Journal of Engineering Mechanics

A rigorous theoretical solution is presented for torsional vibration response of a pipe pile embedded in radial heterogeneous transversely isotropic saturated soil. The method was successfully verified against the analytical solution to a pile embedded in transversely isotropic saturated soil and the analytical solution to a pile embedded in radially inhomogeneous saturated soil. The influence of the construction disturbance effect, the wall thickness of the pipe pile, and especially the soil transverse isotropy on the complex impedance, twist angle, and torque of the pipe pile in the frequency domain were investigated comprehensively. The results revealed that (1) if the influence of the soil transverse isotropy is neglected, the maximum deviation rate of both dynamic stiffness $K_T$ and dynamic damping $C_T$ can reach 40%, and may result in 25% underestimation and 40% overestimation of the twist angle at pile head, and 40% underestimation and 104% overestimation at pile midsection; (2) ignoring the effect of the construction disturbance, the overestimation rate of $C_T$ can reach 42% and 167% for $f=15$ and 30 Hz, respectively; and (3) using a solid pile to simulate a pipe pile with wall thickness of 0.01 m, the average underestimation deviation rate of $K_T$ would be 71% in the range 0–30 Hz, and $C_T$ would be underestimated by 82%–360%. The deviation rate of the twist angle at the pile top and the torque at the pile end were approximately 250%–320% and 1,900%–2,900%, respectively. The present solution is applicable for identifying various pile defects through torsional reflection analysis of pipe piles.

The investigation of optimal sensor location problems in the field of vibration-based structural identification is predominantly performed for classically damped systems. In this study, a methodology is introduced to obtain the optimal sensor locations for identifying the structural (modal as well as physical) parameters of a nonclassically damped system. The optimal sensor locations are obtained by maximizing the determinant of the estimated Fisher information matrix out of all possible sensor combinations, such that the measurements would have maximum information about the parameters of interest. To deal with the inherently complex characteristics of the eigenvalues and mode shapes of nonclassically damped structures, the formulation is carried out in the state-space framework. To illustrate the approach numerically, primary-secondary systems exhibiting nonclassical damping behavior have been used. The methodology is also validated with experimental data from shake-table tests conducted on a primary-secondary structure. It is shown that the uncertainty in the estimated parameters is minimum when the sensors are placed at the optimal locations.

Fluid resonance in the narrow gap formed by a two-box system under irregular wave actions is investigated by employing a viscous numerical wave flume based on the OpenFOAM package. The accuracy of the numerical model is validated by comparing it with previous experimental data and numerical results in the literature. It can be observed that the viscous fluid flow model can work well in predicting the free surface amplitudes around the resonant frequency, while the potential flow model overpredicts the resonant amplitude. Numerical simulations suggested that the periods of wave responses in the narrow gap are always around the resonant period with small standard deviations. This can be explained by the spectral analysis that the wave energy in the narrow gap is concentrated at the resonant frequency. The normalized wave amplitudes calculated from the samplings of the large free surface amplitudes are always smaller than the samplings of the small free surface amplitudes. With the increase of the peak enhancement factor, the normalized significant wave heights under irregular wave actions increase and decrease around resonant and nonresonant frequencies, respectively. Compared to the results under regular wave actions, smaller and larger wave amplitudes appeared in the results of irregular wave actions around the resonant and nonresonant frequency ranges, respectively. The decreased normalized wave amplitudes with the increase of incident irregular wave amplitudes can be observed at all the frequency ranges.

Cables are used for engineering applications such as transport systems that involve mobile cables suspended between supports for carrying attached vehicles. Because of the inherent cable’s flexibility and the modification of dynamics properties during movement, such systems are sensitive to self-sustained oscillations under steady-state conditions. To provide an understanding of such vibratory excitation sources and a design method to prevent operating problems, this paper proposes a real case study of a chairlift and the development of an original model. The aim is to highlight the mechanisms responsible for the dynamic response amplification of the cable line. The method is based on a reduction of the complete dynamic model to a single mode, which localizes the vibration energy along the cable loop. The reduced model thus obtained takes the form of a Mathieu–Hill parametric excitation oscillator. The stability study reveals zones of instability in which the dynamic system response increases. The approach is then validated on the real case study by positioning the chairlift’s operating points in the stability diagram according to different configurations. Operating points are determined using the signal of the evolution of the static tension of the cable during the movement of the vehicles. Based on the case study, a general methodology for modifying design parameters is proposed to avoid undesirable line dynamics.

