Journal of Engineering Mechanics

The estimation of flexural stiffness from static loading test data is the basis of many methods assessing the condition of structural elements. These methods are usually developed under the assumption of having sufficiently accurate data available. Hence, their performance deteriorates as the differences between the measured and true values of the response, often denoted as noise, increase. The proposed methodology is specifically designed to mitigate errors derived from noisy static data when estimating flexural stiffness. It relies on the linearization of the equations relating displacements to stiffness through the unit-force theorem, combined with regularization tools such as L-curve and generalized cross-validation. The methodology is tested using theoretical simulations of the static response of a simply supported beam subjected to a 4-point flexural test for several levels of noise, two types of responses (deflections and rotations), and different levels of discretization. Recommendations for selecting the optimal regularization tool and parameter are provided. The use of rotations as inputs for predicting stiffness is shown to outperform deflections. Finally, the methodology is extended to a statically indeterminate beam.

A general framework for analyzing the failure probability of concrete specimens with the mean strength sampled from a large database is presented. The framework explicitly takes into account the level of uncertainty of the existing strength database involving different concretes tested in different labs. This uncertainty strongly influences the probability distribution of the nominal strength of each structure. The energetic (nonstatistical) size effect on structural strength is also incorporated into the analysis. The proposed framework is demonstrated by analyzing the reliability of reinforced concrete beams against diagonal shear failure. The analysis considers four different levels of uncertainty of the mean strength database, with coefficients of variation 5%, 10%, 25%, and 40%. It is shown that the overall failure probability strongly depends on the structure size, and that this size effect is also influenced by the uncertainty level of the database. In addition, an approximate solution procedure is developed for calculating the failure probability in the spirit of the first-order reliability method. Compared to the existing procedure, the proposed model is shown to yield a more realistic estimate of the structural failure risk and to lead to an analytical solution of the safety factor that can be used for reliability-based structural design.

Clustering analysis of sequential data is of great interest and importance in many science and engineering areas thanks to the explosive growth of time-series data. Effective methods, especially for sequence clustering, are strongly needed to extract features from data for better representation learning. This paper presents an unsupervised machine learning algorithm for sequence clustering based on dynamic $k$-means. Specifically, the clustering problem is firstly formulated rigorously to an optimization problem, which is then solved by a proposed three-step alternating-direction optimization approach. The performance of the proposed approach is successfully illustrated through three examples with both synthetic data sets and field ground-motion measurements. In particular, this approach is applied to ground-motion clustering/selection and shows satisfactory results. Overall, the results demonstrate that the proposed algorithm is able to effectively cluster sequential data through mining latent inherent characteristics.

A rigid body dynamics algorithm is presented in this paper to simulate the interaction between two rigid bodies, a free-standing rigid object, and a pedestal that has infinite mass, in the presence of static and kinetic friction forces. Earlier algorithms led to different solutions for the contact forces when parameters external to problem description, such as the ordering of contact points, are changed. This paper addresses the issue of selecting an appropriate solution for the contact forces and impulses from the infinite set of solutions by picking the solution that is closest to the previous state of the rigid body. The capability of this algorithm in simulating pure rocking, pure sliding, and coupled rocking-sliding response modes of a rectangular block is validated using analytical/semianalytical results. This validated algorithm is later used to identify the various response modes of a rectangular block, which is given an initial tilt and then released.

Accurate representations of aggregates in stone-based materials are crucial to conducting reliable discrete-element (DE) simulations based on the microstructure of such materials. The objective of this study was to develop an adaptive representation method for aggregates to obtain corresponding clumps of spheres that closely fit realistic shapes and the inertia of the aggregates. Based on the developed three-dimensional (3D) solid model of each aggregate, the methodology consisted of three main steps, as follows: (1) the aggregate contour was displaced with surface spheres of different sizes in predefined fitting accuracy; (2) consequently, the internal space of the model was filled with inner spheres; and (3) eight spheres for inertia calibration were incorporated, with the sphere clump consisting of surface and inner spheres to generate the DE representation of the aggregate. DE representations of 11 aggregate particles were developed using the proposed method. Results imply that the obtained DE representation can occupy the volume of the aggregate more than 99.5% with a properly defined fitting accuracy and fit the aggregate in inertia very well. A numerical simulation of asphalt mixture compaction was conducted using the aggregate models generated in this study. The numerical simulation indicates that the aggregate models generated using the proposed method can be successfully used to generate stone-based materials such as asphalt mixtures.

