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Mathematical Problems in Engineering is a broad-based journal publishes results of rigorous engineering research across all disciplines, carried out using mathematical tools.
Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.
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Free Vibration and Static Bending Analysis of Piezoelectric Functionally Graded Material Plates Resting on One Area of Two-Parameter Elastic Foundation
Free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of the two-parameter elastic foundation is firstly investigated in this paper. The third-order shear deformation theory of Reddy and 8-node plate elements are employed to derive the finite element formulations of the structures; this theory does not need any shear correction factors; however, the mechanical response of the structure is described exactly. Verification problems are performed to evaluate the accuracy of the proposed theory and mathematical model. A wide range of parameter study is investigated to figure out the effect of geometrical, physical, and material properties such as the plate dimension, volume fraction index, piezoelectric effect, elastic foundation coefficients, and the square size of the area of the foundation on the free vibration and static bending of piezoelectric functionally graded material plates. These numerical results of this work aim to contribute to scientific knowledge of these smart structures in engineering practice.
Modeling and Analysis of a Large-Scale Double-Level Guyed Mast for Membrane Antennas
This paper proposes a double-level guyed membrane antenna for stiffness improvement of a large-scale tri-prism deployable mast using the collapsible tubular mast (CTM). Initially, the construction of the antenna and the modeling of the CTM boom are illustrated. Afterwards, the central mast with isosceles triangular cross section is mathematically equivalent to a continuum beam, in which the equations of motion and the constitutive relations are derived. Based on the equivalent central beam, the double-level guyed mast for the membrane antenna is modeled as a 2(3-SPS-S) mechanism, and then velocity Jacobian matrices and stiffness matrices of SPS branches are constructed. Additionally, the total stiffness matrix of the equivalent mechanism is derived with the principle of virtual work and then evaluated as an accurate approach. Finally, with the aim to improve the static stiffness of the double-level guyed mast, the numerical analysis using the Genetic Algorithm (GA) is carried out for optimizing the distribution of guys in terms of anchor positions and attachment heights.
GPS Data in Urban Online Car-Hailing: Simulation on Optimization and Prediction in Reducing Void Cruising Distance
Ride-hailing, as a popular shared-transportation method, has been operated in many areas all over the world. Researchers conducted various researches based on global cases. They argued on whether car-hailing is an effective travel mode for emission reduction and drew different conclusions. The detailed emission performance of the ride-hailing system depends on the cases. Therefore, there is an urgent demand to reduce the overall picking up distance during the dispatch. In this study, we try to satisfy this demand by proposing an optimization method combined with a prediction model to minimize the global void cruising distance when solving the dispatch problem. We use Didi ride-hailing data on one day for simulation and found that our method can reduce the picking up distance by 7.51% compared with the baseline greedy algorithm. The proposed algorithm additionally makes the average waiting time of passengers more than 4 minutes shorter. The statistical results also show that the performance of our method is stable. Almost the metric in all cases can be kept in a low interval. What is more, we did a day-to-day comparison. We found that, despite the different spatial-temporal distribution of orders and drivers on different day conditions, there are little differences in the performance of the method. We also provide temporal analysis on the changing pattern of void cruising distance and quantity of orders on weekdays and weekends. Our findings show that our method can averagely reduce more void cruising distance when ride-hailing is active compared with the traditional greedy algorithm. The result also shows that the method can stably reduce void cruising distance by about 4000 to 5000 m per order across one day. We believe that our findings can improve deeper insight into the mechanism of the ride-hailing system and contribute to further studies.
Study on Chaotic Peculiarities of Magnetic-Mechanical Coupled System of Giant Magnetostrictive Actuator
We studied the chaotic peculiarities of magnetic-mechanical coupled system of GMA. Based on the working principle of GMA and according to Newton’s second law of motion, first piezomagnetic equation, disk spring design theory, and structural dynamics principle of GMA, the present study established a GMA magnetic-mechanical coupled system model. By carrying out data modeling of this coupled system model, the bifurcation chart of the system with the variation of damping factor, excitation force, and exciting frequency parameters as well as the homologous offset oscillogram, phase plane trace chart, and Poincaré diagram was obtained, and the chaotic peculiarities of the system were analyzed. The influence of parametric errors on the coupled system was studied. The analytical results showed that the oscillation equation of the GMA magnetic-mechanical coupled system had nonlinearity and the movement morphology was complicated and diversified. By adjusting the damping factor, exciting frequency, and excitation force parameters of the system, the system could work under the stable interval, which provided theoretical support for the stability design of GMA.
Stabilization of a Class of Nonlinear Underactuated Robotic Systems through Nonsingular Fast Terminal Sliding Mode Control
To facilitate the stabilization of nonlinear underactuated robotic systems under perturbation, a novel nonsingular fast terminal sliding mode control method is proposed. Based on the system transformation into an integrator chain, the combination of twisting-like algorithm and a nonsingular fast terminal sliding mode control technique is employed to achieve the stabilization of the studied systems, which can drive the robot states (joint positions and velocities) to the desired region and then maintain the system at the equilibrium point in finite time. The robustness of the proposed method is validated by the Lyapunov direct method. Finally, numerical simulation results further demonstrate that the proposed method has better performance on the convergent speed of the system state (robot joint positions and velocities) than state-of-the-art methods, especially for the underactuated joints.
A Multisource Monitoring Data Coupling Analysis Method for Stress States of Oil Pipelines under Permafrost Thawing Settlement Load
Thaw settlement is one of the common geohazard threats for safe operation of buried pipelines crossing permafrost regions, as pipes need to bear additional bending stress induced by settlement load. In the presented study, a novel coupled data analysis method was proposed for stress state estimation of buried steel pipeline under thawing settlement load. Multisource data including pipe bending strain derived by inertial measurement unit, pipe longitudinal strain derived by strain gauges, and thawing displacement loads derived by soil temperature monitoring were used to estimate the pipe’s mechanical states. Based on the derived data, finite element method-based pipe soil interaction model was established to predict pipe’s actual stress distribution. A monitored pipe segment of one crude oil pipeline in northeast China operated since 2010 was adopted as a prototype for the investigation, monitoring data derived in the last ten years was employed to predict the settlement loading, and relative accurate stress results was obtained via the established pipe soil interaction model. The mean absolute error (MAE) of the predicted pipe stresses compared with the monitoring results in 2014, 2017, and 2018 are 5.77%, 12.13%, and 13.55%, respectively. Based on the analyzed stress results, it can be found that the investigated pipe was subjected to an increasing settlement load from 2010–2016, made the bending stress increased up to 149.5 MPa. While after 2016, due to the depth of frost soil in this area is no more than 3.5 m, the thawing settlement load almost remained constant after 2016. As the investigated pipe is made by X65 line pipe steel, the von-Mises stress in pipe is much smaller than the allowable one indicating pipe’s structural safety status so far. The proposed method can also be referenced in the status monitoring of buried pipeline crossing other geological hazard regions.