Wave propagation in elastic solids is analyzed by a space-time discontinuous Galerkin quadrature element method. First, the space-time quadrature element is conveniently formulated based on the space-time discontinuous Galerkin formulation. This method treats both the spatial and temporal domains in a unified manner, enabling it to handle not only structured space-time meshes but also unstructured ones. It effectively captures discontinuities or sharp gradients in the solution. To transform the formulation into a system of algebraic equations, the Gauss-Lobatto quadrature rule and the differential quadrature analog are utilized. High-order elements are constructed simply by increasing the order of integration and differentiation without the laborious construction of shape functions. Then, dispersion analysis is conducted for one- and two-dimensional elements. The analysis reveals that as the Courant number decreases, the total dispersion error monotonically converges to the spatial dispersion error, which can be reduced by increasing the element order. Additionally, high-order elements nearly eliminate numerical anisotropy in different directions. Finally, several numerical examples of elastic wave propagation validate the method’s effectiveness and high accuracy.

Abstract

When cables use many wires packed in a hexagonal pattern wrapped by bands around the surface, effective stiffness plays an important role in structural integrity and safety. This paper studies cylindrical wires packed in a hexagonal lattice tightened up by wrapping bands. When a transverse load is applied, the stress transferred through the contacts between the wires can be represented by a center-center force network with the Hertz contact theory. When yielding is considered in the contact zone, an elastoplastic contact model is developed. The Singum model simulates the singular forces by the stress between continuum particles. The effective stress-strain relationship changes with the stress of the wrapping bands and exhibits isotropic behavior in the cross section. Therefore, the overall elastic behavior of the cable is transversely isotropic with a tailorable stiffness in the cross section by the wrapping force. This method is general for mechanical modeling of packed parallel wire cables, and its application to bridge cable testing and repair with development length prediction is underway.

Practical Applications

This study introduces a novel approach, the Singum model, for analyzing the overall mechanical properties of packed wire cables, which are crucial for ensuring structural integrity and safety in various engineering applications. By investigating the effective transverse stiffness of packed wire cables through a combination of theoretical modeling, finite element analysis (FEM), and experimental tests, this research provides valuable insights into optimizing cable design and performance across diverse engineering applications such as cable domes, electric transmission lines, tramways, cable-stayed bridges, and suspension bridges. The findings highlight the significant impact of wrapping force on the effective stiffness of packed cylinders, offering engineers a means to tailor the stiffness of cable cross sections for specific requirements in these applications. This study provides a robust framework for advancing the understanding and optimization of packed wire cable systems in engineering practice with reasonable assumptions and simplifications, which can be tailored for specific materials or applications.

An analytical solution is presented for spherically symmetric growth of a fluid-saturated, poroelastic inhomogeneity inclusion embedded within a compressible elastoplastic matrix. A fluid source at the center causes the inclusion growth. The solution considers full poroelastic coupling of the inclusion pore fluid flow and solid phase deformation while solving for large deformation of the matrix via incremental elastoplasticity with associated flow rule and modified Mohr-Coulomb or Drucker-Prager yield models. Results obtained from the compressible (drained) solution are compared against the previously published solution pertaining to incompressible (undrained) matrix. Drained deformation is found to generally cause larger deviatoric stress, less compressive radial and hoop stresses, as well as faster growth of the plastic region, in the matrix. An example case study shows that compared with the undrained case, the drained matrix reaches the same elastoplastic strain with substantially smaller volume of injected fluid inside the embedded inclusion. The solution may be used as a proxy model of caprock integrity problem in ${\mathrm{CO}}_2$ geo-sequestration applications and further as a rigorous benchmark to verify the related numerical solvers.

