Apparently First Closed-Form Solution for Frequency of Beam with Rotational Spring

Summary In summary, the overall properties of the continuous-phase turbulence generated byuniforme uxes of monodispersesphericalparticles moving at near terminal velocities were studied. It was found that many properties of these e ows— including relative turbulence intensities, anisotropies, and PDFs— could be predicted reasonably well based on volume-averaged contributions of the conditional averages of these properties within the laminarlike wake disturbance and turbulent interwake regions of the e ows. The predictions show that most of the unusual properties of these e ows, compared to conventional homogeneous turbulent e ows, 4i 8 come about as a result of effects of mean velocities in the particle wakes, which cannot be separated from the turbulence (barring some type of wake discrimination system ) because the arrival of particle wakes is random.