognized as playing a basic role in the strength of granular specimens, the collaborative contribution of grain loops (grain arrangement) has been highlighted more recently. As a result, the stability of grain loops is expected to strongly govern the stability of the whole assembly. This paper shows that such elementary patterns can be destabilized even though the contact law between granules is elastic. This behavior stems from the nature of the kinematical model describing the geometrical interaction between neighboring grains.

Massively parallel large eddy simulation (LES) experiments were conducted to study the flow fields developed by unidirectional flow over submerged vegetation and wave flow-through emergent vegetation. For the submerged vegetation, vertical profiles of mean and turbulent horizontal and vertical velocities were found to be in good agreement with laboratory experiments. Canopy-averaged bulk drag coefficient calculated from the depth-integrated forces on the cylinders compares well with empirical measurements. For the emergent vegetation, wave-induced drag forces were calculated, and the inertia and pressure-drag coefficients were compared with laboratory experiments, which were found to be in good agreement. Vertical variation of forces and moments about the stem base are presented and compared with a single stem case under a variety of wave conditions and Keulegan-Carpenter (KC) numbers. It is seen that at low KC numbers the effect of the inertia force is significant. The vertical variation of the velocity field near the free surface, within two to three diameters from the cylinder center, was found to be considerably influenced by the free surface flux between the wave trough and the crest, over a time period, which creates a predominant recirculation zone behind the cylinder in the direction of wave propagation.

An efficient analysis procedure has been developed for the random vibration analysis of nonlinear structures subjected to nonstationary random excitations based on the equivalent linearization method and the time-domain explicit formulation method. When the equivalent linearization method is used for the nonstationary random vibration analysis of a nonlinear structural system, equivalent linear systems are constructed for different time instants and the analysis problem is transformed to a series of analyses of these linear systems. Because a large number of linear analyses must be conducted to get reliable results for the original nonlinear system, efficiency of the analysis algorithm for the linear analysis is crucial for its successful application. The time-domain explicit formulation method, recently proposed for the nonstationary random vibration analysis of linear systems, has much higher computational efficiency than other methods owing to the use of explicit expressions of dynamic responses of linear systems. Therefore, a numerical algorithm developed by combining these two methods will be highly efficient. The proposed method is applied to the random vibration analysis of Duffing systems and hysteretic systems under nonstationary excitations. Numerical examples indicate that the proposed approach is feasible and highly efficient.

In this research the tail-equivalent linearization method (TELM) has been applied to a structure with biaxial behavior of materials, using the biaxial Bouc-Wen material model. The modeled structure has been subjected to independent bidirectional excitation with the incident angle $\theta$ with major axes of structure. The direct differentiation method (DDM) has been developed for calculating the response and its derivatives for the first time for the biaxial Bouc-Wen material model, where the application of DDM is more difficult compared with uniaxial Bouc-Wen models due to its coupled constitutive law of material. The method is applied to a structure with a rigid diaphragm, supported by four different columns. The structure is subjected to bidirectional and modulated filtered white noise excitations. The cumulative probability distribution function (CDF), probability density function (PDF), average rate of crossing, and first passage probability of displacement response are calculated for a column in the roof level of the structure. The results have been compared with those of Monte Carlo simulation presenting good agreement. The effects of nonlinearity degree and the levels of threshold have been investigated on the tail-equivalent linear system (TELS). The importance and effects of considering biaxial nonlinear behavior have been assessed by changing its relevant parameter in the Bouc-Wen model to obtain and compare different TELSs. The effects of incident angle have been investigated for independent components of excitation to find the most critical angle related to the minimum reliability index in TELM. Furthermore, system eccentricity, most critical incident angle for different responses, nonlinearity, and spectral intensity ratio of bidirectional excitation are considered.

Viscoelastic (VE) dampers are one of the most popular structural control devices, and serious efforts have been undertaken to develop their availability in civil engineering. However, the performance of VE dampers is dependent on the energy dissipation properties of VE materials. In this study, several kinds of VE materials based on different matrix rubbers were developed, and tests on VE dampers based on nitrile butadiene rubber (NBR) matrix and silicone rubber (SR) matrix were carried out. The results indicate that NBR matrix VE dampers have a high energy dissipation capacity, whereas SR matrix VE dampers have stable performance under different working conditions. To clarify the mechanical properties of VE dampers based on NBR and SR matrices, the equivalent higher-order fractional derivative model, which takes into account the effects of temperature and frequency simultaneously, is proposed. The numerical results using this model are in accord with experimental results.

