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A new preconditioned modified conjugate gradient algorithm based on improved gradient operator and preconditioned technology is proposed for moving force identification of bridge structure in this paper. First, the moving load identification problem is converted into the problem of solving large-scale linear equations by the time-domain deconvolution technology and modal superposition method. Then the large-scale linear equations problem is transformed into easily solved equivalent problem by preprocessing. Subsequently, it is transformed into an unconstrained linear optimization problem by constructing the corresponding objective function. Finally, the problem is solved by the proposed conjugate gradient method. The innovation of the proposed method lies in two aspects. First, the proposed conjugate gradient method is proved by mathematical theory. Second, before constructing the objective function, the preconditioned technique is utilized to simplify the original problem. A series of numerical simulations are carried out to verify the stability and effectiveness of the proposed approach under 21 kinds of noise levels and 6 different sensor configurations, and its performances are compared with several conjugate gradient methods. The results show that the proposed method can reduce the iteration number, and also ensure the load identification accuracy, which indicates that the proposed method can improve the speed of identification and effectively reduce the cost. Meanwhile, the identification situation of different load components is studied by the frequency spectrum analysis method. It is found that the proposed method is a stable and a reliable identification method for static and low-frequency components, which provides a new idea for dynamic weighing of low-frequency loads on bridges.

This paper presents the dynamic responses of a fiber-reinforced composite beam under a moving load. The Timoshenko beam theory was employed to analyze the kinematics of the composite beam. The constitutive equations for motion were obtained by utilizing the Lagrange procedure. The Ritz method with polynomial functions was employed to solve the resulting equations in conjunction with the Newmark average acceleration method (NAAM). The influence of fiber orientation angle, volume fraction, and velocity of the moving load on the dynamic responses of the fiber-reinforced nonhomogeneous beam is presented and discussed.

The review is proposed with the investigations related to the dynamics of the oscillating, moving, and oscillating-moving loads acting on the inner surface of the hollow cylinder surrounded by the elastic medium. All considered investigations are carried out within the framework of the piecewise homogeneous body model by utilizing the exact 3D equations and relations of the linear and linearized elastodynamics. The problems are classified as axisymmetric and 3D non-axisymmetric, as well as the axisymmetric problems related to the case where the constituents of the system have non-homogeneous initial stresses. For further investigations, the subjects related to the dynamics of the moving and oscillating moving load acting in the interior of the hollow cylinder surrounded by the elastic and viscoelastic medium are suggested.

To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced concrete (RC) beam is derived for the dynamic response of the viscoelastic bearing RC beam subjected to a single moving load. Furthermore, based on the simplified shape function, the dynamic response of the viscoelastic bearing RC beam under equidistant moving loads is studied. The results show that the stiffness and damping effect on the dynamic response of the supports cannot be neglected. The support stiffness might adversely increase the dynamic response. Further, due to the effect of support damping, the free vibration response of RC beams in resonance may be significantly suppressed. Finally, when the moving loads leave the bridge, the displacement amplitude of the viscoelastic support beam in free vibration is significantly larger than that of the rigid support beam.

Forced vibrations resulting from moving loads, along with efficient vibration control, are essential in transportation engineering, earthquake engineering, and aerospace engineering. In this study, the vibrational response of an axially functionally graded (AFG) beam subjected to a moving harmonic load within a thermal environment was investigated. The primary aim was to explore the potential of controlling this vibration by incorporating a nonlinear energy sink (NES). A model for the AFG beam, with clamped–clamped boundary conditions, was developed using Euler–Bernoulli beam theory and the Lagrange method, accounting for the effects of the thermal environment and the moving load. The numerical simulations were performed using the Newmark method to solve the governing equations. The results demonstrated the effectiveness of the NES in mitigating the vibrational response of the beam under thermal and dynamic loading conditions. The effective reduction of maximum deflection caused by moving loads was set as the optimization objective to identify the most optimal parameters of the NES. The results were presented through a series of parameter analyses, revealing that the nonlinear damper can quickly dissipate the beam’s energy when the loads exit the structure. Furthermore, a properly designed NES can result in a 2.4-fold increase in suppression efficiency.

The faster and heavier trains in modern railway traffic are getting popularity in the public transportation authorities of many countries. Such trains cause higher stresses and excessive deformations in the ballasted railway track substructure under train dynamic loadings, which raises the risk of track damage and derailment. It is thus essential to investigate the impact of different influencing factors on the dynamic response of ballasted railway track–ground systems. In this study, a sophisticated three-dimensional finite element model simulating realistic train moving loads is presented and used to investigate the dynamic response of ballasted railway tracks in terms of stress transmission and track deflections under various train–track–ground conditions. The influencing factors considered in this study include the modulus and thicknesses of track substructure layers, the amplitude of train moving loads and the train speed. The outcomes of this study encompass important guidance to railway engineers to assist in finding the best possible scheme for the design of ballasted railway tracks and lifetime maintenance.