In the evaluation of the global maximum response of a structure subjected to its design load, damping effects must be included; however, the structure damping is often uncertain. This study develops an efficient method to compute the probability density function (PDF) of the global maximum dynamic response for multi-degree-of-freedom (MDOF) linear systems with uncertain damping when the external excitation is highly irregular. Operated in the complex plane, the proposed method is a pole-residue method that formulates a closed-form solution for the uncertain response at any instant time in terms of the poles and residues of the excitations and those of the system. While the poles and residues of an irregular excitation are deterministic quantities, those of the system are treated as random variables. In the numerical studies, a 100-story shear building subjected to a realistic ground motion is demonstrated, and the correctness of the proposed method is verified by Monte Carlo simulations.

Many high-piled wharves were built in the last century, and some wharf members have been damaged over decades of operation. It is important to use effective means to evaluate the safety status and durability of these high-piled wharf structures and guide reinforcement efforts. At present, the most common safety status evaluation methods for high-piled wharves are site inspections, crack detection, and concrete strength tests. However, it is difficult to provide quantitative safety indicators using these methods. In this paper, a disturbing-energy method is proposed for the safety assessment of high-piled wharves based on the variational principle and minimum potential energy principle. The geometric nonlinear effect is introduced, and formulations are derived for calculating the disturbing energy. A concentric compression bar example is presented to validate the proposed method through a comparison analysis between the Euler method and disturbing-energy method. Through several cases involving different loads applied to the same high-piled wharf structure, the same load applied to different structures, overall stiffness degradation, and member damage, the disturbing-energy method is shown to reflect very well the safety condition or damage condition of the high-piled wharf structure. The disturbing-energy method can also be used to identify the failure path of the structure and optimize the form of the wharf structure.

Semiactive control has received extensive attention because it can attain a similar control gain as active control while requiring a smaller external power supply. The critical step of semiactive control refers to the control parameter design and optimization in terms of a certain probabilistic criterion. However, the existing developments are limited in derivation of the statistical moments of quantities of concern, and knowledge of reliability of the controlled structure still remains open. This paper addresses the seismic reliability–based parameter optimization of magnetorheological (MR) dampers for structural control in semiactive modality under stochastic earthquake ground motion. An integral design scheme is proposed that implements the simultaneous optimization of (1) cost-function weights of active control, and (2) MR damper parameters of semiactive control. Comparative studies on probabilistic criterion, design scheme, and cost-function weight configuration are involved. It is revealed that reliability-based semiactive optimal control attains a safer and more serviceable structural system than the statistical moments–based semiactive optimal control; in addition, the integral design with simultaneous optimization of parameters allows a better balance between control gain and control demand than a previous separated design with sequential optimization of parameters. For verification purposes, a 6-story shear frame deployed with MR dampers subjected to stochastic earthquake ground motion is considered. The numerical example shows that the reliability-based integral design can ensure sufficient structural reliability in a global sense and accommodate smooth structural performance along the story level.

Some elements and structures can be modeled as rigid blocks. To reduce their likelihood of overturning such block-like elements, structures can be coupled with safety devices. In this paper, a model of a rigid block placed on a deformable soil is coupled with a pendulum working as mass-damper dynamic absorber. The deformable ground is modeled as a continuous bed of vertical linear springs and dashpots. To assess the effectiveness of the mass-damper dynamic absorber, a parametric analysis is performed by numerically integrating the equations of motion and considering one-sine pulse and seismic excitations. In the analyses, the geometrical characteristics of the block, the mass and length of the pendulum, and the stiffness of the soil are taken as variable parameters. Under one-sine excitation, the comparison of overturning spectra obtained for blocks with and without a mass-damper dynamic absorber demonstrates the effectiveness of the chosen protection device, especially for soils characterized by high stiffness. The beneficial effect of the mass-damper dynamic absorber on the dynamics of the rigid block under seismic excitations is evaluated by comparing the rocking maps obtained for blocks that are and are not equipped with mass-damper dynamic absorbers. In addition to the reduction of the overturning events of the block, the results show that the protection device has the positive effect of reducing the amplitude of the rocking angle.

