Various experimental and numerical studies have been carried out to study the mixing processes inside rotating drums with a horizontal axis of rotation in the past, but little effort has been made to investigate the rotating drums with an inclined axis of rotation, though such inclined drums exist in industrial waste management, food processing, power and pharmaceutical industries. To fill this gap, in this work, the discrete element method was used to study the mixing phenomena of a rotating drum for different angles of inclination from 0° to 15°. It was found that for inclined rotating drums, the whole bed Lacey mixing index is higher than that for the horizontal drum by 7.2% when the angle of inclination is 10°. The mixing index is related to the area ratio of the active region to the whole bed and volumetric fill. Increase in volumetric fill would lead to the decrease of the mixing index. The mixing index and area ratio exhibit similar patterns along the length of the drum for different angles of inclination.

This study investigates the flow behavior of non-cohesive and cohesive particles in eccentric silos using the Eulerian finite element method. The numerical model was rigorously validated against established experimental data. The effects of outlet eccentricity—concentric (e = 0), intermediate (e = 0.5), and extreme (e = 0.84)—as well as silo scale-up were systematically analyzed in relation to particle flow behavior and mechanical response. The results show that outlet eccentricity has contrasting effects on the granular flow behavior in silos for both non-cohesive and cohesive particles. While non-cohesive particles achieve the highest discharge rates in silos with extreme eccentricity, cohesive particles exhibit the lowest critical cohesion coefficients under the same condition. Wall effects are more pronounced for cohesive particles than for non-cohesive ones and become attenuated under silo scale-up—particularly with Type B scaling—resulting in higher critical cohesion coefficients. Trends in the critical cohesion coefficient remain consistent across all configurations: the coefficient increases with particle fill height before stabilizing. This behavior reflects the competing effects of increasing fill height, namely, increased bottom loading vs enhanced sidewall support. The influence of silo width (i.e., scale) on the critical cohesion coefficient becomes significant only at fill heights exceeding 75ds. These findings underscore the coupled impact of outlet eccentricity, scaling strategy, and fill height on governing arching behavior and flow efficiency. The insights provide actionable guidance for industrial silo design aimed at minimizing flow obstructions and optimizing discharge performance.

Free vibration of a bimaterial circular nano-tube is investigated. The tube is formed by bonding together a Si₃N₄/SUS304 functionally graded upper semi tube and a ZrO₂/Ti-6Al-4V functionally graded lower semi tube. The material properties of the tube are assumed to vary along the radius according to power law with the power index of upper semi tube differing from that of lower semi tube. Based on non-local elasticity theory and Hamilton’s principle, a refined beam model considering the effect of transverse shear deformation is used to derive the governing equations, then analytical solution is obtained by using a two-steps perturbation method. Our results were compared with the existing ones. The effects on tube’s linear and non-linear frequency are analyzed of the factors, including small scale parameter, temperature, the double volume fraction indexes, slenderness ratio and different types of beam model. A new approach is suggested in this article to change the natural frequency of the tubes by adjusting constituent materials. In contrast to conventional approach, the new one can result in more accurate frequency control in the same dimensionless size of tubes.