VIBRATIONAL POWER TRANSMISSION FROM A MACHINE TO ITS SUPPORTING CYLINDRICAL SHELL

Power flows from a vibratory machine to its supporting structure are of primary concern in a passive or active isolation system design. Although in the literature there is a fair number of investigations on the power inputs to beams, plates or the like, few attempts have been made for other commonly used structures such as cylindrical shells. In this paper, the vibratory power flows from a rigid-body machine to an elastic cylindrical shell are studied considering the contributions of the non-radial (tangential and axial) displacements and forces. In particular, it is argued that the notion that the motion of a thin shell is primarily radial does not necessarily dictate that the power transmissions are predominantly carried out by the radial displacement. This point is subsequently illuminated through numerical examples. Another issue discussed here is concerned with the effects on the power flows of the cross couplings of the (different) displacement components. It is shown that even though the contributions of the cross couplings are usually insignificant, they may become important if the vibration isolators are substantially hard as compared with the local shell stiffness or impedance. This assertion is particularly useful when an experimental technique is used to measure the vibratory power flows into a supporting structure.     

Ultracentrifuge Sedimentation during the Period of Constant Acceleration

Initially, the angular velocity of an ultracentrifuge increasesat a uniform rate until a given maximum is reached, after whichit is maintained at a constant value. The concentration distributionduring the accelerating period is obtained as the solution ofa one-dimensional approximation to the diffusion equation, analogousto that previously used (Fujita & MacCosham, 1959) for thecase of constant angular velocity.     

A Numerical and Asymptotic Investigation of Boundary-layer Wake Evolution

The evolution of four characteristically different velocityprofiles in the boundary layer at a trailing edge is studiedboth numerically and analytically; the complete wake flow iscomputed using a finite difference procedure and this is comparedwith asymptotic expansions of the flow in both the near wakeand the far wake. Two of the profiles have direct applicationto physical situations which include the flow in the wake ofa finite flat plate and the flow in the free shear layer downstreamof the point of separation of a supersonic stream from a planewall. The other two profiles demonstrate the structural changeswhich occur in the near wake when part of the initial profileis on the point of separation.     

Phase-winding Solutions for Axisymmetric Convection between Rotating Planes Uniformly Heated from Below

The concept of phase winding, where the argument of a complexamplitude function changes slowly with position, may providea theoretical explanation of observed changes in the wavelengthof concentric roll patterns in shallow circular cylinders uniformlyheated from below. Here it is shown that in an infinite fluidlayer, constraints on phase winding associated with the motionnear the centre of the roll pattern are weaker than, for instance,those associated with a two-dimensional pattern confined bya lateral wall. The theoretical treatment, which is based onthe methods of matched asymptotic expansions and multiple scales,includes the effect of rotation of the layer. The solution forthe weakly nonlinear axisymmetric state at slightly supercriticalRayleigh numbers is found by matching an outer solution, expressedin terms of an amplitude function, to an inner solution validnear the axis of rotation. Some observations are also made,concerning modifications to the solution caused by the presenceof an outer cylindrical wall