In the current study, a two-dimensional multi-relaxation time (MRT) lattice Boltzmann model which can tolerate high density ratios and low viscosity is employed to simulate the liquid droplet impact onto a curved target. The temporal variation of the film thickness at the north pole of the target surface is investigated. Three different temporal phases of the dynamics behavior, namely, the initial drop deformation phase, the inertia dominated phase and the viscosity dominated phase are reproduced and studied. The effect of the Reynolds number, Weber number and Galilei number on the film flow dynamics is investigated. In addition, the dynamic behavior of the droplet impact onto the side of the curved target is shown, and the effect of the contact angle, the Reynolds number and the Weber number are investigated.

The dynamic modeling of a flexible single-link manipulator arm with consideration of backlash in the planetary gear reducer at the joint is presented, and the influence of backlash on the dynamic response of the system is evaluated. A 2K-H planetary gear reducer with backlash was employed as an example to discuss the dynamic modeling of the sub-model of the planetary gear reducer, and the sub-model of the planetary gear reducer was established based on the lumped mass method. The flexible manipulator was regarded as an Euler--Bernoulli beam, and the dynamic model of the flexible manipulator arm with backlash in the planetary gear reducer was determined from Lagrange's equations. Based on the this model, the influence of the backlash in the planetary gear reducer and excitation frequency on the dynamic response of the system were evaluated through simulation, and the results showed that the dynamic response of the system is sensitive to the backlash and the excitation frequency simultaneously, which provides a theoretical foundation for improvement of dynamic modeling and control of the flexible manipulator arm.

This study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

Certaines structures non-linéaires sont dotées d’hystérésis responsables de phénomènes desaut dans les réponses fréquentielles et d’instabilités. Dans ce travail, on étudie cesphénomènes analytiquement, numériquement et expérimentalement sur une poutre encastréelibre dont le comportement non-linéaire est modifiable. La non-linéarité dans la structureest introduite par des actionneurs électromagnétiques. La structure ainsi que lesactionneurs sont dimensionnés afin de mettre en évidence le phénomène de saut. Lesrésultats obtenus analytiquement en utilisant une méthode de perturbation sur un modèlenon-linéaire simplifié ont été validés expérimentalement et par simulations numériques.Ces résultats montrent qu’il est possible de maîtriser le phénomène de saut dans lesréponses fréquentielles en utilisant des actionneurs électromagnétiques.