For tunneling in a deep, soft rock mass, rock deformation and lining pressure, which are time-dependent behaviors, are mainly affected by rock rheology and longitudinal excavation processes. In practice, tunneling operations are often suspended due to various reasons, which will result in changes to the time-dependent behaviors of tunnel systems. To investigate the discontinuous advancement of the tunnel face in a soft rheological rock mass, in this study, closed-form analytical solutions are presented to analyze the time dependency of deep-buried circular lined tunnels. In the derivation, four types of viscoelastic models are utilized to consider the different creep behaviors of the host rock. The coupling effect between rock rheology and tunnel face advancement is also taken into account. To realistically simulate the process of tunnel face advancement, five different excavation methods are considered in the solutions that depend on whether the face stops and on the changes of advancing speeds before and after stoppage. The proposed solutions are validated by comparing the calculated results with those predicted by a finite difference simulation. According to the provided solutions, a series of parametric analyses are systematically performed to investigate the influences of the lining installation time, the duration of the tunnel face stoppage, the tunnel face advancing parameters, and the rheological parameters of the rock on rock stresses and displacement, as well as the support pressure. Finally, the proposed solutions are successfully applied to the Rong Jiawan tunnel when an excavation stoppage occurs halfway before tunnel completion, and the theoretical predictions are in good agreement with the field monitoring data. The solutions proposed in this paper provide an efficient analytical approach for predicting and analyzing the discontinuous excavation of rheological tunnels.

In this study, the analytical and experimental dynamic behavior of a rocking masonry tuff wall was investigated. The considered structural element is a wall clamped at the base that starts to behave as a rigid block once the strength of the interface between mortar and brick is exceeded. Therefore, the rocking motion takes place on an irregular base composed of the same block material. The results of free and forced oscillations are presented: the free responses are obtained by applying different initial displacement amplitudes at the top of the wall; and the forced behavior is explored by imposing harmonic input motions by means of a one-direction shaking table. To interpret the dynamic behavior of the wall, the classical rigid block model and a proposed simplified rocking deformable block model are used. The observation of the experimental curves representing the block frequency versus the oscillation amplitude during the free rocking motion suggests that the block does not always behave as a simply rigid block. The Housner model is used to evaluate the restitution coefficient, whereas the rocking deformable block model is used to describe the main dynamic characteristics of the wall. The good agreement between both the free and the forced motion tests and the analytical results provided by the models assures the correctness of the interpretation of the experimented dynamic behavior of masonry tuff walls.

An interpolation-based technique can effectively reduce the computational demand involved in a traditional simulation of the multivariate wind field utilizing the spectral representation method (SRM). However, errors are introduced by interpolation and are propagated to simulated wind samples. This influences the statistics of the simulated samples, which may exhibit a departure from the target. In order to properly reduce these errors, closed-form expressions of the statistical errors introduced by interpolation are derived, including the apparent wave effect of wind. The closed-form solutions are verified by a numerical example. It is shown that the interpolation brings no additional error to the mean value of the simulated wind velocity, but the statistical errors in the cross power spectral density (CPSD) function depend on the interpolation of the decomposed CPSD matrix. Through a parametric analysis, the influence of factors related to the interpolation steps, involving interpolation functions and interpolation intervals, on the statistical errors are further investigated numerically. The results show that the Hermite interpolation is preferable, because it causes smaller statistical errors in the multivariate wind field. Reducing the interpolation interval may decrease statistical errors quickly when the interpolation intervals are rather large, as used in engineering applications.

