Journal of Engineering Mechanics

A numerical study of the problem of heat transfer to the non-Newtonian power-law fluid over a vertical cone embedded in a porous medium has been investigated, taking into consideration the viscous dissipation effect. The governing equations describing the problem are transformed into a system of nonlinear ordinary differential equations, which is solved numerically using the Chebyshev spectral method. The effects of the power-law index and the viscous dissipation that is characterized by the local Gebhart number on the temperature profiles and the local Nusselt number are discussed.

The paper presents results of three-dimensional discrete element method (DEM) simulations of axisymmetric undrained tests on loose assemblies of polydisperse spheres using a periodic cell. In the work reported, undrained tests were modeled by deforming the samples under constant volume conditions. The undrained (effective) stress paths are shown to be qualitatively similar to published physical experimental results. The onset of liquefaction (or temporary liquefaction) is identified by a redundancy index equal to unity, which defines the transition from solidlike to liquidlike behavior. This corresponds to a critical mechanical coordination number slightly in excess of 4. The results of the simulations also suggest that a reversal in the direction of the undrained stress path does not necessarily indicate temporary liquefaction. The undrained behavior obtained by the DEM simulations is found to be dependent on strain rate and the so-called temporary liquefaction phenomenon is only observed if the strain rate is sufficiently high.

This paper presents some of the interesting effects arising from the nonlinear motion of the liquid-free surface, due to sloshing, in a partially filled rigid container subjected to forced excitation. A two-dimensional meshless local Petrov-Galerkin method is used for the numerical simulation of the problem. A local symmetric weak form (LSWF) for nonlinear sloshing of liquid is developed, and a truly meshless method, based on LSWF and moving least squares (MLS) approximation, is presented for the solution of the Laplace equation with the requisite time-dependent boundary conditions. The MLS approximation with linear basis as well as Gaussian type weight function is employed in the computation. At every instant of time, velocity potential is computed at each node and the nodal positions are updated. The choice of a suitable scaling parameter value in the MLS approximation is discussed in this study. The effectiveness of the developed algorithm is demonstrated through a few numerical examples. The accuracy and stability of the numerical method introduced are verified from the comparison with the existing reference solutions.

The phenomenon of dynamic instability is investigated in this paper for a beam constrained at its end sections by viscoelastic (Kelvin-Voigt) translational and rotational supports, additionally affected by a certain degree of damage, to understand the influence of viscoelasticity and damage in its response under a dynamic axial load. A calculation procedure is developed to investigate the regions of dynamic instability of such a constrained beam by using an exact approach for solving the unloaded case and by applying it to the well-known solution for the boundary frequency domains of the dynamic problem. Damage is supposed to affect the elastic response of the restraints and to follow the scalar isotropic model. With respect to viscoelasticity, the time variable is treated as a parameter to account for the different timescales, according to the two transient phenomena: viscoelasticity and instability caused by an external dynamic load. The regions of dynamic instability for several configurations of the constraints are shown as three-dimensional diagrams in which the aforementioned regions contained in the plane described by the dynamic component of the periodic load and the frequency of the same load are shown here to vary in time and with respect to the level of damage of the constraints. In particular, the first three natural frequencies of the beam for each studied configuration have been taken into account. As expected, for each natural frequency and each configuration, the instability domains settle into asymptotic values ascertaining that the presence of damage in time increases the instability of the beam, since it is proved to move the domains toward lower, more easily reachable values of the external load frequency.

Identifying dynamic characteristics for structures under ambient condition is a very important task for the design verification, model updating, health monitoring, and damage detection of these structures. Among many techniques developed for this purpose, the stochastic subspace identification (SSI) techniques are a robust time-domain method that can simultaneously process large numbers of inputs and outputs. They can potentially extract the most information from the measurement. The SSI method assumes that both the excitation and the measurement noise are stationary white-noise processes and can lead to some errors when this assumption is not met. In this paper, a recursive SSI method using an instrumental variable (IV) technique is proposed for online step-by-step tracking of time-varying modal parameters for a structure under nonwhite but finitely correlated excitation and measurement noise. The IV technique is used to resolve possible estimation bias attributable to the violation of white noise assumption for the SSI method. A bi-iteration subspace tracker is also adopted to make the technique efficient and suitable for online application. The proposed technique is demonstrated on a single-degree-of-freedom structure and the ASCE benchmark frame structure. Results show that the technique can track the time-varying characteristics of structures under nonwhite but finitely correlated excitation and measurement noise.

