Yuhuan Cui’s research while affiliated with North China University of Technology and other places

This paper presents the dynamic response of cantilever beam on fractional-order nonlinear viscoelastic foundation subjected to Gaussian white noise. The control equations of the cantilever beam on viscoelastic foundation are established using Hamilton’s principle. The problem is solved using the shifted Chebyshev polynomial algorithm, and the control equations are transformed into a system of nonlinear algebraic equations. Numerical examples analyse the correction error and the second norm error, confirming the effectiveness and accuracy of the algorithm in solving such problems. Furthermore, the algorithm’s robustness was verified by comparing the responses of Gaussian white noise and non-Gaussian white noise cantilever beam on the viscoelastic foundation. The study examined the impact of various loads and parameters on the cantilever beam, as well as the effect of different harmonic loads on its stress. The research results are in line with the existing literature. These studies offer valuable guidance for practical engineering and enhance comprehension of the dynamic response of cantilevers on foundation in complex environments.

The fractional Kelvin–Voigt (FKV) viscoelastic constitutive model has been employed to build the fractional differential governing equation of viscoelastic foundation plate. Shifted Bernstein polynomial algorithm is implemented to solve the governing equations on a direct time domain numerically. Furthermore, the validity of the method is demonstrated by convergent analysis and error estimation of a math example. Finally, the dynamic analysis of viscoelastic foundation plate under different uniform loads. The movement of plate with different aspect ratios in viscoelastic foundation under the same load is studied. The stress of viscoelastic foundation plates of two materials under identical loading situations is investigated.

This paper applies a recently proposed numerical algorithm to discuss the deflection of viscoelastic micro-beams in the time domain with direct access. A nonlinear-fractional order model for viscoelastic micro-beams is constructed. Before solving the governing equations, the operator matrices of shifted Chebyshev polynomials are derived first. Shifted Chebyshev polynomials are used to approximate the deflection function, and the nonlinear fractional order governing equation is expressed in the form of operator matrices. Next, the collocation method is used to discretize the equations into the form of algebraic equations for solution. It simplifies the calculation. MATLAB software was used to program this algorithm to simulate the numerical solution of the deflection. The effectiveness and accuracy of the algorithm are verified by the numerical example. Finally, numerical simulations are carried out on the viscoelastic micro-beams. It is found that the viscous damping coefficient is inversely proportional to the deflection, and the length scale parameter of the micro-beam is also inversely proportional to the deflection. In addition, the stress and strain of micro-beam, the change of deflection under different simple harmonic loads, and potential energy of micro-beam are discussed. The results of the study fully demonstrated that the shifted Chebyshev polynomial algorithm is effective for the numerical simulations of viscoelastic micro-beams.

The fractional variable-order constitutive model for the viscoelastic plate is analyzed. The fractional variable-order constitutive equations for the plates are solved numerically using the shifted Bernstein polynomials directly in time domain. Numerical displacement of Polyurea and HDPE viscoelastic plates at a variety of loads was investigated. The results show that Polyurea has better bending resistance than HDPE viscoelastic plates, which verifies the practicability of the algorithm.

With the spread of COVID-19 around the world, the education industry faces enormous challenges. Some colleges and universities have launched online teaching. Comprehensive online teaching and student health checkups help students complete the set teaching content and return to school as soon as possible. With the development of big data, combined with the epidemic risk we are facing, the rational use of big data and the internet for innovative online education has become a mainstream teaching method. Colleges and universities are not yet familiar with the development prospects and future of online education. Through the research of this paper, we can understand the combination of online education and the development of big data and promote its application in colleges and universities. Not only have innovative online education platforms such as MOOC and DingTalk been widely used, but innovative online education methods such as virtual classrooms also have been created. Based on the current epidemic background, this paper analyzes the development of online education, introduces the impact of the combination of online education and big data, and introduces innovative online education technologies and their effects. It helps online education under the influence of the new coronavirus epidemic, operating big data technology to analyze the current prospects and development of online education, showing the combination of big data technology and online education through the analysis of big data technology, and ending with more expectations on other aspects of the use of big data, which affects the online education industry as well as other industries. Finally, we summarize the combination of big data and innovative online education since the emergence of COVID-19 and introduce the concepts and methods of combining online education and big data technology in detail. The online education platform also makes a reasonable introduction. The thesis can be used to understand the problems and challenges faced by innovative online education in the context of the new coronavirus epidemic and look forward to the future on this basis.

The shifted Legendre algorithm is used to solve the governing differential equation of variable order cantilever beam in time domain. According to the variable fractional model, the governing equations of viscoelastic polymer cantilever beam are built. The integer order and variable fractional order differential operator matrices are obtained based on the properties of shifted Legendre polynomials. The variable fractional differential equations are converted into algebraic equations and solved in time domain by operator matrix. The convergence analysis confirmed the high efficiency and accuracy of the proposed algorithm for solving differential equations. The deflection and stress of the polymer cantilever beams (PET and HDPE) under various external load (uniformly distributed and harmonic) are studied.

In this paper, a variable fractional derivative model (VFDM) is used to model the viscoelastic circular plate whose thickness varies exponentially. Based on the VFDM, a ternary variable fractional differential equation of viscoelastic circular plate is established. The shifted Chebyshev polynomials (SCPs) algorithm is introduced to numerically solve the complex equation directly in time domain. The effectiveness of proposed SCPs algorithm is verified by convergence analysis. Then the dynamic responses of viscoelastic circular plate are researched under different loads, radius, thickness parameters, boundary conditions and viscoelastic materials by SCPs algorithm. The displacement of circular plate increases with the increasing load. The vibration can be reduced by increasing the thickness of plate, reducing plate area or strengthening the restraint on plate. The bending resistance of polyethylene terephthalate (PET) plate is better than polyurea. These results are consistent with the results of literatures. Therefore, the proposed model and algorithm are correct and sensitive in the numerical simulation of viscoelastic circular plate with different conditions.

In this paper, a kinetic equation of Euler–Bernoulli beam is established with variable order fractional viscoelastic model. An effective numerical algorithm is proposed. This method uses a combination of shifted Bernstein polynomial and Legendre polynomial to approximate the numerical solution. The effectiveness of the algorithm is tested and verified by mathematical examples. The dynamic behavior of viscoelastic beams made of two materials under various loading conditions is studied. © 2022 International Association for Mathematics and Computers in Simulation (IMACS)

The capacity analysis of the existing underwater acoustic network mainly refers to the analysis method of terrestrial wireless network. Network capacity is affected by many factors, such as node distribution, transmission delay, transmission strategy and link layer characteristics. Aiming at the challenges of capacity of underwater acoustic network, a closed solution for one-hop transmission of any node based on three-dimensional stochastic underwater acoustic network under the protocol model is derived, the closed solution takes into account the fact that the vertical transmission efficiency of underwater acoustic signal is more effective than the horizontal transmission efficiency, it is in line with the channel characteristics of underwater acoustic communication, and with different network parameters, there is an optimal communication radiation range of nodes to maximize the throughput of the network. Aiming at the problem that some relay nodes in underwater acoustic network run out of energy prematurely due to overuse, a model predictive control method based on maximum algebra is proposed, which can predict the information generation rate of nodes periodically and estimate the life value of nodes at different routing time points according to the current residual energy of nodes.