In this article, the boundary-element method (BEM) is applied to solve viscoelastic problems with any alteration in load, time, or boundary condition. The innovation of using spherical Hankel element framework instead of the classical Lagrangian approach is an effort to estimate the state variables of essential differential equations of BEM. This approach leads to the simultaneous satisfaction of the first- and second-order Bessel functions and the customary polynomial functions. A computer code has been generated to validate this progressive method. The results of various numerical examples, in which the analytical solution is measured and compared with Lagrangian- and Hankel-based BEM, are illustrated by means of comparative graphs. This evaluation reveals that the new method portrays much better agreement with the analytical solution in contrast to the classic BEM and maintains the accuracy while using the least degrees of freedom, indicating that it has significantly less error percentage owing to the fact that by utilizing the least number of elements, the desired precision is acquired. Thus, the current method is introduced and recommended as it is more economical and time-saving.

This paper proposes a new symplectic transfer-matrix method (STMM) to solve the bending problem of nonuniform beams. The STMM is a hybrid method that combines the symplectic dual solution system and the traditional transfer-matrix method (TMM). It is first necessary to obtain the benchmark solution of uniform beams in a symplectic system. On this basis, this paper derives the transfer matrices under various nonuniform conditions and discusses the mathematical structure of these transfer matrices. After obtaining the global transfer equation, the equation is solved by changing its rows and columns. Three numerical examples are given to verify the correctness and applicability of the STMM. This paper proves that the transfer matrix in the symplectic system is a symplectic matrix in mathematics, whether it is a field transfer matrix, a point transfer matrix, or a global transfer matrix. The STMM reveals the mathematical property of the transfer matrix and provides a theoretical basis for the standardized application of the “transfer type” method in structural analysis.

This study presents measurements of the bed shear stress associated with the three-dimensional boundary layer induced by a wall-bounded swirling jet. The velocity profile within the viscous sublayer was measured in detail using a high-resolution particle image velocimetry system that enables direct evaluation of the bed shear stress from the velocity gradient at the wall. The three-dimensional flow field was reconstructed based on the measurements conducted in a series of intersecting streamwise and transverse planes. At each intersection, the resultant bed shear stress was calculated as the vector sum of its components. The results show that the planar distribution of the bed shear stress is highly asymmetrical about the propeller axis due to the swirling rotation, which furnishes a description of how the jet path migrates over the plane boundary under the swirling effect. Compared with the expected scour hole that the swirling jet could induce on an erodible bed, the results presented in this study shed light on a qualitative understanding of the distinctive jet impingement mechanisms associated with rigid and erodible bed boundaries. Moreover, a close examination of the mean velocity distributions of both individual and resultant velocities reveals a consistent discrepancy from the universal logarithmic law in the log layer, in which the velocity distribution is subjected to outer layer bulk flow properties, thereby highlighting the evident difference in boundary layer flow between an impinging jet and canonical wall-bounded flows.

Analytical solutions for the hydromagnetic flow of incompressible viscous fluids between two infinite horizontal parallel plates, with the lower plate moving in its plane with an arbitrary velocity, are established in the presence of porous effects. For illustration, different motions with technical relevance are examined, and combined magnetic and porous effects, as well as the influence of Reynolds number on the dimensionless velocity and shear stress fields, are graphically depicted and discussed for motions persuaded by a suddenly moved or constantly accelerating plate. The solutions for oscillatory motions are expressed as the sum of permanent (steady state) and transient components, and the necessary time to attain the steady state is established graphically. It was found that this time is lower for motions due to cosine oscillations of the plate. Moreover, the steady state is rather obtained under the effect of a magnetic field or for flows through a porous medium.

