Journal of Engineering Mechanics

Allowing slender structures to uplift has been used as an efficient means of controlling their seismic response. Oftentimes rocking structures will exhibit some degree of flexibility and cannot be adequately represented by single-mass or rigid systems. In this paper, we examine the dynamic response of multistory flexible rocking bodies equipped with inerters at their ground level. First, numerical models of inerter-equipped rocking structures are formulated and validated. These models are used to assess the effect of the inerter on the elastic deformations and base rotations demands of a set of structures ranging from 3 to 9 stories. Importantly, we examine the interaction between impact forces and higher vibration modes and evaluate the effectiveness of the inerter in controlling the associated acceleration demands and increased bending moments along the height. The efficiency of the inerter was not found to be affected by practical variations of the stiffness of the rocking surface. Although the inerter increased the moment demands at the first level, the proposed strategy successfully controlled seismic demands along the height of the structure.

The influence line is an important static property in bridges. The shape and magnitude of the girder bridge influence line contain stiffness information for the bridge supports and beam. This research sought to directly identify the rotational stiffness of bridge supports and the flexural stiffness of beams from extracted influence lines, which provides a quantification method for bridge damage and performance degradation. The paper first reviews the influence line identification method from vehicle-induced bridge responses. Then, the complete theoretical formulations of the deflection, rotation, and strain influence line for a general girder bridge are derived. Based on these derivations, the rotational stiffness at two supports and the equivalent flexural stiffness value of the beam are identified. Next, a certain span of a continuous girder bridge is converted to an equivalent simply supported system, and the flexural stiffness distribution of the beam is estimated based on the bending moment-curvature relationship and Betti’s law. The paper then presents a three-span continuous girder bridge verification example. The stiffness estimation results under different test conditions combined with the bridge influence line identification algorithm are presented to verify the reliability of the proposed method. This stiffness estimation method can be applied to baseline-free bridge performance evaluations based on vehicle-induced bridge responses.

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical methods is how they approximate the physical fields of interest. Physics-informed deep learning (PIDL) is a novel approach developed in recent years for modeling PDE solutions and shows promise to solve computational mechanics problems without using any labeled data (e.g., measurement data is unavailable). The philosophy behind it is to approximate the quantity of interest (e.g., PDE solution variables) by a deep neural network (DNN) and embed the physical law to regularize the network. To this end, training the network is equivalent to minimization of a well-designed loss function that contains the residuals of the governing PDEs as well as initial/boundary conditions (I/BCs). In this paper, we present a physics-informed neural network (PINN) with mixed-variable output to model elastodynamics problems without resort to the labeled data, in which the I/BCs are forcibly imposed. In particular, both the displacement and stress components are taken as the DNN output, inspired by the hybrid finite-element analysis, which largely improves the accuracy and the trainability of the network. Since the conventional PINN framework augments all the residual loss components in a soft manner with Lagrange multipliers, the weakly imposed I/BCs may not be well satisfied especially when complex I/BCs are present. To overcome this issue, a composite scheme of DNNs is established based on multiple single DNNs such that the I/BCs can be satisfied forcibly in a forcible manner. The proposed PINN framework is demonstrated on several numerical elasticity examples with different I/BCs, including both static and dynamic problems as well as wave propagation in truncated domains. Results show the promise of PINN in the context of computational mechanics applications.

As one of the most promising smart materials, magnetorheological (MR) gels have been widely applied in the vibration mitigation of engineering structures. An accurate and effective model for MR gels is of great significance for its in-depth research and engineering application. Existing models for MR materials mainly follow the magnetic dipole theory used for MR fluid, but this theory takes no account of the particle size and, thus, cannot apply to MR gels with a relatively higher volume fraction of particles. In this paper, a micromechanical model for MR gels was proposed and experimentally verified based on the planar current loop model. Firstly, high-performance MR gels were prepared, and basic performance characterizations, including the magnetization property and the sedimentation stability, were carried out. Then the magnetic energy of particles calculated by the magnetic dipole model and the planar current loop model were compared, and the micromechanical model of MR gels was proposed based on the planar current loop model. In the parameter determination process, the data obtained by magnetization tests of the particles were fitted to form the magnetization curve with higher accuracy. Finally, the yield shear stresses of the prepared MR gels were obtained by property tests, and the effectiveness and accuracy of the proposed micromechanical model were verified by comparing the test data with the theoretical values calculated by the proposed model.

Railroad bridge inspectors are interested in measuring the maximum total transverse displacement of railroad bridges under trains, but these values are generally not easy to obtain in the field without sensors. Engineers use LVDTs, analog accelerometers, or wireless smart sensors (WSS). However, these sensors need to be attached to the bridge prior to the train-crossing event, which requires time, costs money, and is unsafe for engineers. This paper describes the design of a new sensor-equipped, low-cost unmanned aerial vehicle (UAV) system that enables the safe, cost-efficient, and noncontact total transverse displacements measurement of railroad bridges. The new system integrates laser and camera measurements from a UAV flying near the moving structure. The design and assembly of the new system is followed by methodology, field experiment, and results. The authors compared the estimations of the new system with ground-truth data obtained using an LVDT to quantify the capabilities of the new system. The results support the value of the proposed method to measure noncontact railroad bridge displacements in the field.

A computational approach is presented to estimate the in vivo magnitude and spatial distribution of mechanical material properties of soft tissues. This strategy utilizes an optimization-type inverse problem solution procedure with a shape-based objective function to estimate the difference between the measured and predicted tissue behavior and estimate mechanical properties from standard untagged clinical imaging data. A set of simulated inverse problems was used to evaluate the inverse solution estimation procedure based on estimating the passive elasticity of the human right and left ventricle walls from standard cardiac imaging data and corresponding hemodynamic measurements. Results showed that the proposed shape-based approach can estimate mechanical material properties accurately, although the accuracy is dependent on the spatial region considered and the relative stiffness. The solution accuracy also was shown to be tolerant to the presence of model error. Moreover, additional tests showed that the accuracy of the material property estimate of a priority region of the structure of interest can be improved, while simultaneously desensitizing the solution to additional model error, by selecting an appropriate portion of the response shape to use within the objective function.

Understanding the nonlinearity of pendulum tuned mass dampers (PTMDs) under large-amplitude vibration is important to enhance control performance. Here, the nonlinear effects of PTMDs on vibration control of a single-degree-of-freedom (SDOF) system under harmonic excitation are explored. The nonlinear governing equations of the linear SDOF structure coupled with the PTMD are formulated. The results obtained via the method of harmonic balance under various excitation amplitudes are compared with those obtained employing the linearized system. It is shown that the effects of PTMD nonlinearity can be ignored when the PTMD rotation angle is below about 9°. Upon increasing the excitation amplitude, remarkable differences are observed between the nonlinear and linear frequency response functions (FRFs). Large mass ratios of PTMD are found to lead to reduced PTMD motion and attenuated nonlinear effects. A parametric study is performed to find the optimal parameters of the nonlinear PTMD under various excitation amplitudes. The results indicate that the optimal tuning frequency ratio increases significantly with excitation amplitudes, whereas the optimal damping is less sensitive to excitation amplitudes. Finally, a 61-m-high steel chimney structure subjected to harmonic and random wind loadings is investigated to verify the proposed PTMD design method.

A new total stress failure criterion applicable to both isotropic and anisotropic soils under undrained conditions is proposed. The new criterion, which is motivated by elastic anisotropy in the underlying effective stress-strain behavior, is shown to be consistent with reported data for undrained shear strengths obtained in triaxial compression, triaxial extension, and direct simple shear tests.