Segregation simulation of binary granular matter under horizontal pendulum vibrations

Segregation of binary granular matter with different densities under horizontal pendulum vibrations was investigated through numerical simulation using a 3D discrete element method (DEM). The particle segregation mechanism was theoretically analyzed using gap filling, momentum and kinetic energy. The effect of vibrator geometry on granular segregation was determined using the Lacey mixing index. This study shows that dynamic changes in particle gaps under periodic horizontal pendulum vibrations create a premise for particle segregation. The momentum of heavy particles is higher than that of light particles, which causes heavy particles to sink and light particles to float. With the same horizontal vibration parameters, segregation efficiency and stability, which are affected by the vibrator with a cylindrical convex geometry, are superior to that of the original vibrator and the vibrator with a cross-bar structure. Moreover, vibrator geometry influences the segregation speed of granular matter. Simulation results of granular segregation by using the DEM are consistent with the final experimental results, thereby confirming the accuracy of the simulation results and the reliability of the analysis.

On Vibrational Stabilization of a Horizontal Pendulum

This paper describes control design and stability analysis for a horizontal pendulum using translational control of the pivot. The system is a one-link mechanism subject to linear damping and moving in the horizontal plane. The goal is to drive the system to a desired configuration such that the system oscillates in an arbitrarily small neighborhood of that desired configuration. We consider two cases: prescribed displacement inputs and prescribed force inputs. The proposed control law has two parts, a proportional-derivative part for control of actuated coordinates, and a high-frequency, high-amplitude oscillatory forcing to control the motion of unactuated coordinate. The control system is a high-frequency, time-periodic system. Therefore we use averaging techniques to determine the necessary input amplitudes and control gains. We show that using a certain oscillatory input, the amplitudes of that input must follow a constraint equation. We discuss the geometric interpretation of constraint equation and stability conditions of the system. We also discuss the effects of damping and relative phase of the oscillatory inputs on the system and their physical and geometric interpretation.

Wave Power Generation Using Nonlinear Roll-Pitch Coupling in a Ship

When there is a two to one internal resonance ratio between the natural frequencies of the pitch motion and the roll motion of a ship, a nonlinear energy transfer occurs between the modes. If the ship is excited near the pitch natural frequency and at a large enough excitation amplitude, the pitch mode transfers energy to the roll mode. We use this interesting phenomenon to develop a wave power device for off-shore purposes. In this paper, we experimentally show that we can use a horizontal pendulum and use the quadratic nonlinear coupling between the pitch and the roll mode to get full rotation of the pendulum inside the ship. A rotating pendulum will generate orders of magnitude more power than a locally oscillating one when connected to a DC generator. This article measures the angle of the pendulum at the pitch frequency excitation of the ship to experimentally confirm the expected theoretical results on this phenomenon.