Analysis of the Influence of Motors Installed in Passenger Car Wheels on the Torsion Beam of the Rear Axle Suspension

The influence of mounting motors in wheels’ hubs and flexibility of the twist beam rear suspension on their dynamics and strength is presented in the paper. The international roughness indicator (IRI) is applied to assess the overcoming of road unevenness. This indicator is a combination of a shape of the road unevenness and of overcoming velocity. The movement of a wheel’s axis during obstacles overcoming is described. For the needs of the dynamics analysis, the mathematical model of the rear suspension system with embedded motors is developed using the MSC.Adams-ANSYS interface. The discrete model of the twist beam is prepared in the ANSYS software, which is used in the next step to construct the dynamics model of the rear suspension system using the MSC.Adams program. The vertical components of displacement and acceleration of the wheel’s centre, forces in the suspension’s springs and dampers, as well as forces in the joints are analyzed. The analysis of the suspension beam’s stress during the road unevenness overcoming is also carried out.

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model. Positivity, boundedness, the basic reproduction number and asymptotic stability properties of the model are analyzed rigorously. By the Lyapunov stability theory and the Poincare-Bendixson theorem in combination with the Bendixson-Dulac criterion, we show that a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number $\mathcal{R}_0 \leq 1$ and a disease-endemic equilibrium point is globally asymptotically stable whenever $\mathcal{R}_0 > 1$. Next, we apply the Mickens’ methodology to propose a dynamically consistent nonstandard finite difference (NSFD) scheme for the continuous model. By rigorously mathematical analyses, it is proved that the constructed NSFD scheme preserves essential mathematical features of the continuous model for all finite step sizes. Finally, numerical experiments are conducted to illustrate the theoretical findings and to demonstrate advantages of the NSFD scheme over standard ones. The obtained results in this work not only improve but also generalize some existing recognized works.

Analysis of Brand Communication Influence of Professional Sports Clubs Based on Complex System Discrete Model

In recent years, because the complex system discrete model has brought good results in the application of many research directions such as human management analysis, control system prediction, and animal group prediction, how to combine the complex system discrete model with the prediction of enterprise brand communication effect has become a current research hotspot. Based on this, this paper studies the application of the discrete model based on the complex system in sports club to enterprise brand communication and designs a model of the impact of professional sports club on enterprise brand communication based on the SIR model and PSO algorithm. Firstly, this paper analyzes the research status of the impact on enterprise brand communication at home and abroad and optimizes and improves the impact of professional sports clubs on enterprise brand communication and the shortcomings of big data analysis technology in the current research. The complex system discrete model can accurately analyze the enterprise brand communication and conduct big data mining analysis with known professional sports clubs to achieve accurate calculation. The results show that in the process of analyzing the impact of professional sports clubs and enterprise brand communication, the communication mode design of professional sports clubs based on SIR-PSO algorithm can not only effectively deal with various complex discrete data evaluated by club users but also analyze and evaluate the impact of professional sports clubs on enterprise brand communication.

The Influence of Multimedia Input Mode Based on Complex System Discrete Model on College Students’ English Ability

With the rapid development of the Internet, the amount of data increases sharply. In this network age, data have been generated, such as multimedia, social networks, and search records. Due to the generation of data, complex system discrete model technology is also widely used in all walks of life. Multimedia learning is a popular teaching mode in the world. Through the discrete model technology of the complex system, this paper deeply studies the impact of multimedia input on college students’ English ability. Because the modeling and sampling of complex systems are abstract and not fixed, approximation and control methods are adopted in discrete time, which greatly improves the reliability of the final research results. Compared with the original discrete modeling technology, this paper adds data sampling compression and assimilation technology on the basis of the original discrete modeling technology of the complex system. The results show that, by adding the technical application of controllable and observable systems, the discrete model of the whole complex system can reduce the error of the final output data. At the same time, this paper compresses and simplifies the data nodes at the microlevel. Macroscopically, it reduces the scale, especially the number of node data compression. The final result also realizes the data scale and greatly shortens the calculation time. This study has greatly improved the accuracy of the impact of multimedia on Chinese college students’ English ability in practical application.