In real ocean environments, currents generally exist simultaneously with ocean waves. However, the most previous investigations for the seabed response have only considered wave loading, ignoring currents. In this study, unlike previous studies, currents are included in the model of seabed response with waves, based on Biot’s poroelastic dynamic theory ($u-p$ approximation). Numerical results reveal that the consideration of currents has significant effect on the seabed response. The opposing current is beneficial to prevent liquefaction, while the following current would worsen the stability of the seabed. The parametric studies indicate that the wave period, water depth, saturation, soil permeability, and thickness of the seabed significantly affect the seabed response under combined loading of waves and currents. The maximum relative difference of the pore pressure between the cases with currents (velocity is $-2\mathrm{m}/\mathrm{s}$) and without currents $(p_{\mathrm{current}}-p_{\mathrm{nocurrent}})/p_0$ can reach up to 25% in both coarse and fine sand. The analysis of transient liquefaction in the fine sand seabed indicates that the maximum liquefaction depth increases with the following currents, but it decreases with the opposing current.

In this paper, stability analysis of thick annular sector plates under mechanical and thermal loads based on third-order shear deformation theory (TSDT) is investigated. The equilibrium and stability equations based on TSDT are obtained and solved analytically by doing some mathematical manipulation. Then, for nine possible boundary conditions, the buckling load and temperature are calculated and compared with those obtained using different plate theories. As the results show, for boundary conditions that include simply supported and clamped edges, the minimum value for buckling load and temperature is predicted by first-order shear deformation theory (FSDT) and maximum value is predicted by classical plate theory (CPT). Also, for boundary conditions containing free edges, the value obtained by TSDT is larger than that obtained using CPT and FSDT for some values of thickness/length ratio. It is worthy to mention that the results obtained from CPT for boundary conditions containing free edges in a wide range of thickness/length ratio are acceptable.

This paper presents a recursive Hilbert-Huang transform method for the time-varying property identification of shear-type buildings under base excitations. To overcome nonorthogonality and modal perturbation issues, all significant intrinsic mode functions of each signal and their Hilbert transforms were summed to track any variation of structural parameters of a multistory building over time. Given floor masses, both the stiffness and damping coefficients of the building were identified one by one from the top to bottom story. The overall accuracy of the identified parameters was measured by an index of accuracy based on the weighted root-mean-squared evaluation proposed in this study. One- and two-story shear buildings with abruptly, gradually, and periodically varying parameters were used as examples. The numerical results indicated that the proposed method is efficient, robust, and accurate in tracking variations of the properties of multistory buildings. Finally, the proposed method was applied into the identification of the time-varying natural frequency of a real-world high-voltage switch structure due to the friction mechanism used in the switch. The range of the identified frequency by the proposed method was in good agreement with that attained by the conventional least-squares method.

This paper presents the results of an experimental study of regular resonant vibrations of steel cables using a camera-based three-dimensional (3D) motion analysis system. The cable had one fixed end, and the other end was subjected to harmonic vertical excitation. Retroreflective markers were fixed to the cable and evenly distributed along it. The 3D motion analysis system was used to obtain 3D time traces of all marker vibrations; these traces were then entered into other programs for further signal processing. Time-varying modal coordinates were extracted from the trajectories of the markers using a modal decomposition technique. The resonant vibrations observed include isolated and simultaneous $1:1$, $2:2:1$, $1:1:2:2$, and $4:2:4:2$ internal resonances. Subharmonic and superharmonic resonances, period-doubling bifurcations, hardening nonlinearity effect, and complex traveling vibrations were observed and studied. The resonant vibrations were characterized by examining time-varying vibration profiles, vibration modal coordinates and their frequency spectra, single-point vibration trajectories, Poincaré sections, etc. Using the 3D motion analysis system, this experimental study offers a distinctive interpretation of the characteristics of nonlinear resonant vibration of cables in the spatial domain (based on mode-shape information of the entire cable), in addition to one in the time domain (based on real-time traces of one single point). Detailed experimental result analyses were made on the responses within certain excitation intervals (responses of intervals) and those of similar characteristics in the entire excitation frequency (responses of branches). This paper follows a previously published article by the same authors, in which the detailed description of the test as well as details on the modal identification process can be found.

A hole inside a rectangular thin plate is optimized for maximization of an eigenfrequency of the structure. The shape of the hole is represented by an ellipse parametrization to guarantee a smooth curve along the boundary; and the hole’s center position, semiaxes, and rotation are treated as shape design variables. The Rayleigh-Ritz approach is applied to constitute the vibration frequency equation such that an exact procedure can be presented for the frequency sensitivity analysis. The hole shape optimization is performed by using a combined mathematical programming algorithm with different search directions for two sets of design variables in relation to the constraint of the hole’s size. In addition, a simple optimality criterion is provided for the optimum profile design of the internal hole of a given area. Several illustrative examples demonstrate the validity and effectiveness of the design sensitivity analysis and the proposed optimization method.

