应用数学和力学

Variable Damping Characteristics and a Dynamic Analysis Method for Magnesium Alloy

XU Wentao, ZHANG Yanhui, TANG Guangwu, PAN Genji

2020, 41(12): 1297-1310. doi: 10.21656/1000-0887.410144

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Abstract:
The damping characteristics of the GW63K magnesium alloy were studied by means of the dynamic thermomechanical analyzer (DMA) based on the viscoelastic damping theory. The magnitude, variation characteristics and dependence sensitivity of this magnesium alloy's damping were given from the angle of dynamic applications. For the first time the damping parameters of this type of magnesium alloy could be qualitatively described as variables in the dynamic analysis, and the damping change laws with the service environment temperature and excitation frequency were quantitatively given. For the nonlinear solution problem with variable damping in the dynamic system, the time-dependent manner of damping was established. Based on the pseudo excitation method, a quasi-non-stationary stochastic analysis method was built for stationary problems, and an efficient numerical analysis method for variable-damping problems of magnesium alloys under random vibration was proposed. Numerical and experimental verifications of the structural dynamic responses of magnesium alloy components were carried out respectively, to reveal the obvious difference between the analysis results based on constant damping and variable damping. The dynamic model based on variable damping gives results in better agreement with the experimental results. It is concluded that in the fields where high accuracy is required, the variable-damping model should be chosen to analyze the magnesium alloy material structure.

Homoclinic Bifurcations and Chaos Thresholds of Tristable Piezoelectric Vibration Energy Harvesting Systems

LI Haitao, DING Hu, CHEN Liqun, QIN Weiyang

2020, 41(12): 1311-1322. doi: 10.21656/1000-0887.410164

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Abstract:
Nonlinear dynamic performances such as homoclinic bifurcation and chaos were investigated for tristable vibration energy harvesting systems. The analytical expression of the symmetric and asymmetric homoclinic solution was obtained through the Padé approximation, which was consistent with the numerical solution. According to the Melnikov theory, the qualitative method of studying the homoclinic bifurcation of the energy harvesting system with a triple well was developed, and the necessary condition for the occurrence of homoclinic bifurcation was obtained. Numerical simulations yielded bifurcation diagrams and maximum Lyapunov exponents that demonstrated the inter-well responses predicted with the Melnikov method. Compared with the system with symmetric potential energy, the system with asymmetric potential energy has a lower threshold of homoclinic bifurcation. For a low excitation level, the system with asymmetric potential energy witnesses inter-well chaos, while the response of the system with symmetric potential energy still keeps trapped in a single well. The change of symmetry of the system potential energy function improves the output voltage due to the increase in the probability of generating a large periodical inter-well oscillation response. The research on the homoclinic bifurcation of nonlinear energy harvesting systems with symmetric and asymmetric triple potential wells provides an effective tool for the parametric design of high-performance energy harvesters.

A Multibody System Dynamics Vector Model and the Multistep Block Numerical Method

WANG Zhen, DING Jieyu

2020, 41(12): 1323-1335. doi: 10.21656/1000-0887.400340

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Abstract:
A multi-body system dynamics model was described with the direction vector method, and the index 3 differential-algebraic equation was reduced to index 1. The multistep block numerical solution scheme was built for the long-time simulation of multi-body systems. The simulation results show that, under the same time step, the multistep block method is better than the classical Runge-Kutta method in terms of the energy error, the position constraint, the speed constraint, the acceleration constraint and the direction vector constraint. The multistep block schemes constructed with the Chebyshev nodes and the Legendre nodes are better than that with the equidistant nodes in terms of the maximum energy error and the direction vector constraint error. The Runge-Kutta method is not suitable for long-time simulation, but the multistep block method can maintain good computational accuracy for long-time simulation.

A Mixed Integer Optimization Model Based on Inelastic Contraction for Cable Adjustment of Cable-Stayed Bridges

WANG Jialin, WANG Chengyan, CAO Kerui

2020, 41(12): 1336-1345. doi: 10.21656/1000-0887.410148

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Abstract:
For the cable force adjustment of cable-stayed bridges, truss elements were used to simulate the cables, and the amount of inelastic contraction was introduced into the degree-of-freedom vector of the cables. Through matrix transformation of the overall structural balance equations, an influence matrix based on the amount of inelastic contraction was established. With the obtained influence matrix, in the case of the full-bridge cable adjustment, the target cable force can be accurately achieved in theory. In response to the needs of some cable adjustments in actual projects, variables 0 and 1 were introduced to indicate that no adjustment is needed, or some cable is to be adjusted. Based on the integer variables and the adjustment length of the cable, a mixed integer optimization model was established to conveniently realize partial cable adjustment and optimization analysis of the cable. The calculation example demonstrates the effectiveness and feasibility of the optimization model.

