Vol. 6, No. 4 (2022): Regular Issue

In this paper, the forced vibration of a cantilever beam at the free end constrained by two stops is studied. During vibration, the cantilever beam will impact and stuck with the two stops at the free end. Thus, the beam vibration will have different boundary conditions. It should be considered how many modes of vibrations can be used to describe the beam vibration. For impacting chatter and stuck at the free end of the beam, the constrained cantilever beam vibration is discussed in this paper, and analytical conditions for motion switching at the boundary of the cantilever beam are presented. From the analytical conditions, numerical simulations of periodic motions with motion switching are given for illustrations.

Smoking or passive smoking is not only harmful to health, but also easy to cause fires. However, there has been a lack of effective supervision of smoking behavior in public places. Most of the existing supervision methods rely on on-site patrols by supervisors, video surveillance or smoke alarms. These methods have problems such as low efficiency and low accuracy. In order to solve the problems, this paper proposes the T-Yolov4-tiny detection algorithm based on the Yolo lightweight network Yolov4-tiny. Specifically, multiple convolution layers are added to the original network to improve the CSPBlock Network structure; the 1$\mathrm{\times}$1 convolutional layers are used to reduce the amount of network calculations; the scale of the input image is increased to improve the ability of small target detection; the K-means clustering algorithm is utilized to optimize the anchor box size considering the actual target size in the data set, in order to improve the accuracy of the model. Then, a smoking behavior data set (named as Smoking-YBU) was collected by both web crawlers and manual collection. The experimental results show that, compared with the Yolov4-tiny algorithm, the mean average precision (mAP) of the T-Yolov4-tiny algorithm proposed in this paper increases by 12.69\% on the Smoking-YBU, and the detection speed can also meet real-time requirements.

This research studies the periodic temperature oscillations of a temperature control system. The nonlinear differential equation of a micro-controller-based temperature control system is derived using the energy balance method. The system parameters are optimized based on the experimental data. The method of implicit mapping is introduced. Through this mapping structures of periodic temperature responses, the analytical solutions of the steady-state temperature oscillations are computed which can be used to predict the experimental response. From the results of the implicit mapping, the amplitude curves of the Fourier series are calculated. Finally, the comparisons of the numerical, analytical, and experimental results are presented.

A nonlinear theory for the development and persistence of cellular two-dimensional patterns behind the shock front in self-sustained detonations is developed. A recent, significantly simplified and carefully-validated, detonation model is used as the basis for the analysis.In the spirit of earlier investigations of a variety of hydrodynamic and hydromagnetic instabilities, crossed-field microwave sources, tokamak edge plasmas, and other areas, our first approach here replaces the actual numerically computed equilibrium profiles by box-shaped ones having a jump discontinuity. The results for both the shapes and dimensions of the persistent two-dimensional cells picked out by our nonlinear analysis agree well with those in earlier simulations for the same sets of parameters. Our theory goes further, allowing predictions of non-trivial regions in the multiparameter space where persistent two-dimensional cells are possible. The only significant discrepancy from numerical results is in the wavelength of the cellular patterns along the reaction channel.Approximations of actual equilibrium profiles by step discontinuities, as done here, are most accurate for long-wavelength regimes where the waves essentially do not register the actual spatial profiles. Future work towards remedying the above discrepancy will be based on generalized normal forms in the spirit of what is usually referred to as 'collective coordinate' analysis, involving coefficients which are integrals over the spatially inhomogeneous equilibrium profiles.

This paper studies the locomotion of a monopod robot mounted to a vertical slider. The robot is driven by two electric motors attached to its hip. Although the system is often used to develop and test low-level controllers of legged robots, its dynamics was only studied from the lumped model with massless legs. The actual system is more complex and interesting because it is over-actuated and single-degree-of-freedom during the stance phase but under-actuated and three-degree-of-freedom during the flight phase. In this paper, the equations of motion of the legged robot during stance and flight phases are established through the Euler-Lagrange method. The switching law governing phase transitions is derived based on the assumption of conversation of angular momentum. A phase-switching controller is proposed to stabilize dynamic gaits of the robot. Numerical simulations of the robot's locomotion with/without control are carried out through a Stateflow model. Results are validated through numerical simulations powered by Simscape Multibody. The effect of mass distribution of the hip and legs on jump height is discussed for optimized deign.