The mathematical models governing the dynamics of various engineering systems, such as airplane wings and bridge decks subjected to aerodynamic forces, mechanical and civil structures interacting with fluid or soil, or systems with time delays, yield transcendental eigenvalue problems. In this work, a general transcendental eigenvalue problem is first formulated and a biorthogonality relationship between eigenvectors is derived. Then, the sensitivities of eigenvalues and eigenvectors with respect to a system parameter are obtained. The method is employed to analyze in detail a transcendental eigenvalue problem arising in the analysis of a bridge deck subjected to aerodynamic forces. The sensitivities of eigenvalues and eigenvectors are successfully used to improve the performance of an iterative method used for solving the eigenvalue problem.

State-of-the-art smart sensor technology enables deployment of dense arrays of sensors, which is critical for structural health monitoring (SHM) of complicated and large-scale civil structures. Despite recent successful implementation of various wireless smart sensor networks (WSSNs) for full-scale SHM, the low-cost micro-electro-mechanical systems (MEMS) sensors commonly used in smart sensors cannot readily measure low-level ambient vibrations because of their relatively low resolution. Combined use of conventional wired high-sensitivity sensors with low-cost wireless smart sensors has been shown to provide improved spectral estimates of response that can lead to improved experimental modal analysis. However, such a heterogeneous network of wired and wireless sensors requires central collection of an enormous amount of raw data and off-network processing to achieve global time synchronization; consequently, many of the advantages of WSSNs for SHM are lost. In this paper, the development of a new high-sensitivity accelerometer board (SHM-H) for the Imote2 wireless smart sensor (WSS) platform is presented. The use of a small number of these high-sensitivity WSSs, composed of the SHM-H and Imote2, as reference sensors in the Natural Excitation Technique—based decentralized WSSN strategy is explored and is shown to provide a cost-effective means of improving modal feature extraction in the decentralized WSSN for SHM.

The classical first-passage reliability problem for linear elastic single-degree-of-freedom (SDOF) oscillators subjected to stationary and nonstationary Gaussian excitations is explored. Several analytical approximations are available in the literature for this problem: the Poisson, classical Vanmarcke, and modified Vanmarcke approximations. These analytical approximations are widely used because of their simplicity and their lower computational cost compared with simulation techniques. However, little is known about their accuracy in estimating the time-variant first-passage failure probability (FPFP) for varying oscillator properties, failure thresholds, and types of loading. In this paper, a new analytical approximation of the FPFP for linear SDOF systems is proposed by modifying the classical Vanmarcke hazard function. This new approximation is verified by comparing its failure probability estimates with the results obtained using existing analytical approximations and the importance sampling using elementary events method for a wide range of oscillator properties, threshold levels, and types of input excitations. It is shown that the newly proposed analytical approximation of the hazard function yields a significantly more accurate estimate of the FPFP compared with the Poisson, classical Vanmarcke, and modified Vanmarcke approximations.

This study considers an air-filled heavy geomembrane tube section on a rigid horizontal foundation. All quantities are normalized to obtain similarity solutions. Integral terms of the semianalytic solutions are evaluated analytically, resulting in closed-form solutions. The closed-form solutions are expressed as simple functions of the pressure parameter. The validity of these solutions is confirmed, and some results are shown for characteristic values and shapes.

Random fields, such as the wind velocity field and the seismic ground motion field, are usually simulated by the spectral representation method (SRM). The SRM mainly relies on two methods: the random amplitudes method and the random phases method. However, the temporal statistics estimated from one SRM-simulated sample process differs from the target characteristics. Such differences can usually be assessed by the statistical errors, i. e., bias errors and stochastic errors. The closed-form solutions of statistical errors produced by random phases method have been given. This paper gives the closed-form solutions of statistical errors produced by the random phases methods and compares the statistical errors produced by both methods. The comparison of the stochastic errors of power spectral density functions produced by different methods demonstrates that (1) the random amplitudes method exhibits higher but more uniformly distributed stochastic errors than the random phases method; and (2) the stochastic errors produced by the random phases method are dependent on the decomposition method, whereas those produced by the random amplitudes method are not.

This paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response evolutionary power spectral density (PSD) functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudoexcitation method and the Gauss precise time step integration method. The evolutionary nonstationary random response analysis is converted into step-by-step integration computations using the pseudoexcitation method. The formulas of the pseudoresponses and their first and second derivatives with respect to the structural design variables are derived based on the Gauss precise time step integration method. The evolutionary PSD functions, their sensitivity, and the Hessian matrix are calculated using the pseudoresponses and their first and second derivatives, respectively. Finally, the evolutionary PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method.