Rapid and accurate identification of moving load is crucial for bridge operation management and early warning of overload events. However, it is hard to obtain them rapidly via traditional machine learning methods, due to their massive model parameters and complex network structure. To this end, this paper proposes a novel method to perform moving loads identification using MobileNetV2 and transfer learning. Specifically, the dynamic responses of a vehicle–bridge interaction system are firstly transformed into a two-dimensional time-frequency image by continuous wavelet transform to construct the database. Secondly, a pre-trained MobileNetV2 model based on ImageNet is transferred to the moving load identification task by transfer learning strategy for describing the mapping relationship between structural response and these specified moving loads. Then, load identification can be performed through inputting bridge responses into the established relationship. Finally, the effectiveness of the method is verified by numerical simulation. The results show that it can accurately identify the vehicle weight, vehicle speed information, and presents excellent strong robustness. In addition, MobileNetV2 has faster identification speed and requires less computational resources than several traditional deep convolutional neural network models in moving load identification, which can provide a novel idea for the rapid identification of moving loads.

This paper aims to present a modified continuum mathematical model capable on investigation of dynamic behavior and response of perforated microbeam under the effect of moving mass/load for the first time. A size-dependent finite element model with non-classical shape function is exploited to solve the mathematical model and obtain the dynamic response of perforated Timoshenko microbeams under moving loads. To that end, first, equivalent material and geometrical parameters for perforated beam are developed, based on the regular squared perforation configuration. Second, both the stiffness and mass property matrices including the microstructure effect based on modified couple stress theory and Timoshenko first-order shear beam theory are derived for two-node finite element using new shape function. After that, the interaction between the load and beam is modeed and unified with the equation of motion of the beam incorporating mass inertia effects of moving load. The developed procedure is validated and compared. Effects of perforation parameters, moving load velocities, inertia of mass, and the microstructure size parameter on the dynamic response of perforated microbeam structures have been investigated in a wide context. The achieved results are helpful for the design and production of MEMS structures such as frequency filters, resonators, relay switches, accelerometers and mass flow sensors, with perforation.

In order to analyze the impact of axle spacing on the vibration response of railway bridges, it is essential to use moving loads with non-uniform intervals, namely a non-equidistant moving load model of the train. In this paper, by incorporating this model and using the Fourier transform and modulus extraction, the corresponding moving load amplitude spectrum (MLAS) related to the moving loads and the vibration modes of bridges is deduced in the frequency domain, which can thus effectively reflect the displacement amplitude laws of the bridge free vibration. Hence, the resonance and cancelation phenomena of simply supported bridges under trains are comprehensively investigated using the presented MLAS. On the one hand, the corresponding resonance speeds obtained by the MLAS are not only related to the length of carriages, bridge frequencies, and spans, but also to the number of carriages, presenting a supplement to the traditional resonance speed, which sometimes does not cause the maximum displacement response of bridges. On the other hand, the cancelation phenomena in this paper are divided into type I and type II, and the closed-form solutions of the corresponding cancelation speeds are derived from the proposed MLAS, thus providing a more comprehensive understanding of the influencing factors of cancelation phenomena. In addition, through the MLAS comparison of different train models, it is found that the non-equidistant moving loads cannot be completely replaced by the equidistant moving loads in analyzing the resonance phenomenon of railway bridges, which is related to the ratio of the carriage length to the bridge span. The type II cancelation speeds are consistent whether moving loads are equidistant or non-equidistant. However, the type I cancelation speeds are inconsistent, and the difference is reflected in the influence of the distance between the wheel centers of each bogie and the distance between the bogie centers. These research results have been validated by time domain analyses in numerical examples. Therefore, the presented frequency domain method based on the MLAS is very valuable for comprehensively investigating the resonance and cancelation phenomena of simply supported bridges under non-equidistant moving loads.

Bridge infrastructures are continuously subject to degradation due to aging and excess loading, placing users at risk. It has now become a major concern worldwide, where the majority of bridge infrastructures are approaching their design life. This compels the engineering community to develop robust methods for continuous monitoring of bridge infrastructures including the loads passing over them. Here, a moving load identification method based on the explicit form of Newmark-β method and Generalized Tikhonov Regularization is proposed. Most of the existing studies are based on the state space method, suffering from the errors of a large discretization and a low sampling frequency. The accuracy of the proposed method is investigated numerically and experimentally. The numerical study includes a single simply supported bridge and a three-span continuous bridge, and the experimental study includes a single-span simply supported bridge installed by sensors. The effects of factors such as the number of sensors, sensor locations, road roughness, measurement noise, sampling frequency and vehicle speed are investigated. Results indicate that the method is not sensitive to sensor placement and sampling frequencies. Furthermore, it is able to identify moving loads without disruptions when passing through supports of a continuous bridge, where most the existing methods fail.