Buckling Analysis of Composite Laminate Plates Based on the n-order Shear Deformation Theory

SHI Feng, MA Hongying, SUN Yizhen, XIANG Song, WANG Yanbing, LUAN Tingting

2020, 41(12): 1346-1357. doi: 10.21656/1000-0887.410061

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Abstract:
The buckling of composite laminate plates was analyzed with the nth-order shear deformation theory. The virtual work principle was used to derive the governing equations for the critical buckling of laminate pates under in-plane loads. The comparison between the present results and the results of previous literatures shows good agreement and high calculation accuracy.

Research On P2P Optimal Scheduling of User Side Distributed Generation Under Ubiquitous Power Internet of Things

XIAO Yong, YU Jie, ZHANG Xinsen, QIAN Bin, WANG Yan, ZHANG Tongtong

2020, 41(12): 1358-1368. doi: 10.21656/1000-0887.410126

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Abstract:
The ubiquitous power internet of things (UPIoT) can make full use of advanced communication technologies to realize the wide interconnection of power generation, transmission, distribution and use in the power system, thus providing technical support for the massive access of distributed generations (DGs). Under the background of the UPIoT, the idea of the P2P technology was applied to establish the decentralized scheduling architecture of distributed generations, so that the optimal scheduling could be completed through information interaction based on communication among distributed generations. The distributed sub-gradient algorithm was applied to solve the established P2P optimal scheduling model, and the doubly stochastic matrix was introduced to construct the connection matrix between nodes in the UPIoT. Finally, the feasibility and effectiveness of the optimization model and its solution method were verified through simulation examples, and the interrupts and errors that may be encountered in the communication process were also discussed.

State Feedback Control of Predator-Prey Systems With Holling Ⅳ Functional Responses

WANG Xiaoe, LIN Xiaolin, LI Jianquan

2020, 41(12): 1369-1380. doi: 10.21656/1000-0887.400314

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Abstract:
A class of predator-prey systems with Holling IV functional responses under state feedback control were studied. The sufficient conditions for the existence and stability of semi-trivial solutions and order-1 periodic solutions were obtained by means of the analogue of the Poincare criterion and the geometric theory for semi-continuous dynamical systems. The numerical simulation verifies the correctness of the conclusion and the effectiveness of the state feedback control, and reveals abundant dynamic behaviors of the state feedback control system, such as the fold bifurcation, the flip bifurcation and chaos.

Adaptive Synchronization of Neutral-Type Coupled Neural Networks With Stochastic Perturbations and Markovian Jumpings

ZHANG Zhishu, GAO Yan

2020, 41(12): 1381-1391. doi: 10.21656/1000-0887.410079

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Abstract:
The adaptive synchronization problem of neutral-type neural networks with time-varying delays and stochastic perturbations was discussed. Stochastic perturbations were described as the Brownian motion. Through the Lyapunov stability theory, the LMI analysis techniques and the matrix theory were used to study the adaptive synchronization of neutral-type neural networks with stochastic perturbations and Markovian jumpings. The sufficient conditions for the system synchronization were given and proved. The criterion for adaptive synchronization of neutral-type neural networks with time-varying delays and stochastic perturbations was obtained. Finally, numerical examples show the effectiveness and applicability of the proposed approach.

A Delayed Feedback Control Method for Fractional-Order Chaotic Financial Models

XU Changjin>, DUAN Zhenhua

2020, 41(12): 1392-1404. doi: 10.21656/1000-0887.400323

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Abstract:
The chaos control of a class of fractional-order delayed financial models was studied. The chaotic behavior was successfully controlled by means of the time delayed feedback control method. The sufficient condition to ensure the stability and the existence of the Hopf bifurcation was established. The effects of the delay and the fractional order on the stability and bifurcation were revealed. Numerical simulations verify the correctness of the theoretical analysis. The obtained results provide a theoretical foundation for financial stability.

Finite-Time Function Projective Synchronization of Unknown Cohen-Grossberg Neural Networks With Time Delays and Stochastic Disturbances and Its Application in Secure Communication

ZHANG Yamei, HAO Tao, YIN Sibei, ZHANG Meng

2020, 41(12): 1405-1416. doi: 10.21656/1000-0887.410025

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Abstract:
The finite-time function projective synchronization of unknown Cohen-Grossberg neural networks with time delays and stochastic disturbances was investigated. A hybrid control scheme combining open-loop control and feedback control was designed to guarantee that the drive and response networks can be synchronized up to a scaling function in a finite time with parameter identification by means of the finite-time stability theory. Besides, the upper bounds of the settling time of synchronization were estimated. Finally, the corresponding numerical simulation and its application in secure communication were provided to demonstrate the validity of the presented synchronization method.

2020 Vol. 41, No. 12