Mixed Edges Research Articles

Vibration of a plate of arbitrary shape with free and simply supported mixed edges

This paper is concerned with a method for solving vibration problems of a plate of arbitrary shape with free and simply supported mixed edges. In the analysis the exact solution of the equation of motion which includes terms representing the reaction forces of the simply supported edges is applied. The boundary conditions along the edges of arbitrary shape have been satisfied directly by making use of the Fourier expansion collocation method which has been developed by the author on vibration, dynamic response, and wave propagation problems of membranes, plates, and rods with arbitrarily shaped boundaries. The equation for finding the eigenfrequencies of plates of arbitrary shape with free and simply supported mixed edges has been obtained. As applications of the present result, numerical calculations have been carried out for polygonal plates, trapezoidal plates, truncated elliptical plates, and parabolic plates with the mixed edges.

Precipitation Initiation Mechanisms and Droplet Characteristics of Some Convective Cloud Cores

Samplings of the unmixed cores and the mixed edges of convective clouds at various heights were made in an aircraft using standard instrumentation and a Continuous Particle Collector (CPC). The unmixed cores are defined as regions where constant values are indicated on the hot wire type, liquid water content meter. The various correction factors relating these CPC replicas to the true droplet and drop situation in the cloud are not well established, but the observations are nevertheless sufficiently accurate 1) to give some useful data on the relative size distributions of small droplets, and 2) to show that drizzle-size drops can develop quickly within the cloud core. The evolution of the distributions of small droplets (<40μ diameter) with height is shown. Droplet concentrations are of the order of 1000 cm−3 near cloud base, and some correlation between concentration and upcurrent strength at cloud base is noted. The large droplets from which drizzle-size drops evolve can be present, even at cloud base, in concentrations of about 20 liter−1. Possible sources of these large droplets are discussed. Graupel was encountered at −5 and −6 C, mostly outside the convective cores, presumably resulting from the freezing and riming of the larger liquid drops at relatively warm temperatures.