Lagrangian and Eulerian descriptions of inertial particles in random flows

We study how the spatial distribution of inertial particles evolves with time in a random flow. We describe an explosive appearance of caustics and show how they influence an exponential growth of clusters due to smooth parts of the flow, leading in particular to an exponential growth of the average distance between particles. We demonstrate how caustics restrict applicability of Lagrangian description to inertial particles.

Simulation of robot manipulator control strategies

The high capital cost of robots prohibit their economic application. One method of making their application more economic is to increase their operating speed. This can be done in a number of ways e.g. redesign of robot geometry, improving actuators and improving control system design. In this thesis the control system design is considered. It is identified in the literature review that two aspects in relation to robot control system design have not been addressed in any great detail by previous researchers. These are: how significant are the coupling terms in the dynamic equations of the robot and what is the effect of the coupling terms on the performance of a number of typical independent axis control schemes?. The work in this thesis addresses these two questions in detail. A program was designed to automatically calculate the path and trajectory and to calculate the significance of the coupling terms in an example application of a robot manipulator tracking a part on a moving conveyor. The inertial and velocity coupling terms have been shown to be of significance when the manipulator was considered to be directly driven. A simulation of the robot manipulator following the planned trajectory has been established in order to assess the performance of the independent axis control strategies. The inertial coupling was shown to reinforce the control torque at the corner points of the trajectory, where there was an abrupt demand in acceleration in each axis but of opposite sign. This reduced the tracking error however, this effect was not controllable. A second effect was due to the velocity coupling terms. At high trajectory speeds it was shown, by means of a root locus analysis, that the velocity coupling terms caused the system to become unstable.

Dynamic analysis of submerged microscale plates:the effects of acoustic radiation and viscous dissipation

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate- fluid interaction problem is developed on the basis of linearized Navier-Stokes equations and noslip conditions. Analytical expression for the fluidloading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers beingmass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.