This study proposes a computational method for estimating in vivo mechanical properties of tissues using clinical imaging data. In particular, a new level-set-based objective functional to compare a target and estimated shape of a tissue structure is introduced, along with its integration into an optimization-based approach for inverse material parameter estimation. The approach employs a continuous shape comparison metric using signed distance functions and combines the adjoint method for efficient gradient-based optimization. Simulated inverse problems based upon estimating cardiac ventricular wall stiffness from untagged imaging and hemodynamic data are used to assess the capability of the proposed approach. The results show that the proposed method is able to consistently and effectively minimize the shape-based objective functional to estimate material parameters. The minimization of this shape difference is capable of providing relatively accurate estimates of material parameters, although naturally depending on the sensitivity of the shape change to the particular parameters, and the process is tolerant to the inclusion of model error. Thus, the approach has the potential capability to provide estimates of in vivo mechanical properties of tissues from the shape of the tissue structure as can be directly estimated from imaging data.

Model updating (i.e., inverse problems) involving high-dimension and nonlinearity plays an increasingly important role in various research fields, e.g., digital twin model updating. Bayesian updating has become a robust and rigorous probabilistic means for parameter uncertainty quantification. However, it remains a challenging task to simultaneously ensure theoretically rigorous and computationally efficient solving of inverse problems involving high-dimensionality and nonlinearity. To address the issue, by applying the basic idea of subset simulation (SuS) to the ensemble Kalman filter (EnKF) that is computationally efficient and applicable to high-dimensional inverse problems, we designed an efficient Monte Carlo method, termed ensemble Kalman filter with subset simulation (EnKF-SuS). In EnKF-SuS, SuS provides a rigorous theoretical basis for guiding EnKF to adaptively search and explore the true target space(s), while avoiding the disadvantages of Markov chain Monte Carlo (MCMC)-based sampling methods by utilizing EnKF to generate updated ensemble samples. The performance of EnKF-SuS was validated and analyzed through three case studies involving multimodal posterior, strongly nonlinear, or high-dimensional problems. Moreover, based on a simplified model for longitudinal response analysis of shield tunnels, we present the application of EnKF-SuS in model updating using centrifuge data and field data, respectively. Results indicate that EnKF-SuS can accurately and efficiently sample from general target posterior distributions, especially in the tested strongly nonlinear or high-dimensional problems, and it is computationally one to two orders of magnitude faster than tested with MCMC-sampling methods.

Zero-plane is an important reference level included in the logarithmic velocity profile. The prediction of the zero-plane displacement remains challenging, especially in open-channel flows with submerged vegetation. In this study, we first review the existing formulas for estimating the zero-plane displacement. Then, we conducted a series of laboratory experiments of open-channel flows with submerged rigid vegetation, by varying flow rate, water depth, vegetation density, and stem diameter. By utilizing particle image velocimetry (PIV) technique, the spatio-temporal averaged (double-averaged) flow velocity and Reynolds shear stress profiles were obtained. The data analysis shows that the zero-plane displacement is almost proportional to the surface layer depth for the shallow flow cases. As the flow depth increases, the zero-plane displacement tends to be constant and increases with decreasing vegetation density. This result substantiates the hypothesis that the zero-plane displacement is related to large-scale eddies. Lastly, a heuristic model is developed to explain possible variations of the large-scale eddies, which yields a formula for predicting the zero-plane displacement for flows subjected to submerged rigid vegetation.

In recent decades, the outcrossing rate method has gained popularity for structural time-dependent reliability assessments (TRA). Despite numerous efforts, developing a general analytical outcrossing rate method for a nonstationary non-Gaussian performance function to estimate the failure probability within the forecast time interval remains a significant challenge. This paper introduces an analytical outcrossing rate method for non-Gaussian cases, named the three-moments-based outcrossing rate (TMO) method. The outcrossing rate is formulated based on the third-moment outcrossing rate with no assumption of the correlation between the performance function and its derivative process, allowing for a comprehensive understanding of the performance characteristics of a structure. Following the development of the proposed outcrossing rate, a TRA methodology is established to evaluate the failure probability of the nonstationary non-Gaussian performance function. Notably, the TMO method only requires statistical moments of the nonstationary non-Gaussian performance function, which are easy to calculate, facilitating efficient implementation. Three numerical examples are presented to demonstrate the applicability, efficiency, and accuracy of the proposed TMO method. It can be concluded that the proposed TMO method provides an accurate and useful approach for TRA in engineering applications.