Boundary effects on the vibration statistics of a random plate

This paper considers the estimation of statistics of displacement of a vibrating rectangular plate with random wave scatterers. The influence of uncertainty is investigated using point impedance theory. Coherent boundary effects are seen, which decrease when the number of scatterers increases. The boundary effect is investigated using images and the first side and corner reflections are found to be a minimum requirement to estimate the spatial correlation. Statistics for point driven response are investigated under the assumption that the statistics of the natural frequencies follow those of the Gaussian Orthogonal Ensemble (GOE). The estimates are compared with Monte Carlo simulation results, and they show good agreement. © 2012 Elsevier Ltd. All rights reserved.

Reynolds number influence on turbulent blocking effects of a rigid plane boundary (2nd report, direct numerical simulation using townsend's eddy forcing)

The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method using 'simple model eddies' (Townsend 1976) for DNS of stationary homogeneous isotropic turbulence is proposed. A force field is obtained in real space by sprinkling many space-filling 'simple model eddies' whose centers are randomly but uniformly distributed in space and whose axes of rotation are random. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects are investigated. The results show that stationary homogeneous isotropic turbulence is generated in real space using the present method. By using different model eddies with different sizes and rotation speeds, we could change the turbulence properties such as the integral and micro scales, the turbulent Reynolds number and the isotropy of turbulence. Turbulence intensities near the wall showed good agreements with the previous measurement and the linear analysis based on a rapid distortion theory (RDT). The splat effect (i.e., turbulence intensities of the components parallel to the boundary are amplified) occurs near the boundary and the viscous effect prohibits the splat effect at the quasi steady state at low Reynolds number.