A closed-form, multiple-scales, analytic approximation of a Kelvin-Voight viscoelastic model is developed to describe water hammer pressure wave attenuation in polymer pipe. The analytical results show that the evolution of water hammer for the single-pipe experiment considered in this paper is described by the Kelvin-Voight model as a weak strain-rate feedback occurring over three timescales. The wave transit and frictional timescales are augmented by a third intermediate timescale governed by the weakness of the strain-rate feedback. The scaling analysis also shows that, for weak strain-rate feedback, it is possible to use an optimization approach to estimate the scale of Kelvin-Voight parameters without experimental data. The optimal choice for weakness of the strain-rate feedback also determines the extent to which a weak strain-rate feedback description may be appropriate to describe an experimental design.

After a brief review of time- and frequency-domain tail-equivalent linearization methods (TELM) for uniform excitation problems, this paper extends TELM for application to nonlinear systems subjected to multisupport seismic excitations. The spatial variability of the ground motion is represented by a coherency function that characterizes the incoherence, wave-passage, and site-response effects. It is found that for multisupport excitation problems, it is most convenient to formulate TELM by using the ground displacement as input. The resulting tail-equivalent linear system (TELS) is defined by frequency-response functions relating the response quantity of interest to each support displacement. A method to reduce the number of random variables in the TELM analysis is introduced. The proposed method is demonstrated through numerical examples with varying structural properties and ground motion coherency in order to investigate various aspects of TELM and the major influences of differential support motions on a nonlinear system.

In this study, an anisotropic thermal-elastic-plastic (TEP) constitutive model is developed for soft clays. Two yield surfaces, namely the current yield surface and reference yield surface, are adopted to characterize the development of plastic volumetric strain (i.e., the unique internal variable of the two surfaces) due to either mechanical or thermal loading. The model is formulated based on the framework of the Modified Cam-Clay model, with only two additional parameters introduced (i.e., $\alpha$ and $\theta$), to account for stress-induced anisotropy and thermal-induced translation of compression curves, respectively. Based on the model, a simplified equation is proposed to quantify the effect of drained heating on the undrained shear strength of clay. The predictive capability of the proposed model and the simplified equation for undrained shear strength are verified against published results of temperature-controlled triaxial tests on soft clay. By assessing seven different types of clays, the thermal-related parameters $\theta$ are found to almost linearly increase with the plastic index ($I_p$) of soil. Empirical correlations are then proposed for a quick approximation of $\theta$, in case that data from temperature-controlled tests are not readily available.

This paper investigates the fundamental nature of the polynomial chaos (PC) response of dynamic systems with uncertain parameters in the frequency domain. The eigenfrequencies of the extended matrix arising from a PC formulation govern the convergence of the dynamic response. It is shown that, in the particular case of uncertainties and with Hermite and Legendre polynomials, the PC eigenfrequencies are related to the roots of the underlying polynomials, which belong to the polynomial chaos set used to derive the polynomial chaos expansion. When Legendre polynomials are used, the PC eigenfrequencies remain in a bounded interval close to the deterministic eigenfrequencies because they are related to the roots of a Legendre polynomial. The higher the PC order, the higher the density of the PC eigenfrequencies close to the bounds of the interval, and this tends to smooth the frequency response quickly. In contrast, when Hermite polynomials are used, the PC eigenfrequencies spread from the deterministic eigenfrequencies (the highest roots of the Hermite polynomials tend to infinity when the order tends to infinity). Consequently, when the PC number increases, the smoothing effect becomes inefficient.

This study presents a scaling analysis of the time development of clear-water scour depth at bridge piers. It shows that the widely-used exponential formula can be theoretically derived with scaling arguments. The derivation provides connections between the physical pier-scouring process and two empirical constants used in the formula. The dependence of the two constants on sediment coarseness is calibrated using published laboratory data with scour duration ranging from 49 to 1094 h. The analysis presented is restricted to conditions, including steady flow, clear-water scour, narrow circular cylindrical pier, and uniform sediment with low coarseness.

This paper presents a parametric study on storm-surge reduction by flexible vegetation in coastal wetlands under idealized prototype conditions. A vegetation-induced flow resistance model that considers flow depth, flow velocity, and vegetation properties has been developed and verified using laboratory data. The model computes the drag resulting from deformable vegetation under both emergent and submerged conditions. Numerical experiments were conducted to reveal the potential of wetlands in reducing storm surge, and to examine the role of the vegetation field in obstructing surge water. Although a constant Manning’s coefficient is used commonly in hydrodynamic models simulating storm surge over coastal wetlands, the current study reveals the extraordinary temporal variation in the Manning’s coefficient. The dynamic Manning’s coefficient felt by the flow is not only a function of vegetation properties, such as stiffness, diameter, vegetation height and population density, but also varies with the water depth and flow velocity. Before vegetation becomes submerged during a storm event, the dynamic Manning’s coefficient increases with a rising water level; once the plants become submerged the coefficient decreases. The dynamic variation is attributed to the interaction between flow conditions and vegetation stiffness. Both the storm dynamics and vegetation biomechanical properties need to be taken into account for the parameterization of vegetation-induced drag and the assessment of flood risk reduction by coastal wetlands.