A mechanical model of a particle damper (PD) was established which has a friction effect between the damper particle and the damper cavity. PD parameters can have a significant effect on the particle damper’s ability to control vibrations. These parameters include the coefficient of collision recovery between particle and cavity, the coefficient of rolling resistance between particle and cavity, and the particle radius, all of which affect the PD’s damping mechanism and performance. To address this issue, the authors calculated the kinetic energy, elastic potential energy, damping energy, and input energy of a single-degree-of-freedom (SDOF) mechanical system with a PD. The computational analysis utilized the energy method and its development law. The results show that under the conditions studied, the damping effect of PD increases with the decrease of the coefficient of collision recovery and the increase of coefficient of rolling resistance, although the influence of particle radius can be neglected. The influence of PD and a tuned mass damper (TMD) on the damping effect was compared using the same parameters; the TMD had a better damping effect under resonance excitation, whereas the PD had a better damping effect under nonresonant excitation. The mechanical model of the PD constructed in this paper was verified by a shaking table test for a single-layer steel frame. The damping effect of PD is the result of the comprehensive influence of its parameters.

In this paper, we conduct a systematic dynamic investigation of partial-interaction composite beams under various sophisticated loading conditions that have seldom been presented in the literature. For the purpose of easy implementation of the present theory and the convenience of interested readers, we utilize the dynamic variational principles under the same framework of the (extended) Hamilton’s principle to develop finite-element (FE) formulations for the dynamic responses of composite beams with Timoshenko’s beam theory. The forced vibrations of composite beams are focused with a transverse point load, a moving mass, or a moving mass-spring-damper system, respectively, some of which are important in the consideration of the vehicle–bridge (structure) interaction. The explicit expressions of the local FE expressions are also given in the appendixes. The developed dynamic FE theoretical framework is validated against numerical results in the literature with excellent agreement. We believe that the present work provides a solid theoretical foundation for the future research of vehicle/load–composite beam interactions that have seldom been studied.

As a passive control device, tuned mass dampers (TMDs) are widely used in structural vibration control. Due to the nonlinear characteristics of a TMD, it is important to consider nonlinearity in the design process. In this study, the authors analyzed the control results for the traditional design method of a TMD and concluded that the traditional design method is not sufficiently effective when considering the nonlinear behavior of TMDs. Furthermore, it is demonstrated that the improved design method proposed previously by researchers may not provide the best control effect in some cases. To accurately incorporate the nonlinearities in the design process, the harmonic balance method (HBM) is used to determine the steady-state amplitude of a single-degree-of-freedom structure controlled by a nonlinear TMD. The result of the analysis is used to calculate the optimal frequency ratio of the TMD, which is subsequently used in the design. Finally, the calculated optimal frequency is compared with the numerically obtained optimal result. Through the simulation, it can be shown that the proposed method can effectively incorporate both hardening and softening nonlinearity.

Acrylate rubber molecules contain sterically hindered and highly polar ester groups, which can generate a large amount of internal friction energy under external alternating stress and exhibit high internal friction for energy dissipation. Based on previous studies on the formulation of acrylate viscoelastic materials, the optimal formulation was prepared and made into acrylate viscoelastic dampers and the mechanical properties of the corresponding damper specimens were tested. The acrylate viscoelastic dampers at different ambient temperatures, excitation frequencies, and displacement amplitudes were systematically investigated. The experimental results indicate an excellent damping capacity of the acrylate viscoelastic dampers, where the dynamic properties are affected by the ambient temperature and excitation frequency, and the single-loop energy dissipation capacity is significantly affected by the displacement amplitude. To accurately represent the effects of the temperature, frequency, and amplitude on the dynamic properties of the damper, a modified fractional-derivative equivalent model is introduced, where the internal variable theory and temperature-frequency equivalent principle are introduced to reflect the amplitude effect and temperature effect, respectively. Finally, the results calculated by the proposed model were compared with the experimental data, which verified the correctness of the mathematical model.

Interpolation can be used to up-sample a sparsely recorded or simulated data set. Ideal interpolation models such as a Nyquist-bandlimited filter in the frequency domain and sinc function in the time domain are difficult to implement. Previous researchers proposed an interpolation scheme that interpolates data faithfully and preserves the spectral features of the original data. This approach has one possible limitation that the interpolated data may not pass through the original data points exactly. This technical note provides a modification of this scheme to ensure the interpolated data capture the original data points.